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<html><head><meta charset="utf-8"><title>Categories.Object.Product.Morphisms</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="36" class="Comment">-- Various operations and proofs on morphisms between products</a>
<a id="100" class="Comment">-- Perhaps a bit of overkill? There is so much here that it&#39;s impossible to remember</a>
<a id="185" class="Comment">-- it all</a>
<a id="195" class="Keyword">open</a> <a id="200" class="Keyword">import</a> <a id="207" href="Categories.Category.html" class="Module">Categories.Category</a>
<a id="228" class="Keyword">module</a> <a id="235" href="Categories.Object.Product.Morphisms.html" class="Module">Categories.Object.Product.Morphisms</a> <a id="271" class="Symbol">{</a><a id="272" href="Categories.Object.Product.Morphisms.html#272" class="Bound">o</a> <a id="274" href="Categories.Object.Product.Morphisms.html#274" class="Bound">ℓ</a> <a id="276" href="Categories.Object.Product.Morphisms.html#276" class="Bound">e</a><a id="277" class="Symbol">}</a> <a id="279" class="Symbol">(</a><a id="280" href="Categories.Object.Product.Morphisms.html#280" class="Bound">𝒞</a> <a id="282" class="Symbol">:</a> <a id="284" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="293" href="Categories.Object.Product.Morphisms.html#272" class="Bound">o</a> <a id="295" href="Categories.Object.Product.Morphisms.html#274" class="Bound">ℓ</a> <a id="297" href="Categories.Object.Product.Morphisms.html#276" class="Bound">e</a><a id="298" class="Symbol">)</a> <a id="300" class="Keyword">where</a>
<a id="307" class="Keyword">open</a> <a id="312" class="Keyword">import</a> <a id="319" href="Function.html" class="Module">Function</a> <a id="328" class="Keyword">using</a> <a id="334" class="Symbol">(</a><a id="335" href="Function.Base.html#1563" class="Function">flip</a><a id="339" class="Symbol">)</a>
<a id="341" class="Keyword">open</a> <a id="346" class="Keyword">import</a> <a id="353" href="Level.html" class="Module">Level</a>
<a id="360" class="Keyword">open</a> <a id="365" class="Keyword">import</a> <a id="372" href="Categories.Object.Product.Core.html" class="Module">Categories.Object.Product.Core</a> <a id="403" href="Categories.Object.Product.Morphisms.html#280" class="Bound">𝒞</a>
<a id="406" class="Keyword">open</a> <a id="411" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="420" href="Categories.Object.Product.Morphisms.html#280" class="Bound">𝒞</a>
<a id="422" class="Keyword">open</a> <a id="427" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
<a id="441" class="Keyword">private</a>
<a id="451" class="Keyword">variable</a>
<a id="464" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="466" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="468" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="470" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a> <a id="472" href="Categories.Object.Product.Morphisms.html#472" class="Generalizable">E</a> <a id="474" href="Categories.Object.Product.Morphisms.html#474" class="Generalizable">F</a> <a id="476" class="Symbol">:</a> <a id="478" href="Categories.Category.Core.html#559" class="Field">Obj</a>
<a id="486" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="488" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="491" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="493" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="496" href="Categories.Object.Product.Morphisms.html#496" class="Generalizable">h</a> <a id="498" href="Categories.Object.Product.Morphisms.html#498" class="Generalizable">i</a> <a id="500" class="Symbol">:</a> <a id="502" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="504" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="506" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a>
<a id="509" class="Keyword">infix</a> <a id="515" class="Number">10</a> <a id="518" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[_]⟨_,_⟩</a> <a id="527" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[_⇒_]_×_</a>
<a id="536" class="Keyword">infix</a> <a id="542" class="Number">12</a> <a id="545" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[_]]</a> <a id="551" href="Categories.Object.Product.Morphisms.html#714" class="Function Operator">[_]π₁</a> <a id="557" href="Categories.Object.Product.Morphisms.html#776" class="Function Operator">[_]π₂</a>
<a id="[[_]]"></a><a id="564" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[_]]</a> <a id="570" class="Symbol">:</a> <a id="572" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="580" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="582" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="584" class="Symbol">→</a> <a id="586" href="Categories.Category.Core.html#559" class="Field">Obj</a>
<a id="590" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="593" href="Categories.Object.Product.Morphisms.html#593" class="Bound">p</a> <a id="595" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="598" class="Symbol">=</a> <a id="600" href="Categories.Object.Product.Core.html#510" class="Field">Product.A×B</a> <a id="612" href="Categories.Object.Product.Morphisms.html#593" class="Bound">p</a>
<a id="[_]⟨_,_⟩"></a><a id="615" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[_]⟨_,_⟩</a> <a id="624" class="Symbol">:</a> <a id="626" class="Symbol">∀</a> <a id="628" class="Symbol">(</a><a id="629" href="Categories.Object.Product.Morphisms.html#629" class="Bound">p</a> <a id="631" class="Symbol">:</a> <a id="633" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="641" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="643" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="644" class="Symbol">)</a> <a id="646" class="Symbol">→</a> <a id="648" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="650" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="652" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="654" class="Symbol">→</a> <a id="656" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="658" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="660" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="662" class="Symbol">→</a> <a id="664" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="666" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="668" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="671" href="Categories.Object.Product.Morphisms.html#629" class="Bound">p</a> <a id="673" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a>
<a id="676" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="678" href="Categories.Object.Product.Morphisms.html#678" class="Bound">p</a> <a id="680" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="683" href="Categories.Object.Product.Morphisms.html#683" class="Bound">f</a> <a id="685" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="687" href="Categories.Object.Product.Morphisms.html#687" class="Bound">g</a> <a id="689" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="691" class="Symbol">=</a> <a id="693" href="Categories.Object.Product.Core.html#566" class="Field Operator">Product.⟨_,_⟩</a> <a id="707" href="Categories.Object.Product.Morphisms.html#678" class="Bound">p</a> <a id="709" href="Categories.Object.Product.Morphisms.html#683" class="Bound">f</a> <a id="711" href="Categories.Object.Product.Morphisms.html#687" class="Bound">g</a>
<a id="[_]π₁"></a><a id="714" href="Categories.Object.Product.Morphisms.html#714" class="Function Operator">[_]π₁</a> <a id="720" class="Symbol">:</a> <a id="722" class="Symbol">∀</a> <a id="724" class="Symbol">(</a><a id="725" href="Categories.Object.Product.Morphisms.html#725" class="Bound">p</a> <a id="727" class="Symbol">:</a> <a id="729" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="737" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="739" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="740" class="Symbol">)</a> <a id="742" class="Symbol">→</a> <a id="744" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="747" href="Categories.Object.Product.Morphisms.html#725" class="Bound">p</a> <a id="749" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="752" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="754" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a>
<a id="756" href="Categories.Object.Product.Morphisms.html#714" class="Function Operator">[_]π₁</a> <a id="762" class="Symbol">=</a> <a id="764" href="Categories.Object.Product.Core.html#526" class="Field">Product.π₁</a>
<a id="[_]π₂"></a><a id="776" href="Categories.Object.Product.Morphisms.html#776" class="Function Operator">[_]π₂</a> <a id="782" class="Symbol">:</a> <a id="784" class="Symbol">∀</a> <a id="786" class="Symbol">(</a><a id="787" href="Categories.Object.Product.Morphisms.html#787" class="Bound">p</a> <a id="789" class="Symbol">:</a> <a id="791" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="799" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="801" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="802" class="Symbol">)</a> <a id="804" class="Symbol">→</a> <a id="806" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="809" href="Categories.Object.Product.Morphisms.html#787" class="Bound">p</a> <a id="811" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="814" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="816" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a>
<a id="818" href="Categories.Object.Product.Morphisms.html#776" class="Function Operator">[_]π₂</a> <a id="824" class="Symbol">=</a> <a id="826" href="Categories.Object.Product.Core.html#546" class="Field">Product.π₂</a>
<a id="[_⇒_]_×_"></a><a id="838" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[_⇒_]_×_</a> <a id="847" class="Symbol">:</a> <a id="849" class="Symbol">∀</a> <a id="851" class="Symbol">(</a><a id="852" href="Categories.Object.Product.Morphisms.html#852" class="Bound">p₁</a> <a id="855" class="Symbol">:</a> <a id="857" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="865" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="867" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="868" class="Symbol">)</a> <a id="870" class="Symbol">(</a><a id="871" href="Categories.Object.Product.Morphisms.html#871" class="Bound">p₂</a> <a id="874" class="Symbol">:</a> <a id="876" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="884" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="886" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="887" class="Symbol">)</a> <a id="889" class="Symbol">→</a>
<a id="904" class="Symbol">(</a><a id="905" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="907" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="909" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="910" class="Symbol">)</a> <a id="912" class="Symbol">→</a> <a id="914" class="Symbol">(</a><a id="915" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="917" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="919" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="920" class="Symbol">)</a> <a id="922" class="Symbol">→</a> <a id="924" class="Symbol">(</a><a id="925" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="928" href="Categories.Object.Product.Morphisms.html#852" class="Bound">p₁</a> <a id="931" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="934" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="936" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="939" href="Categories.Object.Product.Morphisms.html#871" class="Bound">p₂</a> <a id="942" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a><a id="944" class="Symbol">)</a>
