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<html><head><meta charset="utf-8"><title>Categories.Category.Monoidal.Reasoning</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
<a id="37" class="Keyword">open</a> <a id="42" class="Keyword">import</a> <a id="49" href="Categories.Category.html" class="Module">Categories.Category</a> <a id="69" class="Keyword">using</a> <a id="75" class="Symbol">(</a><a id="76" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="84" class="Symbol">)</a>
<a id="86" class="Keyword">open</a> <a id="91" class="Keyword">import</a> <a id="98" href="Categories.Category.Monoidal.html" class="Module">Categories.Category.Monoidal</a> <a id="127" class="Keyword">using</a> <a id="133" class="Symbol">(</a><a id="134" href="Categories.Category.Monoidal.Core.html#1287" class="Record">Monoidal</a><a id="142" class="Symbol">)</a>
<a id="145" class="Keyword">module</a> <a id="152" href="Categories.Category.Monoidal.Reasoning.html" class="Module">Categories.Category.Monoidal.Reasoning</a> <a id="191" class="Symbol">{</a><a id="192" href="Categories.Category.Monoidal.Reasoning.html#192" class="Bound">o</a> <a id="194" href="Categories.Category.Monoidal.Reasoning.html#194" class="Bound">ℓ</a> <a id="196" href="Categories.Category.Monoidal.Reasoning.html#196" class="Bound">e</a><a id="197" class="Symbol">}</a> <a id="199" class="Symbol">{</a><a id="200" href="Categories.Category.Monoidal.Reasoning.html#200" class="Bound">C</a> <a id="202" class="Symbol">:</a> <a id="204" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="213" href="Categories.Category.Monoidal.Reasoning.html#192" class="Bound">o</a> <a id="215" href="Categories.Category.Monoidal.Reasoning.html#194" class="Bound">ℓ</a> <a id="217" href="Categories.Category.Monoidal.Reasoning.html#196" class="Bound">e</a><a id="218" class="Symbol">}</a> <a id="220" class="Symbol">(</a><a id="221" href="Categories.Category.Monoidal.Reasoning.html#221" class="Bound">M</a> <a id="223" class="Symbol">:</a> <a id="225" href="Categories.Category.Monoidal.Core.html#1287" class="Record">Monoidal</a> <a id="234" href="Categories.Category.Monoidal.Reasoning.html#200" class="Bound">C</a><a id="235" class="Symbol">)</a> <a id="237" class="Keyword">where</a>
<a id="244" class="Keyword">open</a> <a id="249" class="Keyword">import</a> <a id="256" href="Data.Product.html" class="Module">Data.Product</a> <a id="269" class="Keyword">using</a> <a id="275" class="Symbol">(</a><a id="276" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="279" class="Symbol">)</a>
<a id="282" class="Keyword">open</a> <a id="287" class="Keyword">import</a> <a id="294" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="313" class="Keyword">using</a> <a id="319" class="Symbol">(</a><a id="320" href="Categories.Functor.Core.html#248" class="Record">Functor</a><a id="327" class="Symbol">)</a>
<a id="330" class="Keyword">open</a> <a id="335" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="344" href="Categories.Category.Monoidal.Reasoning.html#200" class="Bound">C</a>
<a id="347" class="Keyword">private</a>
<a id="357" class="Keyword">variable</a>
<a id="370" href="Categories.Category.Monoidal.Reasoning.html#370" class="Generalizable">X</a> <a id="372" href="Categories.Category.Monoidal.Reasoning.html#372" class="Generalizable">Y</a> <a id="374" class="Symbol">:</a> <a id="376" href="Categories.Category.Core.html#559" class="Function">Obj</a>
<a id="384" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="386" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="388" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="390" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a> <a id="392" class="Symbol">:</a> <a id="394" href="Categories.Category.Monoidal.Reasoning.html#370" class="Generalizable">X</a> <a id="396" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="398" href="Categories.Category.Monoidal.Reasoning.html#372" class="Generalizable">Y</a>
<a id="401" class="Keyword">open</a> <a id="406" href="Categories.Category.Monoidal.Core.html#1287" class="Module">Monoidal</a> <a id="415" href="Categories.Category.Monoidal.Reasoning.html#221" class="Bound">M</a> <a id="417" class="Keyword">using</a> <a id="423" class="Symbol">(</a><a id="424" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">_⊗₀_</a><a id="428" class="Symbol">;</a> <a id="430" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">_⊗₁_</a><a id="434" class="Symbol">;</a> <a id="436" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a><a id="437" class="Symbol">)</a>
<a id="439" class="Keyword">open</a> <a id="444" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="452" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a> <a id="454" class="Keyword">using</a> <a id="460" class="Symbol">(</a><a id="461" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a><a id="469" class="Symbol">;</a> <a id="471" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a><a id="483" class="Symbol">)</a>
<a id="485" class="Keyword">open</a> <a id="490" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a> <a id="503" class="Keyword">public</a>
<a id="511" class="Keyword">infixr</a> <a id="518" class="Number">6</a> <a id="520" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">_⟩⊗⟨_</a> <a id="526" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨_</a>
<a id="535" class="Keyword">infixl</a> <a id="542" class="Number">7</a> <a id="544" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">_⟩⊗⟨refl</a>
<a id="⊗-resp-≈"></a><a id="554" href="Categories.Category.Monoidal.Reasoning.html#554" class="Function">⊗-resp-≈</a> <a id="563" class="Symbol">:</a> <a id="565" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="567" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="569" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="571" class="Symbol">→</a> <a id="573" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="575" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="577" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a> <a id="579" class="Symbol">→</a> <a id="581" class="Symbol">(</a><a id="582" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="584" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="587" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="588" class="Symbol">)</a> <a id="590" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="592" class="Symbol">(</a><a id="593" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="595" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="598" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="599" class="Symbol">)</a>
<a id="601" href="Categories.Category.Monoidal.Reasoning.html#554" class="Function">⊗-resp-≈</a> <a id="610" href="Categories.Category.Monoidal.Reasoning.html#610" class="Bound">p</a> <a id="612" href="Categories.Category.Monoidal.Reasoning.html#612" class="Bound">q</a> <a id="614" class="Symbol">=</a> <a id="616" href="Categories.Functor.Core.html#696" class="Function">F-resp-≈</a> <a id="625" class="Symbol">(</a><a id="626" href="Categories.Category.Monoidal.Reasoning.html#610" class="Bound">p</a> <a id="628" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="630" href="Categories.Category.Monoidal.Reasoning.html#612" class="Bound">q</a><a id="631" class="Symbol">)</a>
<a id="⊗-resp-≈ˡ"></a><a id="634" href="Categories.Category.Monoidal.Reasoning.html#634" class="Function">⊗-resp-≈ˡ</a> <a id="644" class="Symbol">:</a> <a id="646" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="648" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="650" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="652" class="Symbol">→</a> <a id="654" class="Symbol">(</a><a id="655" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="657" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="660" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="661" class="Symbol">)</a> <a id="663" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="665" class="Symbol">(</a><a id="666" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="668" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="671" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="672" class="Symbol">)</a>
<a id="674" href="Categories.Category.Monoidal.Reasoning.html#634" class="Function">⊗-resp-≈ˡ</a> <a id="684" href="Categories.Category.Monoidal.Reasoning.html#684" class="Bound">p</a> <a id="686" class="Symbol">=</a> <a id="688" href="Categories.Category.Monoidal.Reasoning.html#554" class="Function">⊗-resp-≈</a> <a id="697" href="Categories.Category.Monoidal.Reasoning.html#684" class="Bound">p</a> <a id="699" href="Relation.Binary.Structures.html#1596" class="Function">Equiv.refl</a>
<a id="⊗-resp-≈ʳ"></a><a id="711" href="Categories.Category.Monoidal.Reasoning.html#711" class="Function">⊗-resp-≈ʳ</a> <a id="721" class="Symbol">:</a> <a id="723" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="725" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="727" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a> <a id="729" class="Symbol">→</a> <a id="731" class="Symbol">(</a><a id="732" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="734" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="737" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="738" class="Symbol">)</a> <a id="740" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="742" class="Symbol">(</a><a id="743" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="745" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="748" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="749" class="Symbol">)</a>
<a id="751" href="Categories.Category.Monoidal.Reasoning.html#711" class="Function">⊗-resp-≈ʳ</a> <a id="761" href="Categories.Category.Monoidal.Reasoning.html#761" class="Bound">p</a> <a id="763" class="Symbol">=</a> <a id="765" href="Categories.Category.Monoidal.Reasoning.html#554" class="Function">⊗-resp-≈</a> <a id="774" href="Relation.Binary.Structures.html#1596" class="Function">Equiv.refl</a> <a id="785" href="Categories.Category.Monoidal.Reasoning.html#761" class="Bound">p</a>
<a id="_⟩⊗⟨_"></a><a id="788" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">_⟩⊗⟨_</a> <a id="794" class="Symbol">:</a> <a id="796" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="798" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="800" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="802" class="Symbol">→</a> <a id="804" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="806" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="808" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a> <a id="810" class="Symbol">→</a> <a id="812" class="Symbol">(</a><a id="813" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="815" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="818" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="819" class="Symbol">)</a> <a id="821" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="823" class="Symbol">(</a><a id="824" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="826" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="829" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="830" class="Symbol">)</a>
<a id="832" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">_⟩⊗⟨_</a> <a id="838" class="Symbol">=</a> <a id="840" href="Categories.Category.Monoidal.Reasoning.html#554" class="Function">⊗-resp-≈</a>
<a id="refl⟩⊗⟨_"></a><a id="850" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨_</a> <a id="859" class="Symbol">:</a> <a id="861" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="863" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="865" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a> <a id="867" class="Symbol">→</a> <a id="869" class="Symbol">(</a><a id="870" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="872" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="875" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="876" class="Symbol">)</a> <a id="878" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="880" class="Symbol">(</a><a id="881" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="883" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="886" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="887" class="Symbol">)</a>
<a id="889" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨_</a> <a id="898" class="Symbol">=</a> <a id="900" href="Categories.Category.Monoidal.Reasoning.html#711" class="Function">⊗-resp-≈ʳ</a>
<a id="_⟩⊗⟨refl"></a><a id="911" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">_⟩⊗⟨refl</a> <a id="920" class="Symbol">:</a> <a id="922" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="924" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="926" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="928" class="Symbol">→</a> <a id="930" class="Symbol">(</a><a id="931" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="933" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="936" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="937" class="Symbol">)</a> <a id="939" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="941" class="Symbol">(</a><a id="942" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="944" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="947" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="948" class="Symbol">)</a>
<a id="950" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">_⟩⊗⟨refl</a> <a id="959" class="Symbol">=</a> <a id="961" href="Categories.Category.Monoidal.Reasoning.html#634" class="Function">⊗-resp-≈ˡ</a>
<a id="972" class="Comment">-- This corresponds to the graphical coherence property of diagrams</a>
<a id="1040" class="Comment">-- modelling monoidal categories:</a>
<a id="1074" class="Comment">--</a>
<a id="1077" class="Comment">-- | | | |</a>
<a id="1107" class="Comment">-- [h] [i] [h] [i]</a>