<a id="946" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="948" href="Categories.Object.Product.Morphisms.html#948" class="Bound">p₁</a> <a id="951" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="953" href="Categories.Object.Product.Morphisms.html#953" class="Bound">p₂</a> <a id="956" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="958" href="Categories.Object.Product.Morphisms.html#958" class="Bound">f</a> <a id="960" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="962" href="Categories.Object.Product.Morphisms.html#962" class="Bound">g</a> <a id="965" class="Symbol">=</a> <a id="967" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="969" href="Categories.Object.Product.Morphisms.html#953" class="Bound">p₂</a> <a id="972" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="975" href="Categories.Object.Product.Morphisms.html#958" class="Bound">f</a> <a id="977" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="979" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a> <a id="985" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="987" href="Categories.Object.Product.Morphisms.html#962" class="Bound">g</a> <a id="989" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="991" href="Categories.Object.Product.Core.html#546" class="Function">p₁.π₂</a> <a id="997" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a>
<a id="1001" class="Keyword">where</a> <a id="1007" class="Keyword">module</a> <a id="1014" href="Categories.Object.Product.Morphisms.html#1014" class="Module">p₁</a> <a id="1017" class="Symbol">=</a> <a id="1019" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="1027" href="Categories.Object.Product.Morphisms.html#948" class="Bound">p₁</a>
<a id="1038" class="Keyword">module</a> <a id="1045" href="Categories.Object.Product.Morphisms.html#1045" class="Module">p₂</a> <a id="1048" class="Symbol">=</a> <a id="1050" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="1058" href="Categories.Object.Product.Morphisms.html#953" class="Bound">p₂</a>
<a id="id×id"></a><a id="1062" href="Categories.Object.Product.Morphisms.html#1062" class="Function">id×id</a> <a id="1068" class="Symbol">:</a> <a id="1070" class="Symbol">∀</a> <a id="1072" class="Symbol">(</a><a id="1073" href="Categories.Object.Product.Morphisms.html#1073" class="Bound">p</a> <a id="1075" class="Symbol">:</a> <a id="1077" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1085" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="1087" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="1088" class="Symbol">)</a> <a id="1090" class="Symbol">→</a> <a id="1092" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1094" href="Categories.Object.Product.Morphisms.html#1073" class="Bound">p</a> <a id="1096" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1098" href="Categories.Object.Product.Morphisms.html#1073" class="Bound">p</a> <a id="1100" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1102" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1105" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1107" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1110" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1112" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="1115" href="Categories.Object.Product.Morphisms.html#1062" class="Function">id×id</a> <a id="1121" href="Categories.Object.Product.Morphisms.html#1121" class="Bound">p</a> <a id="1123" class="Symbol">=</a> <a id="1125" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="1133" href="Categories.Object.Product.Core.html#566" class="Field Operator">⟨</a> <a id="1135" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1138" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1140" href="Categories.Object.Product.Core.html#526" class="Field">π₁</a> <a id="1143" href="Categories.Object.Product.Core.html#566" class="Field Operator">,</a> <a id="1145" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1148" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1150" href="Categories.Object.Product.Core.html#546" class="Field">π₂</a> <a id="1153" href="Categories.Object.Product.Core.html#566" class="Field Operator">⟩</a> <a id="1155" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1158" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="1167" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1177" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1187" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1191" href="Categories.Object.Product.Core.html#566" class="Field Operator">⟨</a> <a id="1193" href="Categories.Object.Product.Core.html#526" class="Field">π₁</a> <a id="1196" href="Categories.Object.Product.Core.html#566" class="Field Operator">,</a> <a id="1198" href="Categories.Object.Product.Core.html#546" class="Field">π₂</a> <a id="1201" href="Categories.Object.Product.Core.html#566" class="Field Operator">⟩</a> <a id="1213" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1216" href="Categories.Object.Product.Core.html#797" class="Function">η</a> <a id="1218" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1222" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1244" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="1248" class="Keyword">where</a> <a id="1254" class="Keyword">open</a> <a id="1259" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="1267" href="Categories.Object.Product.Morphisms.html#1121" class="Bound">p</a>
<a id="repack≡id×id"></a><a id="1270" href="Categories.Object.Product.Morphisms.html#1270" class="Function">repack≡id×id</a> <a id="1283" class="Symbol">:</a> <a id="1285" class="Symbol">∀</a> <a id="1287" class="Symbol">(</a><a id="1288" href="Categories.Object.Product.Morphisms.html#1288" class="Bound">p₁</a> <a id="1291" href="Categories.Object.Product.Morphisms.html#1291" class="Bound">p₂</a> <a id="1294" class="Symbol">:</a> <a id="1296" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1304" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="1306" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="1307" class="Symbol">)</a> <a id="1309" class="Symbol">→</a> <a id="1311" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="1318" href="Categories.Object.Product.Morphisms.html#1288" class="Bound">p₁</a> <a id="1321" href="Categories.Object.Product.Morphisms.html#1291" class="Bound">p₂</a> <a id="1324" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1326" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1328" href="Categories.Object.Product.Morphisms.html#1288" class="Bound">p₁</a> <a id="1331" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1333" href="Categories.Object.Product.Morphisms.html#1291" class="Bound">p₂</a> <a id="1336" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1338" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1341" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1343" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="1346" href="Categories.Object.Product.Morphisms.html#1270" class="Function">repack≡id×id</a> <a id="1359" href="Categories.Object.Product.Morphisms.html#1359" class="Bound">p₁</a> <a id="1362" href="Categories.Object.Product.Morphisms.html#1362" class="Bound">p₂</a> <a id="1365" class="Symbol">=</a> <a id="1367" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="1369" class="Symbol">(</a><a id="1370" href="Categories.Object.Product.Core.html#854" class="Function">Product.⟨⟩-cong₂</a> <a id="1387" href="Categories.Object.Product.Morphisms.html#1362" class="Bound">p₂</a> <a id="1390" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1400" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a><a id="1409" class="Symbol">)</a>
<a id="[_⇒_]π₁∘×"></a><a id="1412" href="Categories.Object.Product.Morphisms.html#1412" class="Function Operator">[_⇒_]π₁∘×</a> <a id="1422" class="Symbol">:</a> <a id="1424" class="Symbol">∀</a> <a id="1426" class="Symbol">(</a><a id="1427" href="Categories.Object.Product.Morphisms.html#1427" class="Bound">p₁</a> <a id="1430" class="Symbol">:</a> <a id="1432" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1440" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="1442" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="1443" class="Symbol">)(</a><a id="1445" href="Categories.Object.Product.Morphisms.html#1445" class="Bound">p₂</a> <a id="1448" class="Symbol">:</a> <a id="1450" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1458" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="1460" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="1461" class="Symbol">)</a> <a id="1463" class="Symbol">→</a>
<a id="1479" href="Categories.Object.Product.Core.html#526" class="Field">Product.π₁</a> <a id="1490" href="Categories.Object.Product.Morphisms.html#1445" class="Bound">p₂</a> <a id="1493" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1495" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1497" href="Categories.Object.Product.Morphisms.html#1427" class="Bound">p₁</a> <a id="1500" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1502" href="Categories.Object.Product.Morphisms.html#1445" class="Bound">p₂</a> <a id="1505" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1507" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="1509" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1511" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="1513" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1515" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="1517" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1519" href="Categories.Object.Product.Core.html#526" class="Field">Product.π₁</a> <a id="1530" href="Categories.Object.Product.Morphisms.html#1427" class="Bound">p₁</a>
<a id="1533" href="Categories.Object.Product.Morphisms.html#1412" class="Function Operator">[_⇒_]π₁∘×</a> <a id="1543" class="Symbol">_</a> <a id="1545" href="Categories.Object.Product.Morphisms.html#1545" class="Bound">p₂</a> <a id="1548" class="Symbol">=</a> <a id="1550" href="Categories.Object.Product.Core.html#603" class="Field">Product.project₁</a> <a id="1567" href="Categories.Object.Product.Morphisms.html#1545" class="Bound">p₂</a>
<a id="[_⇒_]π₂∘×"></a><a id="1571" href="Categories.Object.Product.Morphisms.html#1571" class="Function Operator">[_⇒_]π₂∘×</a> <a id="1581" class="Symbol">:</a> <a id="1583" class="Symbol">∀</a> <a id="1585" class="Symbol">(</a><a id="1586" href="Categories.Object.Product.Morphisms.html#1586" class="Bound">p₁</a> <a id="1589" class="Symbol">:</a> <a id="1591" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1599" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="1601" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="1602" class="Symbol">)</a> <a id="1604" class="Symbol">(</a><a id="1605" href="Categories.Object.Product.Morphisms.html#1605" class="Bound">p₂</a> <a id="1608" class="Symbol">:</a> <a id="1610" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1618" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="1620" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="1621" class="Symbol">)</a> <a id="1623" class="Symbol">→</a>
<a id="1639" href="Categories.Object.Product.Core.html#546" class="Field">Product.π₂</a> <a id="1650" href="Categories.Object.Product.Morphisms.html#1605" class="Bound">p₂</a> <a id="1653" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1655" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1657" href="Categories.Object.Product.Morphisms.html#1586" class="Bound">p₁</a> <a id="1660" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1662" href="Categories.Object.Product.Morphisms.html#1605" class="Bound">p₂</a> <a id="1665" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1667" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="1669" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1671" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="1673" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1675" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="1677" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1679" href="Categories.Object.Product.Core.html#546" class="Field">Product.π₂</a> <a id="1690" href="Categories.Object.Product.Morphisms.html#1586" class="Bound">p₁</a>
<a id="1693" href="Categories.Object.Product.Morphisms.html#1571" class="Function Operator">[_⇒_]π₂∘×</a> <a id="1703" class="Symbol">_</a> <a id="1705" href="Categories.Object.Product.Morphisms.html#1705" class="Bound">p₂</a> <a id="1708" class="Symbol">=</a> <a id="1710" href="Categories.Object.Product.Core.html#637" class="Field">Product.project₂</a> <a id="1727" href="Categories.Object.Product.Morphisms.html#1705" class="Bound">p₂</a>
<a id="[_⇒_]×-cong₂"></a><a id="1731" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[_⇒_]×-cong₂</a> <a id="1744" class="Symbol">:</a> <a id="1746" class="Symbol">∀</a> <a id="1748" class="Symbol">(</a><a id="1749" href="Categories.Object.Product.Morphisms.html#1749" class="Bound">p₁</a> <a id="1752" class="Symbol">:</a> <a id="1754" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1762" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="1764" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="1765" class="Symbol">)</a> <a id="1767" class="Symbol">(</a><a id="1768" href="Categories.Object.Product.Morphisms.html#1768" class="Bound">p₂</a> <a id="1771" class="Symbol">:</a> <a id="1773" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="1781" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="1783" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="1784" class="Symbol">)</a> <a id="1786" class="Symbol">→</a>
<a id="1805" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="1807" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1809" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="1811" class="Symbol">→</a> <a id="1813" href="Categories.Object.Product.Morphisms.html#496" class="Generalizable">h</a> <a id="1815" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1817" href="Categories.Object.Product.Morphisms.html#498" class="Generalizable">i</a> <a id="1819" class="Symbol">→</a>
<a id="1838" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1840" href="Categories.Object.Product.Morphisms.html#1749" class="Bound">p₁</a> <a id="1843" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1845" href="Categories.Object.Product.Morphisms.html#1768" class="Bound">p₂</a> <a id="1848" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1850" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="1852" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1854" href="Categories.Object.Product.Morphisms.html#496" class="Generalizable">h</a> <a id="1856" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1858" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="1860" href="Categories.Object.Product.Morphisms.html#1749" class="Bound">p₁</a> <a id="1863" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="1865" href="Categories.Object.Product.Morphisms.html#1768" class="Bound">p₂</a> <a id="1868" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="1870" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="1872" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="1874" href="Categories.Object.Product.Morphisms.html#498" class="Generalizable">i</a>
<a id="1876" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[_⇒_]×-cong₂</a> <a id="1889" href="Categories.Object.Product.Morphisms.html#1889" class="Bound">p₁</a> <a id="1892" href="Categories.Object.Product.Morphisms.html#1892" class="Bound">p₂</a> <a id="1895" href="Categories.Object.Product.Morphisms.html#1895" class="Bound">f≈g</a> <a id="1899" href="Categories.Object.Product.Morphisms.html#1899" class="Bound">h≈i</a> <a id="1903" class="Symbol">=</a>
<a id="1909" href="Categories.Object.Product.Core.html#854" class="Function">Product.⟨⟩-cong₂</a> <a id="1926" href="Categories.Object.Product.Morphisms.html#1892" class="Bound">p₂</a> <a id="1929" class="Symbol">(</a><a id="1930" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="1939" href="Categories.Object.Product.Morphisms.html#1895" class="Bound">f≈g</a> <a id="1943" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a><a id="1953" class="Symbol">)</a> <a id="1955" class="Symbol">(</a><a id="1956" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="1965" href="Categories.Object.Product.Morphisms.html#1899" class="Bound">h≈i</a> <a id="1969" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a><a id="1979" class="Symbol">)</a>
<a id="[_⇒_]×∘⟨⟩"></a><a id="1982" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">[_⇒_]×∘⟨⟩</a> <a id="1992" class="Symbol">:</a> <a id="1994" class="Symbol">∀</a> <a id="1996" class="Symbol">(</a><a id="1997" href="Categories.Object.Product.Morphisms.html#1997" class="Bound">p₁</a> <a id="2000" class="Symbol">:</a> <a id="2002" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="2010" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="2012" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="2013" class="Symbol">)</a> <a id="2015" class="Symbol">(</a><a id="2016" href="Categories.Object.Product.Morphisms.html#2016" class="Bound">p₂</a> <a id="2019" class="Symbol">:</a> <a id="2021" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="2029" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="2031" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="2032" class="Symbol">)</a> <a id="2034" class="Symbol">→</a>
<a id="2050" class="Symbol">(</a><a id="2051" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="2053" href="Categories.Object.Product.Morphisms.html#1997" class="Bound">p₁</a> <a id="2056" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="2058" href="Categories.Object.Product.Morphisms.html#2016" class="Bound">p₂</a> <a id="2061" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="2063" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="2065" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="2067" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a><a id="2068" class="Symbol">)</a> <a id="2070" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2072" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="2074" href="Categories.Object.Product.Morphisms.html#1997" class="Bound">p₁</a> <a id="2077" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="2080" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="2083" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="2085" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="2088" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="2090" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2092" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="2094" href="Categories.Object.Product.Morphisms.html#2016" class="Bound">p₂</a> <a id="2097" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="2100" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="2102" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2104" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="2107" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="2109" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="2111" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2113" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="2116" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a>
<a id="2118" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">[_⇒_]×∘⟨⟩</a> <a id="2128" class="Symbol">{</a><a id="2129" class="Argument">f</a> <a id="2131" class="Symbol">=</a> <a id="2133" href="Categories.Object.Product.Morphisms.html#2133" class="Bound">f</a><a id="2134" class="Symbol">}</a> <a id="2136" class="Symbol">{</a><a id="2137" class="Argument">g</a> <a id="2139" class="Symbol">=</a> <a id="2141" href="Categories.Object.Product.Morphisms.html#2141" class="Bound">g</a><a id="2142" class="Symbol">}</a> <a id="2144" class="Symbol">{</a><a id="2145" class="Argument">f′</a> <a id="2148" class="Symbol">=</a> <a id="2150" href="Categories.Object.Product.Morphisms.html#2150" class="Bound">f′</a><a id="2152" class="Symbol">}</a> <a id="2154" class="Symbol">{</a><a id="2155" class="Argument">g′</a> <a id="2158" class="Symbol">=</a> <a id="2160" href="Categories.Object.Product.Morphisms.html#2160" class="Bound">g′</a><a id="2162" class="Symbol">}</a> <a id="2164" href="Categories.Object.Product.Morphisms.html#2164" class="Bound">p₁</a> <a id="2167" href="Categories.Object.Product.Morphisms.html#2167" class="Bound">p₂</a> <a id="2170" class="Symbol">=</a> <a id="2172" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="2180" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="2182" href="Categories.Object.Product.Morphisms.html#2167" class="Bound">p₂</a> <a id="2185" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="2188" href="Categories.Object.Product.Morphisms.html#2133" class="Bound">f</a> <a id="2190" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2192" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a> <a id="2198" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="2200" href="Categories.Object.Product.Morphisms.html#2141" class="Bound">g</a> <a id="2202" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2204" href="Categories.Object.Product.Core.html#546" class="Function">p₁.π₂</a> <a id="2210" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="2212" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2214" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="2216" href="Categories.Object.Product.Morphisms.html#2164" class="Bound">p₁</a> <a id="2219" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="2222" href="Categories.Object.Product.Morphisms.html#2150" class="Bound">f′</a> <a id="2225" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="2227" href="Categories.Object.Product.Morphisms.html#2160" class="Bound">g′</a> <a id="2230" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="2232" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2235" href="Categories.Object.Product.Core.html#1014" class="Function">p₂.∘-distribʳ-⟨⟩</a> <a id="2252" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="2256" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="2258" href="Categories.Object.Product.Morphisms.html#2167" class="Bound">p₂</a> <a id="2261" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="2264" class="Symbol">(</a><a id="2265" href="Categories.Object.Product.Morphisms.html#2133" class="Bound">f</a> <a id="2267" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2269" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a><a id="2274" class="Symbol">)</a> <a id="2276" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2278" href="Categories.Object.Product.Core.html#566" class="Function Operator">p₁.⟨_,_⟩</a> <a id="2287" href="Categories.Object.Product.Morphisms.html#2150" class="Bound">f′</a> <a id="2290" href="Categories.Object.Product.Morphisms.html#2160" class="Bound">g′</a>