<a id="1138" class="Comment">-- | | ≈ | |</a>
<a id="1168" class="Comment">-- [f] [g] | |</a>
<a id="1198" class="Comment">-- | | | |</a>
<a id="1228" class="Comment">-- [f] [g]</a>
<a id="1259" class="Comment">-- | |</a>
<a id="⊗-distrib-over-∘"></a><a id="1290" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="1307" class="Symbol">:</a> <a id="1309" class="Symbol">((</a><a id="1311" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="1313" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1315" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a><a id="1316" class="Symbol">)</a> <a id="1318" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1321" class="Symbol">(</a><a id="1322" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a> <a id="1324" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1326" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="1327" class="Symbol">))</a> <a id="1330" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1332" class="Symbol">((</a><a id="1334" href="Categories.Category.Monoidal.Reasoning.html#384" class="Generalizable">f</a> <a id="1336" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1339" href="Categories.Category.Monoidal.Reasoning.html#386" class="Generalizable">g</a><a id="1340" class="Symbol">)</a> <a id="1342" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1344" class="Symbol">(</a><a id="1345" href="Categories.Category.Monoidal.Reasoning.html#388" class="Generalizable">h</a> <a id="1347" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1350" href="Categories.Category.Monoidal.Reasoning.html#390" class="Generalizable">i</a><a id="1351" class="Symbol">))</a>
<a id="1354" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="1371" class="Symbol">=</a> <a id="1373" href="Categories.Functor.Core.html#565" class="Function">homomorphism</a>
<a id="1387" class="Comment">-- Parallel commutation</a>
<a id="parallel"></a><a id="1412" href="Categories.Category.Monoidal.Reasoning.html#1412" class="Function">parallel</a> <a id="1421" class="Symbol">:</a> <a id="1423" class="Symbol">∀</a> <a id="1425" class="Symbol">{</a><a id="1426" href="Categories.Category.Monoidal.Reasoning.html#1426" class="Bound">X₁</a> <a id="1429" href="Categories.Category.Monoidal.Reasoning.html#1429" class="Bound">X₂</a> <a id="1432" href="Categories.Category.Monoidal.Reasoning.html#1432" class="Bound">Y₁</a> <a id="1435" href="Categories.Category.Monoidal.Reasoning.html#1435" class="Bound">Y₂</a> <a id="1438" href="Categories.Category.Monoidal.Reasoning.html#1438" class="Bound">Z₁</a> <a id="1441" href="Categories.Category.Monoidal.Reasoning.html#1441" class="Bound">Z₂</a> <a id="1444" href="Categories.Category.Monoidal.Reasoning.html#1444" class="Bound">W₁</a> <a id="1447" href="Categories.Category.Monoidal.Reasoning.html#1447" class="Bound">W₂</a><a id="1449" class="Symbol">}</a>
<a id="1462" class="Symbol">{</a><a id="1463" href="Categories.Category.Monoidal.Reasoning.html#1463" class="Bound">f₁</a> <a id="1466" class="Symbol">:</a> <a id="1468" href="Categories.Category.Monoidal.Reasoning.html#1432" class="Bound">Y₁</a> <a id="1471" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1473" href="Categories.Category.Monoidal.Reasoning.html#1444" class="Bound">W₁</a><a id="1475" class="Symbol">}</a> <a id="1477" class="Symbol">{</a><a id="1478" href="Categories.Category.Monoidal.Reasoning.html#1478" class="Bound">f₂</a> <a id="1481" class="Symbol">:</a> <a id="1483" href="Categories.Category.Monoidal.Reasoning.html#1438" class="Bound">Z₁</a> <a id="1486" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1488" href="Categories.Category.Monoidal.Reasoning.html#1444" class="Bound">W₁</a><a id="1490" class="Symbol">}</a> <a id="1492" class="Symbol">{</a><a id="1493" href="Categories.Category.Monoidal.Reasoning.html#1493" class="Bound">g₁</a> <a id="1496" class="Symbol">:</a> <a id="1498" href="Categories.Category.Monoidal.Reasoning.html#1435" class="Bound">Y₂</a> <a id="1501" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1503" href="Categories.Category.Monoidal.Reasoning.html#1447" class="Bound">W₂</a><a id="1505" class="Symbol">}</a> <a id="1507" class="Symbol">{</a><a id="1508" href="Categories.Category.Monoidal.Reasoning.html#1508" class="Bound">g₂</a> <a id="1511" class="Symbol">:</a> <a id="1513" href="Categories.Category.Monoidal.Reasoning.html#1441" class="Bound">Z₂</a> <a id="1516" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1518" href="Categories.Category.Monoidal.Reasoning.html#1447" class="Bound">W₂</a><a id="1520" class="Symbol">}</a>
<a id="1533" class="Symbol">{</a><a id="1534" href="Categories.Category.Monoidal.Reasoning.html#1534" class="Bound">h₁</a> <a id="1537" class="Symbol">:</a> <a id="1539" href="Categories.Category.Monoidal.Reasoning.html#1426" class="Bound">X₁</a> <a id="1542" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1544" href="Categories.Category.Monoidal.Reasoning.html#1432" class="Bound">Y₁</a><a id="1546" class="Symbol">}</a> <a id="1548" class="Symbol">{</a><a id="1549" href="Categories.Category.Monoidal.Reasoning.html#1549" class="Bound">h₂</a> <a id="1552" class="Symbol">:</a> <a id="1554" href="Categories.Category.Monoidal.Reasoning.html#1426" class="Bound">X₁</a> <a id="1557" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1559" href="Categories.Category.Monoidal.Reasoning.html#1438" class="Bound">Z₁</a><a id="1561" class="Symbol">}</a> <a id="1563" class="Symbol">{</a><a id="1564" href="Categories.Category.Monoidal.Reasoning.html#1564" class="Bound">i₁</a> <a id="1567" class="Symbol">:</a> <a id="1569" href="Categories.Category.Monoidal.Reasoning.html#1429" class="Bound">X₂</a> <a id="1572" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1574" href="Categories.Category.Monoidal.Reasoning.html#1435" class="Bound">Y₂</a><a id="1576" class="Symbol">}</a> <a id="1578" class="Symbol">{</a><a id="1579" href="Categories.Category.Monoidal.Reasoning.html#1579" class="Bound">i₂</a> <a id="1582" class="Symbol">:</a> <a id="1584" href="Categories.Category.Monoidal.Reasoning.html#1429" class="Bound">X₂</a> <a id="1587" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1589" href="Categories.Category.Monoidal.Reasoning.html#1441" class="Bound">Z₂</a><a id="1591" class="Symbol">}</a> <a id="1593" class="Symbol">→</a>
<a id="1606" href="Categories.Category.Monoidal.Reasoning.html#1463" class="Bound">f₁</a> <a id="1609" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1611" href="Categories.Category.Monoidal.Reasoning.html#1534" class="Bound">h₁</a> <a id="1614" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1616" href="Categories.Category.Monoidal.Reasoning.html#1478" class="Bound">f₂</a> <a id="1619" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1621" href="Categories.Category.Monoidal.Reasoning.html#1549" class="Bound">h₂</a> <a id="1624" class="Symbol">→</a> <a id="1626" href="Categories.Category.Monoidal.Reasoning.html#1493" class="Bound">g₁</a> <a id="1629" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1631" href="Categories.Category.Monoidal.Reasoning.html#1564" class="Bound">i₁</a> <a id="1634" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1636" href="Categories.Category.Monoidal.Reasoning.html#1508" class="Bound">g₂</a> <a id="1639" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1641" href="Categories.Category.Monoidal.Reasoning.html#1579" class="Bound">i₂</a> <a id="1644" class="Symbol">→</a>
<a id="1657" href="Categories.Category.Monoidal.Reasoning.html#1463" class="Bound">f₁</a> <a id="1660" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1663" href="Categories.Category.Monoidal.Reasoning.html#1493" class="Bound">g₁</a> <a id="1666" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1668" href="Categories.Category.Monoidal.Reasoning.html#1534" class="Bound">h₁</a> <a id="1671" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1674" href="Categories.Category.Monoidal.Reasoning.html#1564" class="Bound">i₁</a> <a id="1677" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1679" href="Categories.Category.Monoidal.Reasoning.html#1478" class="Bound">f₂</a> <a id="1682" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1685" href="Categories.Category.Monoidal.Reasoning.html#1508" class="Bound">g₂</a> <a id="1688" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1690" href="Categories.Category.Monoidal.Reasoning.html#1549" class="Bound">h₂</a> <a id="1693" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1696" href="Categories.Category.Monoidal.Reasoning.html#1579" class="Bound">i₂</a>
<a id="1699" href="Categories.Category.Monoidal.Reasoning.html#1412" class="Function">parallel</a> <a id="1708" class="Symbol">{</a><a id="1709" class="Argument">f₁</a> <a id="1712" class="Symbol">=</a> <a id="1714" href="Categories.Category.Monoidal.Reasoning.html#1714" class="Bound">f₁</a><a id="1716" class="Symbol">}</a> <a id="1718" class="Symbol">{</a><a id="1719" href="Categories.Category.Monoidal.Reasoning.html#1719" class="Bound">f₂</a><a id="1721" class="Symbol">}</a> <a id="1723" class="Symbol">{</a><a id="1724" href="Categories.Category.Monoidal.Reasoning.html#1724" class="Bound">g₁</a><a id="1726" class="Symbol">}</a> <a id="1728" class="Symbol">{</a><a id="1729" href="Categories.Category.Monoidal.Reasoning.html#1729" class="Bound">g₂</a><a id="1731" class="Symbol">}</a> <a id="1733" class="Symbol">{</a><a id="1734" href="Categories.Category.Monoidal.Reasoning.html#1734" class="Bound">h₁</a><a id="1736" class="Symbol">}</a> <a id="1738" class="Symbol">{</a><a id="1739" href="Categories.Category.Monoidal.Reasoning.html#1739" class="Bound">h₂</a><a id="1741" class="Symbol">}</a> <a id="1743" class="Symbol">{</a><a id="1744" href="Categories.Category.Monoidal.Reasoning.html#1744" class="Bound">i₁</a><a id="1746" class="Symbol">}</a> <a id="1748" class="Symbol">{</a><a id="1749" href="Categories.Category.Monoidal.Reasoning.html#1749" class="Bound">i₂</a><a id="1751" class="Symbol">}</a> <a id="1753" href="Categories.Category.Monoidal.Reasoning.html#1753" class="Bound">hyp₁</a> <a id="1758" href="Categories.Category.Monoidal.Reasoning.html#1758" class="Bound">hyp₂</a> <a id="1763" class="Symbol">=</a> <a id="1765" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="1773" href="Categories.Category.Monoidal.Reasoning.html#1714" class="Bound">f₁</a> <a id="1776" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1779" href="Categories.Category.Monoidal.Reasoning.html#1724" class="Bound">g₁</a> <a id="1782" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1784" href="Categories.Category.Monoidal.Reasoning.html#1734" class="Bound">h₁</a> <a id="1787" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1790" href="Categories.Category.Monoidal.Reasoning.html#1744" class="Bound">i₁</a> <a id="1798" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="1802" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="1819" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="1823" class="Symbol">(</a><a id="1824" href="Categories.Category.Monoidal.Reasoning.html#1714" class="Bound">f₁</a> <a id="1827" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1829" href="Categories.Category.Monoidal.Reasoning.html#1734" class="Bound">h₁</a><a id="1831" class="Symbol">)</a> <a id="1833" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1836" class="Symbol">(</a><a id="1837" href="Categories.Category.Monoidal.Reasoning.html#1724" class="Bound">g₁</a> <a id="1840" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1842" href="Categories.Category.Monoidal.Reasoning.html#1744" class="Bound">i₁</a><a id="1844" class="Symbol">)</a> <a id="1848" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="1851" href="Categories.Category.Monoidal.Reasoning.html#1753" class="Bound">hyp₁</a> <a id="1856" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">⟩⊗⟨</a> <a id="1860" href="Categories.Category.Monoidal.Reasoning.html#1758" class="Bound">hyp₂</a> <a id="1865" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="1869" class="Symbol">(</a><a id="1870" href="Categories.Category.Monoidal.Reasoning.html#1719" class="Bound">f₂</a> <a id="1873" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1875" href="Categories.Category.Monoidal.Reasoning.html#1739" class="Bound">h₂</a><a id="1877" class="Symbol">)</a> <a id="1879" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1882" class="Symbol">(</a><a id="1883" href="Categories.Category.Monoidal.Reasoning.html#1729" class="Bound">g₂</a> <a id="1886" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1888" href="Categories.Category.Monoidal.Reasoning.html#1749" class="Bound">i₂</a><a id="1890" class="Symbol">)</a> <a id="1894" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="1897" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="1914" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="1918" href="Categories.Category.Monoidal.Reasoning.html#1719" class="Bound">f₂</a> <a id="1921" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1924" href="Categories.Category.Monoidal.Reasoning.html#1729" class="Bound">g₂</a> <a id="1927" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1929" href="Categories.Category.Monoidal.Reasoning.html#1739" class="Bound">h₂</a> <a id="1932" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="1935" href="Categories.Category.Monoidal.Reasoning.html#1749" class="Bound">i₂</a> <a id="1943" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="1946" class="Comment">-- Parallel-to-serial conversions</a>
<a id="1980" class="Comment">--</a>
<a id="1983" class="Comment">-- | | | | | |</a>
<a id="2019" class="Comment">-- | | | [g] [f] |</a>
<a id="2055" class="Comment">-- [f] [g] = | | = | |</a>
<a id="2091" class="Comment">-- | | [f] | | [g]</a>
<a id="2128" class="Comment">-- | | | | | |</a>