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<a id="3242" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[_⇒_⇒_]×∘×</a> <a id="3253" class="Symbol">{</a><a id="3254" class="Argument">g</a> <a id="3256" class="Symbol">=</a> <a id="3258" href="Categories.Object.Product.Morphisms.html#3258" class="Bound">g</a><a id="3259" class="Symbol">}</a> <a id="3261" class="Symbol">{</a><a id="3262" class="Argument">i</a> <a id="3264" class="Symbol">=</a> <a id="3266" href="Categories.Object.Product.Morphisms.html#3266" class="Bound">i</a><a id="3267" class="Symbol">}</a> <a id="3269" class="Symbol">{</a><a id="3270" class="Argument">f</a> <a id="3272" class="Symbol">=</a> <a id="3274" href="Categories.Object.Product.Morphisms.html#3274" class="Bound">f</a><a id="3275" class="Symbol">}</a> <a id="3277" class="Symbol">{</a><a id="3278" class="Argument">h</a> <a id="3280" class="Symbol">=</a> <a id="3282" href="Categories.Object.Product.Morphisms.html#3282" class="Bound">h</a><a id="3283" class="Symbol">}</a> <a id="3285" href="Categories.Object.Product.Morphisms.html#3285" class="Bound">p₁</a> <a id="3288" href="Categories.Object.Product.Morphisms.html#3288" class="Bound">p₂</a> <a id="3291" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a> <a id="3294" class="Symbol">=</a> <a id="3296" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="3304" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="3306" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a> <a id="3309" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="3312" href="Categories.Object.Product.Morphisms.html#3258" class="Bound">g</a> <a id="3314" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3316" href="Categories.Object.Product.Core.html#526" class="Function">p₂.π₁</a> <a id="3322" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="3324" href="Categories.Object.Product.Morphisms.html#3266" class="Bound">i</a> <a id="3326" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3328" href="Categories.Object.Product.Core.html#546" class="Function">p₂.π₂</a> <a id="3334" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="3336" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3338" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="3340" href="Categories.Object.Product.Morphisms.html#3288" class="Bound">p₂</a> <a id="3343" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="3346" href="Categories.Object.Product.Morphisms.html#3274" class="Bound">f</a> <a id="3348" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3350" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a> <a id="3356" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="3358" href="Categories.Object.Product.Morphisms.html#3282" class="Bound">h</a> <a id="3360" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3362" href="Categories.Object.Product.Core.html#546" class="Function">p₁.π₂</a> <a id="3368" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="3370" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3373" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">[</a> <a id="3375" href="Categories.Object.Product.Morphisms.html#3288" class="Bound">p₂</a> <a id="3378" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">⇒</a> <a id="3380" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a> <a id="3383" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">]×∘⟨⟩</a> <a id="3389" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="3393" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="3395" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a> <a id="3398" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="3401" href="Categories.Object.Product.Morphisms.html#3258" class="Bound">g</a> <a id="3403" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3405" href="Categories.Object.Product.Morphisms.html#3274" class="Bound">f</a> <a id="3407" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3409" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a> <a id="3415" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="3417" href="Categories.Object.Product.Morphisms.html#3266" class="Bound">i</a> <a id="3419" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3421" href="Categories.Object.Product.Morphisms.html#3282" class="Bound">h</a> <a id="3423" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3425" href="Categories.Object.Product.Core.html#546" class="Function">p₁.π₂</a> <a id="3431" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="3459" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3462" href="Categories.Object.Product.Core.html#854" class="Function">p₃.⟨⟩-cong₂</a> <a id="3474" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="3484" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="3494" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="3498" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="3500" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a> <a id="3503" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="3506" class="Symbol">(</a><a id="3507" href="Categories.Object.Product.Morphisms.html#3258" class="Bound">g</a> <a id="3509" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3511" href="Categories.Object.Product.Morphisms.html#3274" class="Bound">f</a><a id="3512" class="Symbol">)</a> <a id="3514" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3516" href="Categories.Object.Product.Core.html#526" class="Function">p₁.π₁</a> <a id="3522" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="3524" class="Symbol">(</a><a id="3525" href="Categories.Object.Product.Morphisms.html#3266" class="Bound">i</a> <a id="3527" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3529" href="Categories.Object.Product.Morphisms.html#3282" class="Bound">h</a><a id="3530" class="Symbol">)</a> <a id="3532" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3534" href="Categories.Object.Product.Core.html#546" class="Function">p₁.π₂</a> <a id="3540" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="3564" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="3568" class="Keyword">where</a> <a id="3574" class="Keyword">module</a> <a id="3581" href="Categories.Object.Product.Morphisms.html#3581" class="Module">p₁</a> <a id="3584" class="Symbol">=</a> <a id="3586" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="3594" href="Categories.Object.Product.Morphisms.html#3285" class="Bound">p₁</a>
<a id="3605" class="Keyword">module</a> <a id="3612" href="Categories.Object.Product.Morphisms.html#3612" class="Module">p₂</a> <a id="3615" class="Symbol">=</a> <a id="3617" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="3625" href="Categories.Object.Product.Morphisms.html#3288" class="Bound">p₂</a>
<a id="3636" class="Keyword">module</a> <a id="3643" href="Categories.Object.Product.Morphisms.html#3643" class="Module">p₃</a> <a id="3646" class="Symbol">=</a> <a id="3648" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="3656" href="Categories.Object.Product.Morphisms.html#3291" class="Bound">p₃</a>
<a id="[_⇒_⇒_]repack∘×"></a><a id="3660" href="Categories.Object.Product.Morphisms.html#3660" class="Function Operator">[_⇒_⇒_]repack∘×</a> <a id="3676" class="Symbol">:</a> <a id="3678" class="Symbol">∀</a> <a id="3680" class="Symbol">(</a><a id="3681" href="Categories.Object.Product.Morphisms.html#3681" class="Bound">p₁</a> <a id="3684" class="Symbol">:</a> <a id="3686" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="3694" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="3696" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="3697" class="Symbol">)</a> <a id="3699" class="Symbol">(</a><a id="3700" href="Categories.Object.Product.Morphisms.html#3700" class="Bound">p₂</a> <a id="3703" class="Symbol">:</a> <a id="3705" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="3713" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="3715" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="3716" class="Symbol">)</a> <a id="3718" class="Symbol">(</a><a id="3719" href="Categories.Object.Product.Morphisms.html#3719" class="Bound">p₃</a> <a id="3722" class="Symbol">:</a> <a id="3724" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="3732" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="3734" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="3735" class="Symbol">)</a> <a id="3737" class="Symbol">→</a>
<a id="3759" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="3766" href="Categories.Object.Product.Morphisms.html#3700" class="Bound">p₂</a> <a id="3769" href="Categories.Object.Product.Morphisms.html#3719" class="Bound">p₃</a> <a id="3772" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3774" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="3776" href="Categories.Object.Product.Morphisms.html#3681" class="Bound">p₁</a> <a id="3779" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="3781" href="Categories.Object.Product.Morphisms.html#3700" class="Bound">p₂</a> <a id="3784" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="3786" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="3788" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="3790" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="3792" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="3794" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="3796" href="Categories.Object.Product.Morphisms.html#3681" class="Bound">p₁</a> <a id="3799" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="3801" href="Categories.Object.Product.Morphisms.html#3719" class="Bound">p₃</a> <a id="3804" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="3806" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="3808" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="3810" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a>