<a id="serialize₁₂"></a><a id="2165" href="Categories.Category.Monoidal.Reasoning.html#2165" class="Function">serialize₁₂</a> <a id="2177" class="Symbol">:</a> <a id="2179" class="Symbol">∀</a> <a id="2181" class="Symbol">{</a><a id="2182" href="Categories.Category.Monoidal.Reasoning.html#2182" class="Bound">X₁</a> <a id="2185" href="Categories.Category.Monoidal.Reasoning.html#2185" class="Bound">Y₁</a> <a id="2188" href="Categories.Category.Monoidal.Reasoning.html#2188" class="Bound">X₂</a> <a id="2191" href="Categories.Category.Monoidal.Reasoning.html#2191" class="Bound">Y₂</a><a id="2193" class="Symbol">}</a> <a id="2195" class="Symbol">{</a><a id="2196" href="Categories.Category.Monoidal.Reasoning.html#2196" class="Bound">f</a> <a id="2198" class="Symbol">:</a> <a id="2200" href="Categories.Category.Monoidal.Reasoning.html#2182" class="Bound">X₁</a> <a id="2203" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2205" href="Categories.Category.Monoidal.Reasoning.html#2185" class="Bound">Y₁</a><a id="2207" class="Symbol">}</a> <a id="2209" class="Symbol">{</a><a id="2210" href="Categories.Category.Monoidal.Reasoning.html#2210" class="Bound">g</a> <a id="2212" class="Symbol">:</a> <a id="2214" href="Categories.Category.Monoidal.Reasoning.html#2188" class="Bound">X₂</a> <a id="2217" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2219" href="Categories.Category.Monoidal.Reasoning.html#2191" class="Bound">Y₂</a><a id="2221" class="Symbol">}</a> <a id="2223" class="Symbol">→</a>
<a id="2239" href="Categories.Category.Monoidal.Reasoning.html#2196" class="Bound">f</a> <a id="2241" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2244" href="Categories.Category.Monoidal.Reasoning.html#2210" class="Bound">g</a> <a id="2246" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="2248" href="Categories.Category.Monoidal.Reasoning.html#2196" class="Bound">f</a> <a id="2250" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2253" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2256" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2258" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2261" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2264" href="Categories.Category.Monoidal.Reasoning.html#2210" class="Bound">g</a>
<a id="2266" href="Categories.Category.Monoidal.Reasoning.html#2165" class="Function">serialize₁₂</a> <a id="2278" class="Symbol">{</a><a id="2279" class="Argument">f</a> <a id="2281" class="Symbol">=</a> <a id="2283" href="Categories.Category.Monoidal.Reasoning.html#2283" class="Bound">f</a><a id="2284" class="Symbol">}</a> <a id="2286" class="Symbol">{</a><a id="2287" href="Categories.Category.Monoidal.Reasoning.html#2287" class="Bound">g</a><a id="2288" class="Symbol">}</a> <a id="2290" class="Symbol">=</a> <a id="2292" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="2300" href="Categories.Category.Monoidal.Reasoning.html#2283" class="Bound">f</a> <a id="2302" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2305" href="Categories.Category.Monoidal.Reasoning.html#2287" class="Bound">g</a> <a id="2323" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="2327" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="2337" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">⟩⊗⟨</a> <a id="2341" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="2351" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="2355" class="Symbol">(</a><a id="2356" href="Categories.Category.Monoidal.Reasoning.html#2283" class="Bound">f</a> <a id="2358" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2360" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2362" class="Symbol">)</a> <a id="2364" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2367" class="Symbol">(</a><a id="2368" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2371" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2373" href="Categories.Category.Monoidal.Reasoning.html#2287" class="Bound">g</a><a id="2374" class="Symbol">)</a> <a id="2378" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2381" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="2398" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="2402" href="Categories.Category.Monoidal.Reasoning.html#2283" class="Bound">f</a> <a id="2404" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2407" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2410" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2412" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2415" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2418" href="Categories.Category.Monoidal.Reasoning.html#2287" class="Bound">g</a> <a id="2425" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="serialize₂₁"></a><a id="2428" href="Categories.Category.Monoidal.Reasoning.html#2428" class="Function">serialize₂₁</a> <a id="2440" class="Symbol">:</a> <a id="2442" class="Symbol">∀</a> <a id="2444" class="Symbol">{</a><a id="2445" href="Categories.Category.Monoidal.Reasoning.html#2445" class="Bound">X₁</a> <a id="2448" href="Categories.Category.Monoidal.Reasoning.html#2448" class="Bound">Y₁</a> <a id="2451" href="Categories.Category.Monoidal.Reasoning.html#2451" class="Bound">X₂</a> <a id="2454" href="Categories.Category.Monoidal.Reasoning.html#2454" class="Bound">Y₂</a><a id="2456" class="Symbol">}</a> <a id="2458" class="Symbol">{</a><a id="2459" href="Categories.Category.Monoidal.Reasoning.html#2459" class="Bound">f</a> <a id="2461" class="Symbol">:</a> <a id="2463" href="Categories.Category.Monoidal.Reasoning.html#2445" class="Bound">X₁</a> <a id="2466" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2468" href="Categories.Category.Monoidal.Reasoning.html#2448" class="Bound">Y₁</a><a id="2470" class="Symbol">}</a> <a id="2472" class="Symbol">{</a><a id="2473" href="Categories.Category.Monoidal.Reasoning.html#2473" class="Bound">g</a> <a id="2475" class="Symbol">:</a> <a id="2477" href="Categories.Category.Monoidal.Reasoning.html#2451" class="Bound">X₂</a> <a id="2480" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2482" href="Categories.Category.Monoidal.Reasoning.html#2454" class="Bound">Y₂</a><a id="2484" class="Symbol">}</a> <a id="2486" class="Symbol">→</a>
<a id="2502" href="Categories.Category.Monoidal.Reasoning.html#2459" class="Bound">f</a> <a id="2504" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2507" href="Categories.Category.Monoidal.Reasoning.html#2473" class="Bound">g</a> <a id="2509" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="2511" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2514" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2517" href="Categories.Category.Monoidal.Reasoning.html#2473" class="Bound">g</a> <a id="2519" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2521" href="Categories.Category.Monoidal.Reasoning.html#2459" class="Bound">f</a> <a id="2523" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2526" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="2529" href="Categories.Category.Monoidal.Reasoning.html#2428" class="Function">serialize₂₁</a> <a id="2541" class="Symbol">{</a><a id="2542" class="Argument">f</a> <a id="2544" class="Symbol">=</a> <a id="2546" href="Categories.Category.Monoidal.Reasoning.html#2546" class="Bound">f</a><a id="2547" class="Symbol">}</a> <a id="2549" class="Symbol">{</a><a id="2550" href="Categories.Category.Monoidal.Reasoning.html#2550" class="Bound">g</a><a id="2551" class="Symbol">}</a> <a id="2553" class="Symbol">=</a> <a id="2555" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="2563" href="Categories.Category.Monoidal.Reasoning.html#2546" class="Bound">f</a> <a id="2565" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2568" href="Categories.Category.Monoidal.Reasoning.html#2550" class="Bound">g</a> <a id="2586" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="2590" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="2600" href="Categories.Category.Monoidal.Reasoning.html#788" class="Function Operator">⟩⊗⟨</a> <a id="2604" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="2614" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="2618" class="Symbol">(</a><a id="2619" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2622" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2624" href="Categories.Category.Monoidal.Reasoning.html#2546" class="Bound">f</a><a id="2625" class="Symbol">)</a> <a id="2627" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2630" class="Symbol">(</a><a id="2631" href="Categories.Category.Monoidal.Reasoning.html#2550" class="Bound">g</a> <a id="2633" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2635" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2637" class="Symbol">)</a> <a id="2641" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2644" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="2661" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="2665" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2668" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2671" href="Categories.Category.Monoidal.Reasoning.html#2550" class="Bound">g</a> <a id="2673" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2675" href="Categories.Category.Monoidal.Reasoning.html#2546" class="Bound">f</a> <a id="2677" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="2680" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2688" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="2691" class="Comment">-- Split a composite in the first component</a>
<a id="2735" class="Comment">--</a>
<a id="2738" class="Comment">-- | | | | | |</a>
<a id="2774" class="Comment">-- [g] | [g] | [g] [h]</a>
<a id="2811" class="Comment">-- | [h] = | | = | |</a>
<a id="2847" class="Comment">-- [f] | [f] [h] [f] |</a>
<a id="2883" class="Comment">-- | | | | | |</a>
<a id="split₁ʳ"></a><a id="2920" href="Categories.Category.Monoidal.Reasoning.html#2920" class="Function">split₁ʳ</a> <a id="2928" class="Symbol">:</a> <a id="2930" class="Symbol">∀</a> <a id="2932" class="Symbol">{</a><a id="2933" href="Categories.Category.Monoidal.Reasoning.html#2933" class="Bound">X₁</a> <a id="2936" href="Categories.Category.Monoidal.Reasoning.html#2936" class="Bound">Y₁</a> <a id="2939" href="Categories.Category.Monoidal.Reasoning.html#2939" class="Bound">Z₁</a> <a id="2942" href="Categories.Category.Monoidal.Reasoning.html#2942" class="Bound">X₂</a> <a id="2945" href="Categories.Category.Monoidal.Reasoning.html#2945" class="Bound">Y₂</a><a id="2947" class="Symbol">}</a> <a id="2949" class="Symbol">{</a><a id="2950" href="Categories.Category.Monoidal.Reasoning.html#2950" class="Bound">f</a> <a id="2952" class="Symbol">:</a> <a id="2954" href="Categories.Category.Monoidal.Reasoning.html#2936" class="Bound">Y₁</a> <a id="2957" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2959" href="Categories.Category.Monoidal.Reasoning.html#2939" class="Bound">Z₁</a><a id="2961" class="Symbol">}</a> <a id="2963" class="Symbol">{</a><a id="2964" href="Categories.Category.Monoidal.Reasoning.html#2964" class="Bound">g</a> <a id="2966" class="Symbol">:</a> <a id="2968" href="Categories.Category.Monoidal.Reasoning.html#2933" class="Bound">X₁</a> <a id="2971" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2973" href="Categories.Category.Monoidal.Reasoning.html#2936" class="Bound">Y₁</a><a id="2975" class="Symbol">}</a> <a id="2977" class="Symbol">{</a><a id="2978" href="Categories.Category.Monoidal.Reasoning.html#2978" class="Bound">h</a> <a id="2980" class="Symbol">:</a> <a id="2982" href="Categories.Category.Monoidal.Reasoning.html#2942" class="Bound">X₂</a> <a id="2985" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2987" href="Categories.Category.Monoidal.Reasoning.html#2945" class="Bound">Y₂</a><a id="2989" class="Symbol">}</a> <a id="2991" class="Symbol">→</a>
<a id="3003" class="Symbol">(</a><a id="3004" href="Categories.Category.Monoidal.Reasoning.html#2950" class="Bound">f</a> <a id="3006" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3008" href="Categories.Category.Monoidal.Reasoning.html#2964" class="Bound">g</a><a id="3009" class="Symbol">)</a> <a id="3011" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3014" href="Categories.Category.Monoidal.Reasoning.html#2978" class="Bound">h</a> <a id="3016" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3018" href="Categories.Category.Monoidal.Reasoning.html#2950" class="Bound">f</a> <a id="3020" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3023" href="Categories.Category.Monoidal.Reasoning.html#2978" class="Bound">h</a> <a id="3025" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3027" href="Categories.Category.Monoidal.Reasoning.html#2964" class="Bound">g</a> <a id="3029" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3032" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="3035" href="Categories.Category.Monoidal.Reasoning.html#2920" class="Function">split₁ʳ</a> <a id="3043" class="Symbol">{</a><a id="3044" class="Argument">f</a> <a id="3046" class="Symbol">=</a> <a id="3048" href="Categories.Category.Monoidal.Reasoning.html#3048" class="Bound">f</a><a id="3049" class="Symbol">}</a> <a id="3051" class="Symbol">{</a><a id="3052" href="Categories.Category.Monoidal.Reasoning.html#3052" class="Bound">g</a><a id="3053" class="Symbol">}</a> <a id="3055" class="Symbol">{</a><a id="3056" href="Categories.Category.Monoidal.Reasoning.html#3056" class="Bound">h</a><a id="3057" class="Symbol">}</a> <a id="3059" class="Symbol">=</a> <a id="3061" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="3069" class="Symbol">(</a><a id="3070" href="Categories.Category.Monoidal.Reasoning.html#3048" class="Bound">f</a> <a id="3072" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3074" href="Categories.Category.Monoidal.Reasoning.html#3052" class="Bound">g</a><a id="3075" class="Symbol">)</a> <a id="3077" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3080" href="Categories.Category.Monoidal.Reasoning.html#3056" class="Bound">h</a> <a id="3091" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="3095" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨</a> <a id="3103" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="3113" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="3117" class="Symbol">(</a><a id="3118" href="Categories.Category.Monoidal.Reasoning.html#3048" class="Bound">f</a> <a id="3120" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3122" href="Categories.Category.Monoidal.Reasoning.html#3052" class="Bound">g</a><a id="3123" class="Symbol">)</a> <a id="3125" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3128" class="Symbol">(</a><a id="3129" href="Categories.Category.Monoidal.Reasoning.html#3056" class="Bound">h</a> <a id="3131" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3133" href="Categories.Category.Core.html#630" class="Function">id</a><a id="3135" class="Symbol">)</a> <a id="3139" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3142" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="3159" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="3163" href="Categories.Category.Monoidal.Reasoning.html#3048" class="Bound">f</a> <a id="3165" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3168" href="Categories.Category.Monoidal.Reasoning.html#3056" class="Bound">h</a> <a id="3170" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3172" href="Categories.Category.Monoidal.Reasoning.html#3052" class="Bound">g</a> <a id="3174" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3177" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3185" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="split₁ˡ"></a><a id="3188" href="Categories.Category.Monoidal.Reasoning.html#3188" class="Function">split₁ˡ</a> <a id="3196" class="Symbol">:</a> <a id="3198" class="Symbol">∀</a> <a id="3200" class="Symbol">{</a><a id="3201" href="Categories.Category.Monoidal.Reasoning.html#3201" class="Bound">X₁</a> <a id="3204" href="Categories.Category.Monoidal.Reasoning.html#3204" class="Bound">Y₁</a> <a id="3207" href="Categories.Category.Monoidal.Reasoning.html#3207" class="Bound">Z₁</a> <a id="3210" href="Categories.Category.Monoidal.Reasoning.html#3210" class="Bound">X₂</a> <a id="3213" href="Categories.Category.Monoidal.Reasoning.html#3213" class="Bound">Y₂</a><a id="3215" class="Symbol">}</a> <a id="3217" class="Symbol">{</a><a id="3218" href="Categories.Category.Monoidal.Reasoning.html#3218" class="Bound">f</a> <a id="3220" class="Symbol">:</a> <a id="3222" href="Categories.Category.Monoidal.Reasoning.html#3204" class="Bound">Y₁</a> <a id="3225" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3227" href="Categories.Category.Monoidal.Reasoning.html#3207" class="Bound">Z₁</a><a id="3229" class="Symbol">}</a> <a id="3231" class="Symbol">{</a><a id="3232" href="Categories.Category.Monoidal.Reasoning.html#3232" class="Bound">g</a> <a id="3234" class="Symbol">:</a> <a id="3236" href="Categories.Category.Monoidal.Reasoning.html#3201" class="Bound">X₁</a> <a id="3239" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3241" href="Categories.Category.Monoidal.Reasoning.html#3204" class="Bound">Y₁</a><a id="3243" class="Symbol">}</a> <a id="3245" class="Symbol">{</a><a id="3246" href="Categories.Category.Monoidal.Reasoning.html#3246" class="Bound">h</a> <a id="3248" class="Symbol">:</a> <a id="3250" href="Categories.Category.Monoidal.Reasoning.html#3210" class="Bound">X₂</a> <a id="3253" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3255" href="Categories.Category.Monoidal.Reasoning.html#3213" class="Bound">Y₂</a><a id="3257" class="Symbol">}</a> <a id="3259" class="Symbol">→</a>
<a id="3271" class="Symbol">(</a><a id="3272" href="Categories.Category.Monoidal.Reasoning.html#3218" class="Bound">f</a> <a id="3274" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3276" href="Categories.Category.Monoidal.Reasoning.html#3232" class="Bound">g</a><a id="3277" class="Symbol">)</a> <a id="3279" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3282" href="Categories.Category.Monoidal.Reasoning.html#3246" class="Bound">h</a> <a id="3284" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3286" href="Categories.Category.Monoidal.Reasoning.html#3218" class="Bound">f</a> <a id="3288" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3291" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3294" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3296" href="Categories.Category.Monoidal.Reasoning.html#3232" class="Bound">g</a> <a id="3298" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3301" href="Categories.Category.Monoidal.Reasoning.html#3246" class="Bound">h</a>
<a id="3303" href="Categories.Category.Monoidal.Reasoning.html#3188" class="Function">split₁ˡ</a> <a id="3311" class="Symbol">{</a><a id="3312" class="Argument">f</a> <a id="3314" class="Symbol">=</a> <a id="3316" href="Categories.Category.Monoidal.Reasoning.html#3316" class="Bound">f</a><a id="3317" class="Symbol">}</a> <a id="3319" class="Symbol">{</a><a id="3320" href="Categories.Category.Monoidal.Reasoning.html#3320" class="Bound">g</a><a id="3321" class="Symbol">}</a> <a id="3323" class="Symbol">{</a><a id="3324" href="Categories.Category.Monoidal.Reasoning.html#3324" class="Bound">h</a><a id="3325" class="Symbol">}</a> <a id="3327" class="Symbol">=</a> <a id="3329" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="3337" class="Symbol">(</a><a id="3338" href="Categories.Category.Monoidal.Reasoning.html#3316" class="Bound">f</a> <a id="3340" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3342" href="Categories.Category.Monoidal.Reasoning.html#3320" class="Bound">g</a><a id="3343" class="Symbol">)</a> <a id="3345" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3348" href="Categories.Category.Monoidal.Reasoning.html#3324" class="Bound">h</a> <a id="3359" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="3363" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨</a> <a id="3371" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="3381" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="3385" class="Symbol">(</a><a id="3386" href="Categories.Category.Monoidal.Reasoning.html#3316" class="Bound">f</a> <a id="3388" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3390" href="Categories.Category.Monoidal.Reasoning.html#3320" class="Bound">g</a><a id="3391" class="Symbol">)</a> <a id="3393" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3396" class="Symbol">(</a><a id="3397" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3400" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3402" href="Categories.Category.Monoidal.Reasoning.html#3324" class="Bound">h</a><a id="3403" class="Symbol">)</a> <a id="3407" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3410" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="3427" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="3431" href="Categories.Category.Monoidal.Reasoning.html#3316" class="Bound">f</a> <a id="3433" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3436" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3439" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3441" href="Categories.Category.Monoidal.Reasoning.html#3320" class="Bound">g</a> <a id="3443" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3446" href="Categories.Category.Monoidal.Reasoning.html#3324" class="Bound">h</a> <a id="3453" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="3456" class="Comment">-- Split a composite in the second component</a>
<a id="3501" class="Comment">--</a>
<a id="3504" class="Comment">-- | | | | | |</a>
<a id="3540" class="Comment">-- | [h] | [h] [f] [h]</a>
<a id="3577" class="Comment">-- [f] | = | | = | |</a>
<a id="3613" class="Comment">-- | [g] [f] [g] | [g]</a>
<a id="3650" class="Comment">-- | | | | | |</a>
<a id="split₂ʳ"></a><a id="3687" href="Categories.Category.Monoidal.Reasoning.html#3687" class="Function">split₂ʳ</a> <a id="3695" class="Symbol">:</a> <a id="3697" class="Symbol">∀</a> <a id="3699" class="Symbol">{</a><a id="3700" href="Categories.Category.Monoidal.Reasoning.html#3700" class="Bound">X₁</a> <a id="3703" href="Categories.Category.Monoidal.Reasoning.html#3703" class="Bound">Y₁</a> <a id="3706" href="Categories.Category.Monoidal.Reasoning.html#3706" class="Bound">X₂</a> <a id="3709" href="Categories.Category.Monoidal.Reasoning.html#3709" class="Bound">Y₂</a> <a id="3712" href="Categories.Category.Monoidal.Reasoning.html#3712" class="Bound">Z₂</a><a id="3714" class="Symbol">}</a> <a id="3716" class="Symbol">{</a><a id="3717" href="Categories.Category.Monoidal.Reasoning.html#3717" class="Bound">f</a> <a id="3719" class="Symbol">:</a> <a id="3721" href="Categories.Category.Monoidal.Reasoning.html#3700" class="Bound">X₁</a> <a id="3724" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3726" href="Categories.Category.Monoidal.Reasoning.html#3703" class="Bound">Y₁</a><a id="3728" class="Symbol">}</a> <a id="3730" class="Symbol">{</a><a id="3731" href="Categories.Category.Monoidal.Reasoning.html#3731" class="Bound">g</a> <a id="3733" class="Symbol">:</a> <a id="3735" href="Categories.Category.Monoidal.Reasoning.html#3709" class="Bound">Y₂</a> <a id="3738" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3740" href="Categories.Category.Monoidal.Reasoning.html#3712" class="Bound">Z₂</a><a id="3742" class="Symbol">}</a> <a id="3744" class="Symbol">{</a><a id="3745" href="Categories.Category.Monoidal.Reasoning.html#3745" class="Bound">h</a> <a id="3747" class="Symbol">:</a> <a id="3749" href="Categories.Category.Monoidal.Reasoning.html#3706" class="Bound">X₂</a> <a id="3752" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3754" href="Categories.Category.Monoidal.Reasoning.html#3709" class="Bound">Y₂</a><a id="3756" class="Symbol">}</a> <a id="3758" class="Symbol">→</a>
<a id="3770" href="Categories.Category.Monoidal.Reasoning.html#3717" class="Bound">f</a> <a id="3772" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3775" class="Symbol">(</a><a id="3776" href="Categories.Category.Monoidal.Reasoning.html#3731" class="Bound">g</a> <a id="3778" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3780" href="Categories.Category.Monoidal.Reasoning.html#3745" class="Bound">h</a><a id="3781" class="Symbol">)</a> <a id="3783" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3785" href="Categories.Category.Monoidal.Reasoning.html#3717" class="Bound">f</a> <a id="3787" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3790" href="Categories.Category.Monoidal.Reasoning.html#3731" class="Bound">g</a> <a id="3792" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3794" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3797" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3800" href="Categories.Category.Monoidal.Reasoning.html#3745" class="Bound">h</a>
<a id="3802" href="Categories.Category.Monoidal.Reasoning.html#3687" class="Function">split₂ʳ</a> <a id="3810" class="Symbol">{</a><a id="3811" class="Argument">f</a> <a id="3813" class="Symbol">=</a> <a id="3815" href="Categories.Category.Monoidal.Reasoning.html#3815" class="Bound">f</a><a id="3816" class="Symbol">}</a> <a id="3818" class="Symbol">{</a><a id="3819" href="Categories.Category.Monoidal.Reasoning.html#3819" class="Bound">g</a><a id="3820" class="Symbol">}</a> <a id="3822" class="Symbol">{</a><a id="3823" href="Categories.Category.Monoidal.Reasoning.html#3823" class="Bound">h</a><a id="3824" class="Symbol">}</a> <a id="3826" class="Symbol">=</a> <a id="3828" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="3836" href="Categories.Category.Monoidal.Reasoning.html#3815" class="Bound">f</a> <a id="3838" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3841" class="Symbol">(</a><a id="3842" href="Categories.Category.Monoidal.Reasoning.html#3819" class="Bound">g</a> <a id="3844" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3846" href="Categories.Category.Monoidal.Reasoning.html#3823" class="Bound">h</a><a id="3847" class="Symbol">)</a> <a id="3858" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="3862" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="3872" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">⟩⊗⟨refl</a> <a id="3880" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="3884" class="Symbol">(</a><a id="3885" href="Categories.Category.Monoidal.Reasoning.html#3815" class="Bound">f</a> <a id="3887" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3889" href="Categories.Category.Core.html#630" class="Function">id</a><a id="3891" class="Symbol">)</a> <a id="3893" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3896" class="Symbol">(</a><a id="3897" href="Categories.Category.Monoidal.Reasoning.html#3819" class="Bound">g</a> <a id="3899" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3901" href="Categories.Category.Monoidal.Reasoning.html#3823" class="Bound">h</a><a id="3902" class="Symbol">)</a> <a id="3906" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3909" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="3926" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="3930" href="Categories.Category.Monoidal.Reasoning.html#3815" class="Bound">f</a> <a id="3932" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3935" href="Categories.Category.Monoidal.Reasoning.html#3819" class="Bound">g</a> <a id="3937" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3939" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3942" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="3945" href="Categories.Category.Monoidal.Reasoning.html#3823" class="Bound">h</a> <a id="3952" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="split₂ˡ"></a><a id="3955" href="Categories.Category.Monoidal.Reasoning.html#3955" class="Function">split₂ˡ</a> <a id="3963" class="Symbol">:</a> <a id="3965" class="Symbol">∀</a> <a id="3967" class="Symbol">{</a><a id="3968" href="Categories.Category.Monoidal.Reasoning.html#3968" class="Bound">X₁</a> <a id="3971" href="Categories.Category.Monoidal.Reasoning.html#3971" class="Bound">Y₁</a> <a id="3974" href="Categories.Category.Monoidal.Reasoning.html#3974" class="Bound">X₂</a> <a id="3977" href="Categories.Category.Monoidal.Reasoning.html#3977" class="Bound">Y₂</a> <a id="3980" href="Categories.Category.Monoidal.Reasoning.html#3980" class="Bound">Z₂</a><a id="3982" class="Symbol">}</a> <a id="3984" class="Symbol">{</a><a id="3985" href="Categories.Category.Monoidal.Reasoning.html#3985" class="Bound">f</a> <a id="3987" class="Symbol">:</a> <a id="3989" href="Categories.Category.Monoidal.Reasoning.html#3968" class="Bound">X₁</a> <a id="3992" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3994" href="Categories.Category.Monoidal.Reasoning.html#3971" class="Bound">Y₁</a><a id="3996" class="Symbol">}</a> <a id="3998" class="Symbol">{</a><a id="3999" href="Categories.Category.Monoidal.Reasoning.html#3999" class="Bound">g</a> <a id="4001" class="Symbol">:</a> <a id="4003" href="Categories.Category.Monoidal.Reasoning.html#3977" class="Bound">Y₂</a> <a id="4006" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4008" href="Categories.Category.Monoidal.Reasoning.html#3980" class="Bound">Z₂</a><a id="4010" class="Symbol">}</a> <a id="4012" class="Symbol">{</a><a id="4013" href="Categories.Category.Monoidal.Reasoning.html#4013" class="Bound">h</a> <a id="4015" class="Symbol">:</a> <a id="4017" href="Categories.Category.Monoidal.Reasoning.html#3974" class="Bound">X₂</a> <a id="4020" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4022" href="Categories.Category.Monoidal.Reasoning.html#3977" class="Bound">Y₂</a><a id="4024" class="Symbol">}</a> <a id="4026" class="Symbol">→</a>