<a id="3812" href="Categories.Object.Product.Morphisms.html#3660" class="Function Operator">[_⇒_⇒_]repack∘×</a> <a id="3828" class="Symbol">{</a><a id="3829" class="Argument">f</a> <a id="3831" class="Symbol">=</a> <a id="3833" href="Categories.Object.Product.Morphisms.html#3833" class="Bound">f</a><a id="3834" class="Symbol">}</a> <a id="3836" class="Symbol">{</a><a id="3837" class="Argument">g</a> <a id="3839" class="Symbol">=</a> <a id="3841" href="Categories.Object.Product.Morphisms.html#3841" class="Bound">g</a><a id="3842" class="Symbol">}</a> <a id="3844" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="3847" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3850" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="3853" class="Symbol">=</a> <a id="3855" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="3863" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="3870" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3873" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="3876" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3878" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="3880" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="3883" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="3885" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3888" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="3890" href="Categories.Object.Product.Morphisms.html#3833" class="Bound">f</a> <a id="3892" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="3894" href="Categories.Object.Product.Morphisms.html#3841" class="Bound">g</a> <a id="3907" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3910" href="Categories.Object.Product.Morphisms.html#1270" class="Function">repack≡id×id</a> <a id="3923" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3926" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="3929" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="3937" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="3941" class="Symbol">(</a><a id="3942" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="3944" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3947" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="3949" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="3952" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="3954" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="3957" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="3959" href="Categories.Category.Core.html#630" class="Field">id</a><a id="3961" class="Symbol">)</a> <a id="3963" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3965" class="Symbol">(</a><a id="3966" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="3968" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="3971" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="3973" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3976" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="3978" href="Categories.Object.Product.Morphisms.html#3833" class="Bound">f</a> <a id="3980" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="3982" href="Categories.Object.Product.Morphisms.html#3841" class="Bound">g</a><a id="3983" class="Symbol">)</a> <a id="3985" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3988" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[</a> <a id="3990" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="3993" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="3995" href="Categories.Object.Product.Morphisms.html#3847" class="Bound">p₂</a> <a id="3998" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="4000" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="4003" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">]×∘×</a> <a id="4008" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="4012" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="4014" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="4017" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="4019" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="4022" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="4024" class="Symbol">(</a><a id="4025" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4028" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4030" href="Categories.Object.Product.Morphisms.html#3833" class="Bound">f</a><a id="4031" class="Symbol">)</a> <a id="4033" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="4035" class="Symbol">(</a><a id="4036" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4039" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4041" href="Categories.Object.Product.Morphisms.html#3841" class="Bound">g</a><a id="4042" class="Symbol">)</a> <a id="4056" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="4059" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[</a> <a id="4061" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="4064" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">⇒</a> <a id="4066" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="4069" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">]×-cong₂</a> <a id="4078" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="4088" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="4098" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="4102" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="4104" href="Categories.Object.Product.Morphisms.html#3844" class="Bound">p₁</a> <a id="4107" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="4109" href="Categories.Object.Product.Morphisms.html#3850" class="Bound">p₃</a> <a id="4112" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="4114" href="Categories.Object.Product.Morphisms.html#3833" class="Bound">f</a> <a id="4116" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="4118" href="Categories.Object.Product.Morphisms.html#3841" class="Bound">g</a> <a id="4146" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="[_⇒_⇒_]repack∘repack"></a><a id="4149" href="Categories.Object.Product.Morphisms.html#4149" class="Function Operator">[_⇒_⇒_]repack∘repack</a> <a id="4170" class="Symbol">:</a> <a id="4172" class="Symbol">∀</a> <a id="4174" class="Symbol">(</a><a id="4175" href="Categories.Object.Product.Morphisms.html#4175" class="Bound">p₁</a> <a id="4178" href="Categories.Object.Product.Morphisms.html#4178" class="Bound">p₂</a> <a id="4181" href="Categories.Object.Product.Morphisms.html#4181" class="Bound">p₃</a> <a id="4184" class="Symbol">:</a> <a id="4186" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4194" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4196" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="4197" class="Symbol">)</a> <a id="4199" class="Symbol">→</a> <a id="4201" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="4208" href="Categories.Object.Product.Morphisms.html#4178" class="Bound">p₂</a> <a id="4211" href="Categories.Object.Product.Morphisms.html#4181" class="Bound">p₃</a> <a id="4214" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4216" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="4223" href="Categories.Object.Product.Morphisms.html#4175" class="Bound">p₁</a> <a id="4226" href="Categories.Object.Product.Morphisms.html#4178" class="Bound">p₂</a> <a id="4229" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="4231" href="Categories.Object.Product.Core.html#2078" class="Function">repack</a> <a id="4238" href="Categories.Object.Product.Morphisms.html#4175" class="Bound">p₁</a> <a id="4241" href="Categories.Object.Product.Morphisms.html#4181" class="Bound">p₃</a>
<a id="4244" href="Categories.Object.Product.Morphisms.html#4149" class="Function Operator">[_⇒_⇒_]repack∘repack</a> <a id="4265" class="Symbol">=</a> <a id="4267" href="Categories.Object.Product.Core.html#2168" class="Function">repack∘</a>
<a id="[_⇒_]_×id"></a><a id="4276" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[_⇒_]_×id</a> <a id="4286" class="Symbol">:</a> <a id="4288" class="Symbol">∀</a> <a id="4290" class="Symbol">(</a><a id="4291" href="Categories.Object.Product.Morphisms.html#4291" class="Bound">p₁</a> <a id="4294" class="Symbol">:</a> <a id="4296" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4304" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4306" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="4307" class="Symbol">)</a> <a id="4309" class="Symbol">(</a><a id="4310" href="Categories.Object.Product.Morphisms.html#4310" class="Bound">p₂</a> <a id="4313" class="Symbol">:</a> <a id="4315" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4323" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="4325" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="4326" class="Symbol">)</a> <a id="4328" class="Symbol">→</a> <a id="4330" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4332" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="4334" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="4336" class="Symbol">→</a> <a id="4338" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="4341" href="Categories.Object.Product.Morphisms.html#4291" class="Bound">p₁</a> <a id="4344" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="4347" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="4349" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="4352" href="Categories.Object.Product.Morphisms.html#4310" class="Bound">p₂</a> <a id="4355" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a>
<a id="4358" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="4360" href="Categories.Object.Product.Morphisms.html#4360" class="Bound">p₁</a> <a id="4363" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="4365" href="Categories.Object.Product.Morphisms.html#4365" class="Bound">p₂</a> <a id="4368" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="4370" href="Categories.Object.Product.Morphisms.html#4370" class="Bound">f</a> <a id="4372" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="4376" class="Symbol">=</a> <a id="4378" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="4380" href="Categories.Object.Product.Morphisms.html#4360" class="Bound">p₁</a> <a id="4383" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="4385" href="Categories.Object.Product.Morphisms.html#4365" class="Bound">p₂</a> <a id="4388" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="4390" href="Categories.Object.Product.Morphisms.html#4370" class="Bound">f</a> <a id="4392" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="4394" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="[_⇒_]id×"></a><a id="4398" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[_⇒_]id×</a> <a id="4407" class="Symbol">:</a> <a id="4409" class="Symbol">∀</a> <a id="4411" class="Symbol">(</a><a id="4412" href="Categories.Object.Product.Morphisms.html#4412" class="Bound">p₁</a> <a id="4415" class="Symbol">:</a> <a id="4417" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4425" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4427" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="4428" class="Symbol">)</a> <a id="4430" class="Symbol">(</a><a id="4431" href="Categories.Object.Product.Morphisms.html#4431" class="Bound">p₂</a> <a id="4434" class="Symbol">:</a> <a id="4436" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4444" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4446" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="4447" class="Symbol">)</a> <a id="4449" class="Symbol">→</a> <a id="4451" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="4453" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="4455" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="4457" class="Symbol">→</a> <a id="4459" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="4462" href="Categories.Object.Product.Morphisms.html#4412" class="Bound">p₁</a> <a id="4465" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a> <a id="4468" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="4470" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">[[</a> <a id="4473" href="Categories.Object.Product.Morphisms.html#4431" class="Bound">p₂</a> <a id="4476" href="Categories.Object.Product.Morphisms.html#564" class="Function Operator">]]</a>