<a id="4038" href="Categories.Category.Monoidal.Reasoning.html#3985" class="Bound">f</a> <a id="4040" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4043" class="Symbol">(</a><a id="4044" href="Categories.Category.Monoidal.Reasoning.html#3999" class="Bound">g</a> <a id="4046" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4048" href="Categories.Category.Monoidal.Reasoning.html#4013" class="Bound">h</a><a id="4049" class="Symbol">)</a> <a id="4051" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4053" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4056" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4059" href="Categories.Category.Monoidal.Reasoning.html#3999" class="Bound">g</a> <a id="4061" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4063" href="Categories.Category.Monoidal.Reasoning.html#3985" class="Bound">f</a> <a id="4065" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4068" href="Categories.Category.Monoidal.Reasoning.html#4013" class="Bound">h</a>
<a id="4070" href="Categories.Category.Monoidal.Reasoning.html#3955" class="Function">split₂ˡ</a> <a id="4078" class="Symbol">{</a><a id="4079" class="Argument">f</a> <a id="4081" class="Symbol">=</a> <a id="4083" href="Categories.Category.Monoidal.Reasoning.html#4083" class="Bound">f</a><a id="4084" class="Symbol">}</a> <a id="4086" class="Symbol">{</a><a id="4087" href="Categories.Category.Monoidal.Reasoning.html#4087" class="Bound">g</a><a id="4088" class="Symbol">}</a> <a id="4090" class="Symbol">{</a><a id="4091" href="Categories.Category.Monoidal.Reasoning.html#4091" class="Bound">h</a><a id="4092" class="Symbol">}</a> <a id="4094" class="Symbol">=</a> <a id="4096" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="4104" href="Categories.Category.Monoidal.Reasoning.html#4083" class="Bound">f</a> <a id="4106" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4109" class="Symbol">(</a><a id="4110" href="Categories.Category.Monoidal.Reasoning.html#4087" class="Bound">g</a> <a id="4112" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4114" href="Categories.Category.Monoidal.Reasoning.html#4091" class="Bound">h</a><a id="4115" class="Symbol">)</a> <a id="4126" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="4130" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="4140" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">⟩⊗⟨refl</a> <a id="4148" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
<a id="4152" class="Symbol">(</a><a id="4153" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4156" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4158" href="Categories.Category.Monoidal.Reasoning.html#4083" class="Bound">f</a><a id="4159" class="Symbol">)</a> <a id="4161" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4164" class="Symbol">(</a><a id="4165" href="Categories.Category.Monoidal.Reasoning.html#4087" class="Bound">g</a> <a id="4167" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4169" href="Categories.Category.Monoidal.Reasoning.html#4091" class="Bound">h</a><a id="4170" class="Symbol">)</a> <a id="4174" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4177" href="Categories.Category.Monoidal.Reasoning.html#1290" class="Function">⊗-distrib-over-∘</a> <a id="4194" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="4198" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4201" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4204" href="Categories.Category.Monoidal.Reasoning.html#4087" class="Bound">g</a> <a id="4206" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4208" href="Categories.Category.Monoidal.Reasoning.html#4083" class="Bound">f</a> <a id="4210" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4213" href="Categories.Category.Monoidal.Reasoning.html#4091" class="Bound">h</a> <a id="4220" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="4223" class="Comment">-- The opposite, i.e. merge</a>
<a id="merge₂ʳ"></a><a id="4251" href="Categories.Category.Monoidal.Reasoning.html#4251" class="Function">merge₂ʳ</a> <a id="4259" class="Symbol">:</a> <a id="4262" class="Symbol">∀</a> <a id="4264" class="Symbol">{</a><a id="4265" href="Categories.Category.Monoidal.Reasoning.html#4265" class="Bound">X₁</a> <a id="4268" href="Categories.Category.Monoidal.Reasoning.html#4268" class="Bound">Y₁</a> <a id="4271" href="Categories.Category.Monoidal.Reasoning.html#4271" class="Bound">X₂</a> <a id="4274" href="Categories.Category.Monoidal.Reasoning.html#4274" class="Bound">Y₂</a> <a id="4277" href="Categories.Category.Monoidal.Reasoning.html#4277" class="Bound">Z₂</a><a id="4279" class="Symbol">}</a> <a id="4281" class="Symbol">{</a><a id="4282" href="Categories.Category.Monoidal.Reasoning.html#4282" class="Bound">f</a> <a id="4284" class="Symbol">:</a> <a id="4286" href="Categories.Category.Monoidal.Reasoning.html#4265" class="Bound">X₁</a> <a id="4289" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4291" href="Categories.Category.Monoidal.Reasoning.html#4268" class="Bound">Y₁</a><a id="4293" class="Symbol">}</a> <a id="4295" class="Symbol">{</a><a id="4296" href="Categories.Category.Monoidal.Reasoning.html#4296" class="Bound">g</a> <a id="4298" class="Symbol">:</a> <a id="4300" href="Categories.Category.Monoidal.Reasoning.html#4274" class="Bound">Y₂</a> <a id="4303" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4305" href="Categories.Category.Monoidal.Reasoning.html#4277" class="Bound">Z₂</a><a id="4307" class="Symbol">}</a> <a id="4309" class="Symbol">{</a><a id="4310" href="Categories.Category.Monoidal.Reasoning.html#4310" class="Bound">h</a> <a id="4312" class="Symbol">:</a> <a id="4314" href="Categories.Category.Monoidal.Reasoning.html#4271" class="Bound">X₂</a> <a id="4317" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4319" href="Categories.Category.Monoidal.Reasoning.html#4274" class="Bound">Y₂</a><a id="4321" class="Symbol">}</a> <a id="4323" class="Symbol">→</a>
<a id="4335" href="Categories.Category.Monoidal.Reasoning.html#4282" class="Bound">f</a> <a id="4337" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4340" href="Categories.Category.Monoidal.Reasoning.html#4296" class="Bound">g</a> <a id="4342" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4344" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4347" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4350" href="Categories.Category.Monoidal.Reasoning.html#4310" class="Bound">h</a> <a id="4352" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4354" href="Categories.Category.Monoidal.Reasoning.html#4282" class="Bound">f</a> <a id="4356" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4359" class="Symbol">(</a><a id="4360" href="Categories.Category.Monoidal.Reasoning.html#4296" class="Bound">g</a> <a id="4362" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4364" href="Categories.Category.Monoidal.Reasoning.html#4310" class="Bound">h</a><a id="4365" class="Symbol">)</a>
<a id="4367" href="Categories.Category.Monoidal.Reasoning.html#4251" class="Function">merge₂ʳ</a> <a id="4375" class="Symbol">=</a> <a id="4377" href="Relation.Binary.Structures.html#1622" class="Function">Equiv.sym</a> <a id="4387" href="Categories.Category.Monoidal.Reasoning.html#3687" class="Function">split₂ʳ</a>
<a id="merge₂ˡ"></a><a id="4396" href="Categories.Category.Monoidal.Reasoning.html#4396" class="Function">merge₂ˡ</a> <a id="4404" class="Symbol">:</a> <a id="4406" class="Symbol">∀</a> <a id="4408" class="Symbol">{</a><a id="4409" href="Categories.Category.Monoidal.Reasoning.html#4409" class="Bound">X₁</a> <a id="4412" href="Categories.Category.Monoidal.Reasoning.html#4412" class="Bound">Y₁</a> <a id="4415" href="Categories.Category.Monoidal.Reasoning.html#4415" class="Bound">X₂</a> <a id="4418" href="Categories.Category.Monoidal.Reasoning.html#4418" class="Bound">Y₂</a> <a id="4421" href="Categories.Category.Monoidal.Reasoning.html#4421" class="Bound">Z₂</a><a id="4423" class="Symbol">}</a> <a id="4425" class="Symbol">{</a><a id="4426" href="Categories.Category.Monoidal.Reasoning.html#4426" class="Bound">f</a> <a id="4428" class="Symbol">:</a> <a id="4430" href="Categories.Category.Monoidal.Reasoning.html#4409" class="Bound">X₁</a> <a id="4433" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4435" href="Categories.Category.Monoidal.Reasoning.html#4412" class="Bound">Y₁</a><a id="4437" class="Symbol">}</a> <a id="4439" class="Symbol">{</a><a id="4440" href="Categories.Category.Monoidal.Reasoning.html#4440" class="Bound">g</a> <a id="4442" class="Symbol">:</a> <a id="4444" href="Categories.Category.Monoidal.Reasoning.html#4418" class="Bound">Y₂</a> <a id="4447" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4449" href="Categories.Category.Monoidal.Reasoning.html#4421" class="Bound">Z₂</a><a id="4451" class="Symbol">}</a> <a id="4453" class="Symbol">{</a><a id="4454" href="Categories.Category.Monoidal.Reasoning.html#4454" class="Bound">h</a> <a id="4456" class="Symbol">:</a> <a id="4458" href="Categories.Category.Monoidal.Reasoning.html#4415" class="Bound">X₂</a> <a id="4461" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4463" href="Categories.Category.Monoidal.Reasoning.html#4418" class="Bound">Y₂</a><a id="4465" class="Symbol">}</a> <a id="4467" class="Symbol">→</a>
<a id="4479" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4482" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4485" href="Categories.Category.Monoidal.Reasoning.html#4440" class="Bound">g</a> <a id="4487" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4489" href="Categories.Category.Monoidal.Reasoning.html#4426" class="Bound">f</a> <a id="4491" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4494" href="Categories.Category.Monoidal.Reasoning.html#4454" class="Bound">h</a> <a id="4496" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4498" href="Categories.Category.Monoidal.Reasoning.html#4426" class="Bound">f</a> <a id="4500" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4503" class="Symbol">(</a><a id="4504" href="Categories.Category.Monoidal.Reasoning.html#4440" class="Bound">g</a> <a id="4506" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4508" href="Categories.Category.Monoidal.Reasoning.html#4454" class="Bound">h</a><a id="4509" class="Symbol">)</a>
<a id="4511" href="Categories.Category.Monoidal.Reasoning.html#4396" class="Function">merge₂ˡ</a> <a id="4519" class="Symbol">=</a> <a id="4521" href="Relation.Binary.Structures.html#1622" class="Function">Equiv.sym</a> <a id="4531" href="Categories.Category.Monoidal.Reasoning.html#3955" class="Function">split₂ˡ</a>
<a id="4540" class="Comment">-- Combined splitting and re-association.</a>
<a id="4583" class="Keyword">module</a> <a id="4590" href="Categories.Category.Monoidal.Reasoning.html#4590" class="Module">_</a> <a id="4592" class="Symbol">{</a><a id="4593" href="Categories.Category.Monoidal.Reasoning.html#4593" class="Bound">X</a> <a id="4595" href="Categories.Category.Monoidal.Reasoning.html#4595" class="Bound">Y</a> <a id="4597" href="Categories.Category.Monoidal.Reasoning.html#4597" class="Bound">Z</a><a id="4598" class="Symbol">}</a> <a id="4600" class="Symbol">{</a><a id="4601" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="4603" class="Symbol">:</a> <a id="4605" href="Categories.Category.Monoidal.Reasoning.html#4593" class="Bound">X</a> <a id="4607" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4609" href="Categories.Category.Monoidal.Reasoning.html#4597" class="Bound">Z</a><a id="4610" class="Symbol">}</a> <a id="4612" class="Symbol">{</a><a id="4613" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="4615" class="Symbol">:</a> <a id="4617" href="Categories.Category.Monoidal.Reasoning.html#4595" class="Bound">Y</a> <a id="4619" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4621" href="Categories.Category.Monoidal.Reasoning.html#4597" class="Bound">Z</a><a id="4622" class="Symbol">}</a> <a id="4624" class="Symbol">{</a><a id="4625" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="4627" class="Symbol">:</a> <a id="4629" href="Categories.Category.Monoidal.Reasoning.html#4593" class="Bound">X</a> <a id="4631" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4633" href="Categories.Category.Monoidal.Reasoning.html#4595" class="Bound">Y</a><a id="4634" class="Symbol">}</a> <a id="4636" class="Symbol">(</a><a id="4637" href="Categories.Category.Monoidal.Reasoning.html#4637" class="Bound">f≈gh</a> <a id="4642" class="Symbol">:</a> <a id="4644" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="4646" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4648" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="4650" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4652" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="4653" class="Symbol">)</a> <a id="4655" class="Keyword">where</a>
<a id="4664" class="Keyword">infixr</a> <a id="4671" class="Number">4</a> <a id="4673" href="Categories.Category.Monoidal.Reasoning.html#4735" class="Function Operator">split₁_⟩∘⟨_</a> <a id="4685" href="Categories.Category.Monoidal.Reasoning.html#5067" class="Function Operator">split₂_⟩∘⟨_</a>
<a id="4699" class="Keyword">infixl</a> <a id="4706" class="Number">5</a> <a id="4708" href="Categories.Category.Monoidal.Reasoning.html#5399" class="Function Operator">_⟩∘⟨split₁_</a> <a id="4720" href="Categories.Category.Monoidal.Reasoning.html#5737" class="Function Operator">_⟩∘⟨split₂_</a>
<a id="4735" href="Categories.Category.Monoidal.Reasoning.html#4735" class="Function Operator">split₁_⟩∘⟨_</a> <a id="4747" class="Symbol">:</a> <a id="4749" class="Symbol">∀</a> <a id="4751" class="Symbol">{</a><a id="4752" href="Categories.Category.Monoidal.Reasoning.html#4752" class="Bound">V</a> <a id="4754" href="Categories.Category.Monoidal.Reasoning.html#4754" class="Bound">W</a><a id="4755" class="Symbol">}</a> <a id="4757" class="Symbol">{</a><a id="4758" href="Categories.Category.Monoidal.Reasoning.html#4758" class="Bound">i</a> <a id="4760" href="Categories.Category.Monoidal.Reasoning.html#4760" class="Bound">j</a> <a id="4762" class="Symbol">:</a> <a id="4764" href="Categories.Category.Monoidal.Reasoning.html#4752" class="Bound">V</a> <a id="4766" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4768" href="Categories.Category.Monoidal.Reasoning.html#4593" class="Bound">X</a> <a id="4770" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4773" href="Categories.Category.Monoidal.Reasoning.html#4754" class="Bound">W</a><a id="4774" class="Symbol">}</a> <a id="4776" class="Symbol">→</a> <a id="4778" href="Categories.Category.Monoidal.Reasoning.html#4758" class="Bound">i</a> <a id="4780" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4782" href="Categories.Category.Monoidal.Reasoning.html#4760" class="Bound">j</a> <a id="4784" class="Symbol">→</a>
<a id="4802" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="4804" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4807" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4810" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4812" href="Categories.Category.Monoidal.Reasoning.html#4758" class="Bound">i</a> <a id="4814" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4816" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="4818" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4821" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4824" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4826" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="4828" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4831" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4834" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4836" href="Categories.Category.Monoidal.Reasoning.html#4760" class="Bound">j</a>
<a id="4840" href="Categories.Category.Monoidal.Reasoning.html#4735" class="Function Operator">split₁_⟩∘⟨_</a> <a id="4852" class="Symbol">{_}</a> <a id="4856" class="Symbol">{_}</a> <a id="4860" class="Symbol">{</a><a id="4861" href="Categories.Category.Monoidal.Reasoning.html#4861" class="Bound">i</a><a id="4862" class="Symbol">}</a> <a id="4864" class="Symbol">{</a><a id="4865" href="Categories.Category.Monoidal.Reasoning.html#4865" class="Bound">j</a><a id="4866" class="Symbol">}</a> <a id="4868" href="Categories.Category.Monoidal.Reasoning.html#4868" class="Bound">i≈j</a> <a id="4872" class="Symbol">=</a> <a id="4874" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="4884" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="4886" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4889" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4892" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4894" href="Categories.Category.Monoidal.Reasoning.html#4861" class="Bound">i</a> <a id="4911" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4914" href="Categories.Category.Monoidal.Reasoning.html#4637" class="Bound">f≈gh</a> <a id="4919" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">⟩⊗⟨refl</a> <a id="4927" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="4931" href="Categories.Category.Monoidal.Reasoning.html#4868" class="Bound">i≈j</a> <a id="4935" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="4941" class="Symbol">(</a><a id="4942" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="4944" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4946" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="4947" class="Symbol">)</a> <a id="4949" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4952" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4955" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4957" href="Categories.Category.Monoidal.Reasoning.html#4865" class="Bound">j</a> <a id="4968" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4971" href="Categories.Category.Monoidal.Reasoning.html#3188" class="Function">split₁ˡ</a> <a id="4979" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="4987" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="4993" class="Symbol">(</a><a id="4994" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="4996" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="4999" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5002" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5004" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5006" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5009" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5011" class="Symbol">)</a> <a id="5013" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5015" href="Categories.Category.Monoidal.Reasoning.html#4865" class="Bound">j</a> <a id="5020" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5023" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="5029" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5035" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5037" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5040" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5043" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5045" class="Symbol">(</a><a id="5046" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5048" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5051" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5054" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5056" href="Categories.Category.Monoidal.Reasoning.html#4865" class="Bound">j</a><a id="5057" class="Symbol">)</a> <a id="5062" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="5067" href="Categories.Category.Monoidal.Reasoning.html#5067" class="Function Operator">split₂_⟩∘⟨_</a> <a id="5079" class="Symbol">:</a> <a id="5081" class="Symbol">∀</a> <a id="5083" class="Symbol">{</a><a id="5084" href="Categories.Category.Monoidal.Reasoning.html#5084" class="Bound">V</a> <a id="5086" href="Categories.Category.Monoidal.Reasoning.html#5086" class="Bound">W</a><a id="5087" class="Symbol">}</a> <a id="5089" class="Symbol">{</a><a id="5090" href="Categories.Category.Monoidal.Reasoning.html#5090" class="Bound">i</a> <a id="5092" href="Categories.Category.Monoidal.Reasoning.html#5092" class="Bound">j</a> <a id="5094" class="Symbol">:</a> <a id="5096" href="Categories.Category.Monoidal.Reasoning.html#5084" class="Bound">V</a> <a id="5098" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5100" href="Categories.Category.Monoidal.Reasoning.html#5086" class="Bound">W</a> <a id="5102" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5105" href="Categories.Category.Monoidal.Reasoning.html#4593" class="Bound">X</a><a id="5106" class="Symbol">}</a> <a id="5108" class="Symbol">→</a> <a id="5110" href="Categories.Category.Monoidal.Reasoning.html#5090" class="Bound">i</a> <a id="5112" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5114" href="Categories.Category.Monoidal.Reasoning.html#5092" class="Bound">j</a> <a id="5116" class="Symbol">→</a>
<a id="5134" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5137" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5140" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5142" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5144" href="Categories.Category.Monoidal.Reasoning.html#5090" class="Bound">i</a> <a id="5146" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5148" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5151" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5154" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5156" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5158" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5161" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5164" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5166" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5168" href="Categories.Category.Monoidal.Reasoning.html#5092" class="Bound">j</a>
<a id="5172" href="Categories.Category.Monoidal.Reasoning.html#5067" class="Function Operator">split₂_⟩∘⟨_</a> <a id="5184" class="Symbol">{_}</a> <a id="5188" class="Symbol">{_}</a> <a id="5192" class="Symbol">{</a><a id="5193" href="Categories.Category.Monoidal.Reasoning.html#5193" class="Bound">i</a><a id="5194" class="Symbol">}</a> <a id="5196" class="Symbol">{</a><a id="5197" href="Categories.Category.Monoidal.Reasoning.html#5197" class="Bound">j</a><a id="5198" class="Symbol">}</a> <a id="5200" href="Categories.Category.Monoidal.Reasoning.html#5200" class="Bound">i≈j</a> <a id="5204" class="Symbol">=</a> <a id="5206" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="5216" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5219" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5222" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5224" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5226" href="Categories.Category.Monoidal.Reasoning.html#5193" class="Bound">i</a> <a id="5243" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5246" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨</a> <a id="5254" href="Categories.Category.Monoidal.Reasoning.html#4637" class="Bound">f≈gh</a> <a id="5259" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="5263" href="Categories.Category.Monoidal.Reasoning.html#5200" class="Bound">i≈j</a> <a id="5267" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5273" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5276" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5279" class="Symbol">(</a><a id="5280" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5282" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5284" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="5285" class="Symbol">)</a> <a id="5287" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5289" href="Categories.Category.Monoidal.Reasoning.html#5197" class="Bound">j</a> <a id="5300" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5303" href="Categories.Category.Monoidal.Reasoning.html#3955" class="Function">split₂ˡ</a> <a id="5311" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="5319" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5325" class="Symbol">(</a><a id="5326" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5329" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5332" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5334" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5336" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5339" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5342" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="5343" class="Symbol">)</a> <a id="5345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5347" href="Categories.Category.Monoidal.Reasoning.html#5197" class="Bound">j</a> <a id="5352" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5355" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="5361" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5367" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5370" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5373" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5375" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5377" class="Symbol">(</a><a id="5378" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5381" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5384" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5386" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5388" href="Categories.Category.Monoidal.Reasoning.html#5197" class="Bound">j</a><a id="5389" class="Symbol">)</a> <a id="5394" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="5399" href="Categories.Category.Monoidal.Reasoning.html#5399" class="Function Operator">_⟩∘⟨split₁_</a> <a id="5411" class="Symbol">:</a> <a id="5413" class="Symbol">∀</a> <a id="5415" class="Symbol">{</a><a id="5416" href="Categories.Category.Monoidal.Reasoning.html#5416" class="Bound">V</a> <a id="5418" href="Categories.Category.Monoidal.Reasoning.html#5418" class="Bound">W</a><a id="5419" class="Symbol">}</a> <a id="5421" class="Symbol">{</a><a id="5422" href="Categories.Category.Monoidal.Reasoning.html#5422" class="Bound">i</a> <a id="5424" href="Categories.Category.Monoidal.Reasoning.html#5424" class="Bound">j</a> <a id="5426" class="Symbol">:</a> <a id="5428" href="Categories.Category.Monoidal.Reasoning.html#4597" class="Bound">Z</a> <a id="5430" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5433" href="Categories.Category.Monoidal.Reasoning.html#5418" class="Bound">W</a> <a id="5435" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5437" href="Categories.Category.Monoidal.Reasoning.html#5416" class="Bound">V</a><a id="5438" class="Symbol">}</a> <a id="5440" class="Symbol">→</a> <a id="5442" href="Categories.Category.Monoidal.Reasoning.html#5422" class="Bound">i</a> <a id="5444" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5446" href="Categories.Category.Monoidal.Reasoning.html#5424" class="Bound">j</a> <a id="5448" class="Symbol">→</a>