<a id="4479" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="4481" href="Categories.Object.Product.Morphisms.html#4481" class="Bound">p₁</a> <a id="4484" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="4486" href="Categories.Object.Product.Morphisms.html#4486" class="Bound">p₂</a> <a id="4489" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="4494" href="Categories.Object.Product.Morphisms.html#4494" class="Bound">g</a> <a id="4496" class="Symbol">=</a> <a id="4498" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="4500" href="Categories.Object.Product.Morphisms.html#4481" class="Bound">p₁</a> <a id="4503" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="4505" href="Categories.Object.Product.Morphisms.html#4486" class="Bound">p₂</a> <a id="4508" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="4510" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4513" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="4515" href="Categories.Object.Product.Morphisms.html#4494" class="Bound">g</a>
<a id="first-id"></a><a id="4518" href="Categories.Object.Product.Morphisms.html#4518" class="Function">first-id</a> <a id="4527" class="Symbol">:</a> <a id="4529" class="Symbol">∀</a> <a id="4531" class="Symbol">(</a><a id="4532" href="Categories.Object.Product.Morphisms.html#4532" class="Bound">p</a> <a id="4534" class="Symbol">:</a> <a id="4536" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4544" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4546" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="4547" class="Symbol">)</a> <a id="4549" class="Symbol">→</a> <a id="4551" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="4553" href="Categories.Object.Product.Morphisms.html#4532" class="Bound">p</a> <a id="4555" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="4557" href="Categories.Object.Product.Morphisms.html#4532" class="Bound">p</a> <a id="4559" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="4561" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4564" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="4568" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="4570" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="4573" href="Categories.Object.Product.Morphisms.html#4518" class="Function">first-id</a> <a id="4582" class="Symbol">=</a> <a id="4584" href="Categories.Object.Product.Morphisms.html#1062" class="Function">id×id</a>
<a id="second-id"></a><a id="4591" href="Categories.Object.Product.Morphisms.html#4591" class="Function">second-id</a> <a id="4601" class="Symbol">:</a> <a id="4603" class="Symbol">∀</a> <a id="4605" class="Symbol">(</a><a id="4606" href="Categories.Object.Product.Morphisms.html#4606" class="Bound">p</a> <a id="4608" class="Symbol">:</a> <a id="4610" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4618" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="4620" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="4621" class="Symbol">)</a> <a id="4623" class="Symbol">→</a> <a id="4625" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="4627" href="Categories.Object.Product.Morphisms.html#4606" class="Bound">p</a> <a id="4629" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="4631" href="Categories.Object.Product.Morphisms.html#4606" class="Bound">p</a> <a id="4633" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="4638" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4641" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="4643" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="4646" href="Categories.Object.Product.Morphisms.html#4591" class="Function">second-id</a> <a id="4656" class="Symbol">=</a> <a id="4658" href="Categories.Object.Product.Morphisms.html#1062" class="Function">id×id</a>
<a id="[_⇒_]×id∘⟨⟩"></a><a id="4665" href="Categories.Object.Product.Morphisms.html#4665" class="Function Operator">[_⇒_]×id∘⟨⟩</a> <a id="4677" class="Symbol">:</a> <a id="4679" class="Symbol">∀</a> <a id="4681" class="Symbol">(</a><a id="4682" href="Categories.Object.Product.Morphisms.html#4682" class="Bound">p₁</a> <a id="4685" class="Symbol">:</a> <a id="4687" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4695" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="4697" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="4698" class="Symbol">)</a> <a id="4700" class="Symbol">(</a><a id="4701" href="Categories.Object.Product.Morphisms.html#4701" class="Bound">p₂</a> <a id="4704" class="Symbol">:</a> <a id="4706" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="4714" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="4716" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="4717" class="Symbol">)</a> <a id="4719" class="Symbol">→</a>
<a id="4739" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="4741" href="Categories.Object.Product.Morphisms.html#4682" class="Bound">p₁</a> <a id="4744" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="4746" href="Categories.Object.Product.Morphisms.html#4701" class="Bound">p₂</a> <a id="4749" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="4751" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="4753" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="4757" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4759" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="4761" href="Categories.Object.Product.Morphisms.html#4682" class="Bound">p₁</a> <a id="4764" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="4767" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="4770" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="4772" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="4775" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="4777" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="4779" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="4781" href="Categories.Object.Product.Morphisms.html#4701" class="Bound">p₂</a> <a id="4784" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="4787" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="4789" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4791" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="4794" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="4796" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="4799" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a>
<a id="4801" href="Categories.Object.Product.Morphisms.html#4665" class="Function Operator">[_⇒_]×id∘⟨⟩</a> <a id="4813" class="Symbol">{</a><a id="4814" class="Argument">f</a> <a id="4816" class="Symbol">=</a> <a id="4818" href="Categories.Object.Product.Morphisms.html#4818" class="Bound">f</a><a id="4819" class="Symbol">}</a> <a id="4821" class="Symbol">{</a><a id="4822" class="Argument">f′</a> <a id="4825" class="Symbol">=</a> <a id="4827" href="Categories.Object.Product.Morphisms.html#4827" class="Bound">f′</a><a id="4829" class="Symbol">}</a> <a id="4831" class="Symbol">{</a><a id="4832" class="Argument">g′</a> <a id="4835" class="Symbol">=</a> <a id="4837" href="Categories.Object.Product.Morphisms.html#4837" class="Bound">g′</a><a id="4839" class="Symbol">}</a> <a id="4841" href="Categories.Object.Product.Morphisms.html#4841" class="Bound">p₁</a> <a id="4844" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a> <a id="4847" class="Symbol">=</a> <a id="4849" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="4857" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="4859" href="Categories.Object.Product.Morphisms.html#4841" class="Bound">p₁</a> <a id="4862" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="4864" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a> <a id="4867" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="4869" href="Categories.Object.Product.Morphisms.html#4818" class="Bound">f</a> <a id="4871" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="4875" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4877" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="4879" href="Categories.Object.Product.Morphisms.html#4841" class="Bound">p₁</a> <a id="4882" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="4885" href="Categories.Object.Product.Morphisms.html#4827" class="Bound">f′</a> <a id="4888" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="4890" href="Categories.Object.Product.Morphisms.html#4837" class="Bound">g′</a> <a id="4893" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="4895" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="4898" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">[</a> <a id="4900" href="Categories.Object.Product.Morphisms.html#4841" class="Bound">p₁</a> <a id="4903" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">⇒</a> <a id="4905" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a> <a id="4908" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">]×∘⟨⟩</a> <a id="4914" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="4918" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="4920" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a> <a id="4923" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="4926" href="Categories.Object.Product.Morphisms.html#4818" class="Bound">f</a> <a id="4928" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4930" href="Categories.Object.Product.Morphisms.html#4827" class="Bound">f′</a> <a id="4933" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="4935" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="4938" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="4940" href="Categories.Object.Product.Morphisms.html#4837" class="Bound">g′</a> <a id="4943" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="4956" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="4959" href="Categories.Object.Product.Core.html#854" class="Function">p₂.⟨⟩-cong₂</a> <a id="4971" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a> <a id="4982" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="4992" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="4996" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="4998" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a> <a id="5001" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5004" href="Categories.Object.Product.Morphisms.html#4818" class="Bound">f</a> <a id="5006" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5008" href="Categories.Object.Product.Morphisms.html#4827" class="Bound">f′</a> <a id="5011" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5013" href="Categories.Object.Product.Morphisms.html#4837" class="Bound">g′</a> <a id="5016" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="5034" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="5038" class="Keyword">where</a> <a id="5044" class="Keyword">module</a> <a id="5051" href="Categories.Object.Product.Morphisms.html#5051" class="Module">p₂</a> <a id="5054" class="Symbol">=</a> <a id="5056" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="5064" href="Categories.Object.Product.Morphisms.html#4844" class="Bound">p₂</a>
<a id="[_⇒_]id×∘⟨⟩"></a><a id="5068" href="Categories.Object.Product.Morphisms.html#5068" class="Function Operator">[_⇒_]id×∘⟨⟩</a> <a id="5080" class="Symbol">:</a> <a id="5082" class="Symbol">∀</a> <a id="5084" class="Symbol">(</a><a id="5085" href="Categories.Object.Product.Morphisms.html#5085" class="Bound">p₁</a> <a id="5088" class="Symbol">:</a> <a id="5090" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5098" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="5100" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="5101" class="Symbol">)</a> <a id="5103" class="Symbol">(</a><a id="5104" href="Categories.Object.Product.Morphisms.html#5104" class="Bound">p₂</a> <a id="5107" class="Symbol">:</a> <a id="5109" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5117" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="5119" href="Categories.Object.Product.Morphisms.html#472" class="Generalizable">E</a><a id="5120" class="Symbol">)</a> <a id="5122" class="Symbol">→</a>
<a id="5143" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="5145" href="Categories.Object.Product.Morphisms.html#5085" class="Bound">p₁</a> <a id="5148" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="5150" href="Categories.Object.Product.Morphisms.html#5104" class="Bound">p₂</a> <a id="5153" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="5158" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="5160" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5162" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="5164" href="Categories.Object.Product.Morphisms.html#5085" class="Bound">p₁</a> <a id="5167" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5170" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="5173" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5175" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="5178" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="5180" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="5182" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="5184" href="Categories.Object.Product.Morphisms.html#5104" class="Bound">p₂</a> <a id="5187" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5190" href="Categories.Object.Product.Morphisms.html#488" class="Generalizable">f′</a> <a id="5193" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5195" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="5197" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5199" href="Categories.Object.Product.Morphisms.html#493" class="Generalizable">g′</a> <a id="5202" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a>
<a id="5204" href="Categories.Object.Product.Morphisms.html#5068" class="Function Operator">[_⇒_]id×∘⟨⟩</a> <a id="5216" class="Symbol">{</a><a id="5217" class="Argument">g</a> <a id="5219" class="Symbol">=</a> <a id="5221" href="Categories.Object.Product.Morphisms.html#5221" class="Bound">g</a><a id="5222" class="Symbol">}</a> <a id="5224" class="Symbol">{</a><a id="5225" class="Argument">f′</a> <a id="5228" class="Symbol">=</a> <a id="5230" href="Categories.Object.Product.Morphisms.html#5230" class="Bound">f′</a><a id="5232" class="Symbol">}</a> <a id="5234" class="Symbol">{</a><a id="5235" class="Argument">g′</a> <a id="5238" class="Symbol">=</a> <a id="5240" href="Categories.Object.Product.Morphisms.html#5240" class="Bound">g′</a><a id="5242" class="Symbol">}</a> <a id="5244" href="Categories.Object.Product.Morphisms.html#5244" class="Bound">p₁</a> <a id="5247" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a> <a id="5250" class="Symbol">=</a> <a id="5252" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="5260" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="5262" href="Categories.Object.Product.Morphisms.html#5244" class="Bound">p₁</a> <a id="5265" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="5267" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a> <a id="5270" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="5275" href="Categories.Object.Product.Morphisms.html#5221" class="Bound">g</a> <a id="5277" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5279" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="5281" href="Categories.Object.Product.Morphisms.html#5244" class="Bound">p₁</a> <a id="5284" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5287" href="Categories.Object.Product.Morphisms.html#5230" class="Bound">f′</a> <a id="5290" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5292" href="Categories.Object.Product.Morphisms.html#5240" class="Bound">g′</a> <a id="5295" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="5297" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="5300" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">[</a> <a id="5302" href="Categories.Object.Product.Morphisms.html#5244" class="Bound">p₁</a> <a id="5305" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">⇒</a> <a id="5307" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a> <a id="5310" href="Categories.Object.Product.Morphisms.html#1982" class="Function Operator">]×∘⟨⟩</a> <a id="5316" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="5320" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="5322" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a> <a id="5325" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5328" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="5331" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5333" href="Categories.Object.Product.Morphisms.html#5230" class="Bound">f′</a> <a id="5336" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5338" href="Categories.Object.Product.Morphisms.html#5221" class="Bound">g</a> <a id="5340" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5342" href="Categories.Object.Product.Morphisms.html#5240" class="Bound">g′</a> <a id="5345" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="5360" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="5363" href="Categories.Object.Product.Core.html#854" class="Function">p₂.⟨⟩-cong₂</a> <a id="5375" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="5385" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a> <a id="5396" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="5400" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">[</a> <a id="5402" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a> <a id="5405" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">]⟨</a> <a id="5408" href="Categories.Object.Product.Morphisms.html#5230" class="Bound">f′</a> <a id="5411" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">,</a> <a id="5413" href="Categories.Object.Product.Morphisms.html#5221" class="Bound">g</a> <a id="5415" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5417" href="Categories.Object.Product.Morphisms.html#5240" class="Bound">g′</a> <a id="5420" href="Categories.Object.Product.Morphisms.html#615" class="Function Operator">⟩</a> <a id="5440" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="5444" class="Keyword">where</a> <a id="5450" class="Keyword">module</a> <a id="5457" href="Categories.Object.Product.Morphisms.html#5457" class="Module">p₂</a> <a id="5460" class="Symbol">=</a> <a id="5462" href="Categories.Object.Product.Core.html#435" class="Module">Product</a> <a id="5470" href="Categories.Object.Product.Morphisms.html#5247" class="Bound">p₂</a>
<a id="[_⇒_⇒_]×id∘×id"></a><a id="5474" href="Categories.Object.Product.Morphisms.html#5474" class="Function Operator">[_⇒_⇒_]×id∘×id</a> <a id="5489" class="Symbol">:</a> <a id="5491" class="Symbol">∀</a> <a id="5493" class="Symbol">(</a><a id="5494" href="Categories.Object.Product.Morphisms.html#5494" class="Bound">p₁</a> <a id="5497" class="Symbol">:</a> <a id="5499" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5507" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="5509" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="5510" class="Symbol">)</a> <a id="5512" class="Symbol">(</a><a id="5513" href="Categories.Object.Product.Morphisms.html#5513" class="Bound">p₂</a> <a id="5516" class="Symbol">:</a> <a id="5518" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5526" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="5528" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="5529" class="Symbol">)</a> <a id="5531" class="Symbol">(</a><a id="5532" href="Categories.Object.Product.Morphisms.html#5532" class="Bound">p₃</a> <a id="5535" class="Symbol">:</a> <a id="5537" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5545" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a> <a id="5547" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="5548" class="Symbol">)</a> <a id="5550" class="Symbol">→</a>
<a id="5575" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5577" href="Categories.Object.Product.Morphisms.html#5513" class="Bound">p₂</a> <a id="5580" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5582" href="Categories.Object.Product.Morphisms.html#5532" class="Bound">p₃</a> <a id="5585" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5587" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="5589" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="5593" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5595" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5597" href="Categories.Object.Product.Morphisms.html#5494" class="Bound">p₁</a> <a id="5600" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5602" href="Categories.Object.Product.Morphisms.html#5513" class="Bound">p₂</a> <a id="5605" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5607" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="5609" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="5613" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="5615" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5617" href="Categories.Object.Product.Morphisms.html#5494" class="Bound">p₁</a> <a id="5620" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5622" href="Categories.Object.Product.Morphisms.html#5532" class="Bound">p₃</a> <a id="5625" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5627" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="5629" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5631" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="5633" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a>