<a id="5466" href="Categories.Category.Monoidal.Reasoning.html#5422" class="Bound">i</a> <a id="5468" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5470" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5472" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5475" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5478" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5480" class="Symbol">(</a><a id="5481" href="Categories.Category.Monoidal.Reasoning.html#5424" class="Bound">j</a> <a id="5483" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5485" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5487" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5490" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5492" class="Symbol">)</a> <a id="5494" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5496" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5498" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5501" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="5506" href="Categories.Category.Monoidal.Reasoning.html#5399" class="Function Operator">_⟩∘⟨split₁_</a> <a id="5518" class="Symbol">{_}</a> <a id="5522" class="Symbol">{_}</a> <a id="5526" class="Symbol">{</a><a id="5527" href="Categories.Category.Monoidal.Reasoning.html#5527" class="Bound">i</a><a id="5528" class="Symbol">}</a> <a id="5530" class="Symbol">{</a><a id="5531" href="Categories.Category.Monoidal.Reasoning.html#5531" class="Bound">j</a><a id="5532" class="Symbol">}</a> <a id="5534" href="Categories.Category.Monoidal.Reasoning.html#5534" class="Bound">i≈j</a> <a id="5538" class="Symbol">=</a> <a id="5540" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="5550" href="Categories.Category.Monoidal.Reasoning.html#5527" class="Bound">i</a> <a id="5552" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5554" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5556" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5559" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5577" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5580" href="Categories.Category.Monoidal.Reasoning.html#5534" class="Bound">i≈j</a> <a id="5584" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="5588" href="Categories.Category.Monoidal.Reasoning.html#4637" class="Bound">f≈gh</a> <a id="5593" href="Categories.Category.Monoidal.Reasoning.html#911" class="Function Operator">⟩⊗⟨refl</a> <a id="5601" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5607" href="Categories.Category.Monoidal.Reasoning.html#5531" class="Bound">j</a> <a id="5609" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5611" class="Symbol">(</a><a id="5612" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5614" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5616" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="5617" class="Symbol">)</a> <a id="5619" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5622" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5634" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5637" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5645" href="Categories.Category.Monoidal.Reasoning.html#3188" class="Function">split₁ˡ</a> <a id="5653" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5659" href="Categories.Category.Monoidal.Reasoning.html#5531" class="Bound">j</a> <a id="5661" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5663" class="Symbol">(</a><a id="5664" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5666" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5669" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5672" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5674" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5676" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5679" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5681" class="Symbol">)</a> <a id="5686" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5689" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a> <a id="5699" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5705" class="Symbol">(</a><a id="5706" href="Categories.Category.Monoidal.Reasoning.html#5531" class="Bound">j</a> <a id="5708" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5710" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5712" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5715" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5717" class="Symbol">)</a> <a id="5719" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5721" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="5723" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5726" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5732" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="5737" href="Categories.Category.Monoidal.Reasoning.html#5737" class="Function Operator">_⟩∘⟨split₂_</a> <a id="5749" class="Symbol">:</a> <a id="5751" class="Symbol">∀</a> <a id="5753" class="Symbol">{</a><a id="5754" href="Categories.Category.Monoidal.Reasoning.html#5754" class="Bound">V</a> <a id="5756" href="Categories.Category.Monoidal.Reasoning.html#5756" class="Bound">W</a><a id="5757" class="Symbol">}</a> <a id="5759" class="Symbol">{</a><a id="5760" href="Categories.Category.Monoidal.Reasoning.html#5760" class="Bound">i</a> <a id="5762" href="Categories.Category.Monoidal.Reasoning.html#5762" class="Bound">j</a> <a id="5764" class="Symbol">:</a> <a id="5766" href="Categories.Category.Monoidal.Reasoning.html#5756" class="Bound">W</a> <a id="5768" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5771" href="Categories.Category.Monoidal.Reasoning.html#4597" class="Bound">Z</a> <a id="5773" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5775" href="Categories.Category.Monoidal.Reasoning.html#5754" class="Bound">V</a><a id="5776" class="Symbol">}</a> <a id="5778" class="Symbol">→</a> <a id="5780" href="Categories.Category.Monoidal.Reasoning.html#5760" class="Bound">i</a> <a id="5782" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5784" href="Categories.Category.Monoidal.Reasoning.html#5762" class="Bound">j</a> <a id="5786" class="Symbol">→</a>
<a id="5804" href="Categories.Category.Monoidal.Reasoning.html#5760" class="Bound">i</a> <a id="5806" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5808" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5811" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5814" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5816" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5818" class="Symbol">(</a><a id="5819" href="Categories.Category.Monoidal.Reasoning.html#5762" class="Bound">j</a> <a id="5821" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5823" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5826" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5829" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a><a id="5830" class="Symbol">)</a> <a id="5832" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5834" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5837" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5840" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a>
<a id="5844" href="Categories.Category.Monoidal.Reasoning.html#5737" class="Function Operator">_⟩∘⟨split₂_</a> <a id="5856" class="Symbol">{_}</a> <a id="5860" class="Symbol">{_}</a> <a id="5864" class="Symbol">{</a><a id="5865" href="Categories.Category.Monoidal.Reasoning.html#5865" class="Bound">i</a><a id="5866" class="Symbol">}</a> <a id="5868" class="Symbol">{</a><a id="5869" href="Categories.Category.Monoidal.Reasoning.html#5869" class="Bound">j</a><a id="5870" class="Symbol">}</a> <a id="5872" href="Categories.Category.Monoidal.Reasoning.html#5872" class="Bound">i≈j</a> <a id="5876" class="Symbol">=</a> <a id="5878" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
<a id="5888" href="Categories.Category.Monoidal.Reasoning.html#5865" class="Bound">i</a> <a id="5890" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5892" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5895" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5898" href="Categories.Category.Monoidal.Reasoning.html#4601" class="Bound">f</a> <a id="5915" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5918" href="Categories.Category.Monoidal.Reasoning.html#5872" class="Bound">i≈j</a> <a id="5922" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="5926" href="Categories.Category.Monoidal.Reasoning.html#850" class="Function Operator">refl⟩⊗⟨</a> <a id="5934" href="Categories.Category.Monoidal.Reasoning.html#4637" class="Bound">f≈gh</a> <a id="5939" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5945" href="Categories.Category.Monoidal.Reasoning.html#5869" class="Bound">j</a> <a id="5947" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5949" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5952" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5955" class="Symbol">(</a><a id="5956" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="5958" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5960" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="5961" class="Symbol">)</a> <a id="5972" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5975" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5983" href="Categories.Category.Monoidal.Reasoning.html#3955" class="Function">split₂ˡ</a> <a id="5991" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="5997" href="Categories.Category.Monoidal.Reasoning.html#5869" class="Bound">j</a> <a id="5999" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6001" class="Symbol">(</a><a id="6002" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6005" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6008" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a> <a id="6010" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6012" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6015" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6018" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a><a id="6019" class="Symbol">)</a> <a id="6024" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6027" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a> <a id="6037" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="6043" class="Symbol">(</a><a id="6044" href="Categories.Category.Monoidal.Reasoning.html#5869" class="Bound">j</a> <a id="6046" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6048" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6051" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6054" href="Categories.Category.Monoidal.Reasoning.html#4613" class="Bound">g</a><a id="6055" class="Symbol">)</a> <a id="6057" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6059" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6062" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6065" href="Categories.Category.Monoidal.Reasoning.html#4625" class="Bound">h</a> <a id="6070" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
<a id="6073" class="Comment">-- Combined merging and re-association.</a>
<a id="6114" class="Keyword">module</a> <a id="6121" href="Categories.Category.Monoidal.Reasoning.html#6121" class="Module">_</a> <a id="6123" class="Symbol">{</a><a id="6124" href="Categories.Category.Monoidal.Reasoning.html#6124" class="Bound">X</a> <a id="6126" href="Categories.Category.Monoidal.Reasoning.html#6126" class="Bound">Y</a> <a id="6128" href="Categories.Category.Monoidal.Reasoning.html#6128" class="Bound">Z</a><a id="6129" class="Symbol">}</a> <a id="6131" class="Symbol">{</a><a id="6132" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a> <a id="6134" class="Symbol">:</a> <a id="6136" href="Categories.Category.Monoidal.Reasoning.html#6126" class="Bound">Y</a> <a id="6138" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6140" href="Categories.Category.Monoidal.Reasoning.html#6128" class="Bound">Z</a><a id="6141" class="Symbol">}</a> <a id="6143" class="Symbol">{</a><a id="6144" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6146" class="Symbol">:</a> <a id="6148" href="Categories.Category.Monoidal.Reasoning.html#6124" class="Bound">X</a> <a id="6150" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6152" href="Categories.Category.Monoidal.Reasoning.html#6126" class="Bound">Y</a><a id="6153" class="Symbol">}</a> <a id="6155" class="Symbol">{</a><a id="6156" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a> <a id="6158" class="Symbol">:</a> <a id="6160" href="Categories.Category.Monoidal.Reasoning.html#6124" class="Bound">X</a> <a id="6162" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6164" href="Categories.Category.Monoidal.Reasoning.html#6128" class="Bound">Z</a><a id="6165" class="Symbol">}</a> <a id="6167" class="Symbol">(</a><a id="6168" href="Categories.Category.Monoidal.Reasoning.html#6168" class="Bound">fg≈h</a> <a id="6173" class="Symbol">:</a> <a id="6175" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a> <a id="6177" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6179" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6181" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6183" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a><a id="6184" class="Symbol">)</a> <a id="6186" class="Keyword">where</a>
<a id="6195" class="Keyword">infixr</a> <a id="6202" class="Number">4</a> <a id="6204" href="Categories.Category.Monoidal.Reasoning.html#6266" class="Function Operator">merge₁_⟩∘⟨_</a> <a id="6216" href="Categories.Category.Monoidal.Reasoning.html#6420" class="Function Operator">merge₂_⟩∘⟨_</a>
<a id="6230" class="Keyword">infixl</a> <a id="6237" class="Number">5</a> <a id="6239" href="Categories.Category.Monoidal.Reasoning.html#6574" class="Function Operator">_⟩∘⟨merge₁_</a> <a id="6251" href="Categories.Category.Monoidal.Reasoning.html#6729" class="Function Operator">_⟩∘⟨merge₂_</a>
<a id="6266" href="Categories.Category.Monoidal.Reasoning.html#6266" class="Function Operator">merge₁_⟩∘⟨_</a> <a id="6278" class="Symbol">:</a> <a id="6280" class="Symbol">∀</a> <a id="6282" class="Symbol">{</a><a id="6283" href="Categories.Category.Monoidal.Reasoning.html#6283" class="Bound">V</a> <a id="6285" href="Categories.Category.Monoidal.Reasoning.html#6285" class="Bound">W</a><a id="6286" class="Symbol">}</a> <a id="6288" class="Symbol">{</a><a id="6289" href="Categories.Category.Monoidal.Reasoning.html#6289" class="Bound">i</a> <a id="6291" href="Categories.Category.Monoidal.Reasoning.html#6291" class="Bound">j</a> <a id="6293" class="Symbol">:</a> <a id="6295" href="Categories.Category.Monoidal.Reasoning.html#6283" class="Bound">V</a> <a id="6297" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6299" href="Categories.Category.Monoidal.Reasoning.html#6124" class="Bound">X</a> <a id="6301" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6304" href="Categories.Category.Monoidal.Reasoning.html#6285" class="Bound">W</a><a id="6305" class="Symbol">}</a> <a id="6307" class="Symbol">→</a> <a id="6309" href="Categories.Category.Monoidal.Reasoning.html#6289" class="Bound">i</a> <a id="6311" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6313" href="Categories.Category.Monoidal.Reasoning.html#6291" class="Bound">j</a> <a id="6315" class="Symbol">→</a>
<a id="6333" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a> <a id="6335" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6338" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6341" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6343" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6345" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6348" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6351" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6353" href="Categories.Category.Monoidal.Reasoning.html#6289" class="Bound">i</a> <a id="6355" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6357" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a> <a id="6359" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6362" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6365" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6367" href="Categories.Category.Monoidal.Reasoning.html#6291" class="Bound">j</a>
<a id="6371" href="Categories.Category.Monoidal.Reasoning.html#6266" class="Function Operator">merge₁_⟩∘⟨_</a> <a id="6383" href="Categories.Category.Monoidal.Reasoning.html#6383" class="Bound">i≈j</a> <a id="6387" class="Symbol">=</a> <a id="6389" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6391" class="Symbol">(</a><a id="6392" href="Categories.Category.Monoidal.Reasoning.html#4735" class="Function Operator">split₁</a> <a id="6399" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6401" href="Categories.Category.Monoidal.Reasoning.html#6168" class="Bound">fg≈h</a> <a id="6406" href="Categories.Category.Monoidal.Reasoning.html#4735" class="Function Operator">⟩∘⟨</a> <a id="6410" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6412" href="Categories.Category.Monoidal.Reasoning.html#6383" class="Bound">i≈j</a><a id="6415" class="Symbol">)</a>
<a id="6420" href="Categories.Category.Monoidal.Reasoning.html#6420" class="Function Operator">merge₂_⟩∘⟨_</a> <a id="6432" class="Symbol">:</a> <a id="6434" class="Symbol">∀</a> <a id="6436" class="Symbol">{</a><a id="6437" href="Categories.Category.Monoidal.Reasoning.html#6437" class="Bound">V</a> <a id="6439" href="Categories.Category.Monoidal.Reasoning.html#6439" class="Bound">W</a><a id="6440" class="Symbol">}</a> <a id="6442" class="Symbol">{</a><a id="6443" href="Categories.Category.Monoidal.Reasoning.html#6443" class="Bound">i</a> <a id="6445" href="Categories.Category.Monoidal.Reasoning.html#6445" class="Bound">j</a> <a id="6447" class="Symbol">:</a> <a id="6449" href="Categories.Category.Monoidal.Reasoning.html#6437" class="Bound">V</a> <a id="6451" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6453" href="Categories.Category.Monoidal.Reasoning.html#6439" class="Bound">W</a> <a id="6455" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6458" href="Categories.Category.Monoidal.Reasoning.html#6124" class="Bound">X</a><a id="6459" class="Symbol">}</a> <a id="6461" class="Symbol">→</a> <a id="6463" href="Categories.Category.Monoidal.Reasoning.html#6443" class="Bound">i</a> <a id="6465" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6467" href="Categories.Category.Monoidal.Reasoning.html#6445" class="Bound">j</a> <a id="6469" class="Symbol">→</a>
<a id="6487" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6490" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6493" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a> <a id="6495" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6497" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6500" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6503" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6505" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6507" href="Categories.Category.Monoidal.Reasoning.html#6443" class="Bound">i</a> <a id="6509" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6511" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6514" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6517" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a> <a id="6519" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6521" href="Categories.Category.Monoidal.Reasoning.html#6445" class="Bound">j</a>
<a id="6525" href="Categories.Category.Monoidal.Reasoning.html#6420" class="Function Operator">merge₂_⟩∘⟨_</a> <a id="6537" href="Categories.Category.Monoidal.Reasoning.html#6537" class="Bound">i≈j</a> <a id="6541" class="Symbol">=</a> <a id="6543" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6545" class="Symbol">(</a><a id="6546" href="Categories.Category.Monoidal.Reasoning.html#5067" class="Function Operator">split₂</a> <a id="6553" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6555" href="Categories.Category.Monoidal.Reasoning.html#6168" class="Bound">fg≈h</a> <a id="6560" href="Categories.Category.Monoidal.Reasoning.html#5067" class="Function Operator">⟩∘⟨</a> <a id="6564" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6566" href="Categories.Category.Monoidal.Reasoning.html#6537" class="Bound">i≈j</a><a id="6569" class="Symbol">)</a>
<a id="6574" href="Categories.Category.Monoidal.Reasoning.html#6574" class="Function Operator">_⟩∘⟨merge₁_</a> <a id="6586" class="Symbol">:</a> <a id="6588" class="Symbol">∀</a> <a id="6590" class="Symbol">{</a><a id="6591" href="Categories.Category.Monoidal.Reasoning.html#6591" class="Bound">V</a> <a id="6593" href="Categories.Category.Monoidal.Reasoning.html#6593" class="Bound">W</a><a id="6594" class="Symbol">}</a> <a id="6596" class="Symbol">{</a><a id="6597" href="Categories.Category.Monoidal.Reasoning.html#6597" class="Bound">i</a> <a id="6599" href="Categories.Category.Monoidal.Reasoning.html#6599" class="Bound">j</a> <a id="6601" class="Symbol">:</a> <a id="6603" href="Categories.Category.Monoidal.Reasoning.html#6128" class="Bound">Z</a> <a id="6605" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6608" href="Categories.Category.Monoidal.Reasoning.html#6593" class="Bound">W</a> <a id="6610" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6612" href="Categories.Category.Monoidal.Reasoning.html#6591" class="Bound">V</a><a id="6613" class="Symbol">}</a> <a id="6615" class="Symbol">→</a> <a id="6617" href="Categories.Category.Monoidal.Reasoning.html#6597" class="Bound">i</a> <a id="6619" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6621" href="Categories.Category.Monoidal.Reasoning.html#6599" class="Bound">j</a> <a id="6623" class="Symbol">→</a>
<a id="6641" class="Symbol">(</a><a id="6642" href="Categories.Category.Monoidal.Reasoning.html#6597" class="Bound">i</a> <a id="6644" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6646" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a> <a id="6648" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6651" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6653" class="Symbol">)</a> <a id="6655" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6657" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6659" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6662" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6665" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6667" href="Categories.Category.Monoidal.Reasoning.html#6599" class="Bound">j</a> <a id="6669" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6671" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a> <a id="6673" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6676" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="6681" href="Categories.Category.Monoidal.Reasoning.html#6574" class="Function Operator">_⟩∘⟨merge₁_</a> <a id="6693" href="Categories.Category.Monoidal.Reasoning.html#6693" class="Bound">i≈j</a> <a id="6697" class="Symbol">=</a> <a id="6699" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6701" class="Symbol">(</a><a id="6702" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6704" href="Categories.Category.Monoidal.Reasoning.html#6168" class="Bound">fg≈h</a> <a id="6709" href="Categories.Category.Monoidal.Reasoning.html#5399" class="Function Operator">⟩∘⟨split₁</a> <a id="6719" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6721" href="Categories.Category.Monoidal.Reasoning.html#6693" class="Bound">i≈j</a><a id="6724" class="Symbol">)</a>
<a id="6729" href="Categories.Category.Monoidal.Reasoning.html#6729" class="Function Operator">_⟩∘⟨merge₂_</a> <a id="6741" class="Symbol">:</a> <a id="6743" class="Symbol">∀</a> <a id="6745" class="Symbol">{</a><a id="6746" href="Categories.Category.Monoidal.Reasoning.html#6746" class="Bound">V</a> <a id="6748" href="Categories.Category.Monoidal.Reasoning.html#6748" class="Bound">W</a><a id="6749" class="Symbol">}</a> <a id="6751" class="Symbol">{</a><a id="6752" href="Categories.Category.Monoidal.Reasoning.html#6752" class="Bound">i</a> <a id="6754" href="Categories.Category.Monoidal.Reasoning.html#6754" class="Bound">j</a> <a id="6756" class="Symbol">:</a> <a id="6758" href="Categories.Category.Monoidal.Reasoning.html#6748" class="Bound">W</a> <a id="6760" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6763" href="Categories.Category.Monoidal.Reasoning.html#6128" class="Bound">Z</a> <a id="6765" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6767" href="Categories.Category.Monoidal.Reasoning.html#6746" class="Bound">V</a><a id="6768" class="Symbol">}</a> <a id="6770" class="Symbol">→</a> <a id="6772" href="Categories.Category.Monoidal.Reasoning.html#6752" class="Bound">i</a> <a id="6774" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6776" href="Categories.Category.Monoidal.Reasoning.html#6754" class="Bound">j</a> <a id="6778" class="Symbol">→</a>
<a id="6796" class="Symbol">(</a><a id="6797" href="Categories.Category.Monoidal.Reasoning.html#6752" class="Bound">i</a> <a id="6799" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6801" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6804" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6807" href="Categories.Category.Monoidal.Reasoning.html#6132" class="Bound">f</a><a id="6808" class="Symbol">)</a> <a id="6810" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6812" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6815" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6818" href="Categories.Category.Monoidal.Reasoning.html#6144" class="Bound">g</a> <a id="6820" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6822" href="Categories.Category.Monoidal.Reasoning.html#6754" class="Bound">j</a> <a id="6824" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6826" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6829" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="6832" href="Categories.Category.Monoidal.Reasoning.html#6156" class="Bound">h</a>
<a id="6836" href="Categories.Category.Monoidal.Reasoning.html#6729" class="Function Operator">_⟩∘⟨merge₂_</a> <a id="6848" href="Categories.Category.Monoidal.Reasoning.html#6848" class="Bound">i≈j</a> <a id="6852" class="Symbol">=</a> <a id="6854" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6856" class="Symbol">(</a><a id="6857" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6859" href="Categories.Category.Monoidal.Reasoning.html#6168" class="Bound">fg≈h</a> <a id="6864" href="Categories.Category.Monoidal.Reasoning.html#5737" class="Function Operator">⟩∘⟨split₂</a> <a id="6874" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6876" href="Categories.Category.Monoidal.Reasoning.html#6848" class="Bound">i≈j</a><a id="6879" class="Symbol">)</a>
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