<a id="5637" href="Categories.Object.Product.Morphisms.html#5474" class="Function Operator">[_⇒_⇒_]×id∘×id</a> <a id="5652" class="Symbol">{</a><a id="5653" class="Argument">f</a> <a id="5655" class="Symbol">=</a> <a id="5657" href="Categories.Object.Product.Morphisms.html#5657" class="Bound">f</a><a id="5658" class="Symbol">}</a> <a id="5660" class="Symbol">{</a><a id="5661" class="Argument">g</a> <a id="5663" class="Symbol">=</a> <a id="5665" href="Categories.Object.Product.Morphisms.html#5665" class="Bound">g</a><a id="5666" class="Symbol">}</a> <a id="5668" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5671" href="Categories.Object.Product.Morphisms.html#5671" class="Bound">p₂</a> <a id="5674" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5677" class="Symbol">=</a> <a id="5679" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="5687" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5689" href="Categories.Object.Product.Morphisms.html#5671" class="Bound">p₂</a> <a id="5692" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5694" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5697" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5699" href="Categories.Object.Product.Morphisms.html#5657" class="Bound">f</a> <a id="5701" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="5705" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5707" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5709" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5712" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5714" href="Categories.Object.Product.Morphisms.html#5671" class="Bound">p₂</a> <a id="5717" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5719" href="Categories.Object.Product.Morphisms.html#5665" class="Bound">g</a> <a id="5721" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="5725" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="5728" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[</a> <a id="5730" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5733" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="5735" href="Categories.Object.Product.Morphisms.html#5671" class="Bound">p₂</a> <a id="5738" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="5740" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5743" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">]×∘×</a> <a id="5748" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="5752" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="5754" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5757" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="5759" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5762" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="5764" class="Symbol">(</a><a id="5765" href="Categories.Object.Product.Morphisms.html#5657" class="Bound">f</a> <a id="5767" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5769" href="Categories.Object.Product.Morphisms.html#5665" class="Bound">g</a><a id="5770" class="Symbol">)</a> <a id="5772" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="5774" class="Symbol">(</a><a id="5775" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="5778" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5780" href="Categories.Category.Core.html#630" class="Field">id</a><a id="5782" class="Symbol">)</a> <a id="5790" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="5793" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[</a> <a id="5795" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5798" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">⇒</a> <a id="5800" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5803" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">]×-cong₂</a> <a id="5812" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a> <a id="5823" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="5833" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="5837" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="5839" href="Categories.Object.Product.Morphisms.html#5668" class="Bound">p₁</a> <a id="5842" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="5844" href="Categories.Object.Product.Morphisms.html#5674" class="Bound">p₃</a> <a id="5847" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="5849" href="Categories.Object.Product.Morphisms.html#5657" class="Bound">f</a> <a id="5851" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="5853" href="Categories.Object.Product.Morphisms.html#5665" class="Bound">g</a> <a id="5855" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="5875" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="[_⇒_⇒_]id×∘id×"></a><a id="5878" href="Categories.Object.Product.Morphisms.html#5878" class="Function Operator">[_⇒_⇒_]id×∘id×</a> <a id="5893" class="Symbol">:</a> <a id="5895" class="Symbol">∀</a> <a id="5897" class="Symbol">(</a><a id="5898" href="Categories.Object.Product.Morphisms.html#5898" class="Bound">p₁</a> <a id="5901" class="Symbol">:</a> <a id="5903" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5911" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="5913" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a><a id="5914" class="Symbol">)</a> <a id="5916" class="Symbol">(</a><a id="5917" href="Categories.Object.Product.Morphisms.html#5917" class="Bound">p₂</a> <a id="5920" class="Symbol">:</a> <a id="5922" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5930" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="5932" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="5933" class="Symbol">)</a> <a id="5935" class="Symbol">(</a><a id="5936" href="Categories.Object.Product.Morphisms.html#5936" class="Bound">p₃</a> <a id="5939" class="Symbol">:</a> <a id="5941" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="5949" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="5951" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="5952" class="Symbol">)</a> <a id="5954" class="Symbol">→</a>
<a id="5981" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="5983" href="Categories.Object.Product.Morphisms.html#5917" class="Bound">p₂</a> <a id="5986" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="5988" href="Categories.Object.Product.Morphisms.html#5936" class="Bound">p₃</a> <a id="5991" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="5996" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="5998" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6000" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6002" href="Categories.Object.Product.Morphisms.html#5898" class="Bound">p₁</a> <a id="6005" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6007" href="Categories.Object.Product.Morphisms.html#5917" class="Bound">p₂</a> <a id="6010" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6015" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="6017" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="6019" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6021" href="Categories.Object.Product.Morphisms.html#5898" class="Bound">p₁</a> <a id="6024" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6026" href="Categories.Object.Product.Morphisms.html#5936" class="Bound">p₃</a> <a id="6029" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a><a id="6033" class="Symbol">(</a><a id="6034" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="6036" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6038" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a><a id="6039" class="Symbol">)</a>
<a id="6041" href="Categories.Object.Product.Morphisms.html#5878" class="Function Operator">[_⇒_⇒_]id×∘id×</a> <a id="6056" class="Symbol">{</a><a id="6057" class="Argument">f</a> <a id="6059" class="Symbol">=</a> <a id="6061" href="Categories.Object.Product.Morphisms.html#6061" class="Bound">f</a><a id="6062" class="Symbol">}</a> <a id="6064" class="Symbol">{</a><a id="6065" class="Argument">g</a> <a id="6067" class="Symbol">=</a> <a id="6069" href="Categories.Object.Product.Morphisms.html#6069" class="Bound">g</a><a id="6070" class="Symbol">}</a> <a id="6072" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6075" href="Categories.Object.Product.Morphisms.html#6075" class="Bound">p₂</a> <a id="6078" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6081" class="Symbol">=</a> <a id="6083" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="6091" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6093" href="Categories.Object.Product.Morphisms.html#6075" class="Bound">p₂</a> <a id="6096" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6098" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6101" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6106" href="Categories.Object.Product.Morphisms.html#6061" class="Bound">f</a> <a id="6108" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6110" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6112" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6115" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6117" href="Categories.Object.Product.Morphisms.html#6075" class="Bound">p₂</a> <a id="6120" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6125" href="Categories.Object.Product.Morphisms.html#6069" class="Bound">g</a> <a id="6127" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="6130" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[</a> <a id="6132" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6135" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6137" href="Categories.Object.Product.Morphisms.html#6075" class="Bound">p₂</a> <a id="6140" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6142" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6145" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">]×∘×</a> <a id="6150" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="6154" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="6156" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6159" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="6161" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6164" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="6166" class="Symbol">(</a><a id="6167" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="6170" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6172" href="Categories.Category.Core.html#630" class="Field">id</a><a id="6174" class="Symbol">)</a> <a id="6176" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="6178" class="Symbol">(</a><a id="6179" href="Categories.Object.Product.Morphisms.html#6061" class="Bound">f</a> <a id="6181" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6183" href="Categories.Object.Product.Morphisms.html#6069" class="Bound">g</a><a id="6184" class="Symbol">)</a> <a id="6190" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="6193" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[</a> <a id="6195" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6198" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">⇒</a> <a id="6200" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6203" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">]×-cong₂</a> <a id="6212" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="6222" href="Relation.Binary.Structures.html#1577" class="Function">Equiv.refl</a> <a id="6233" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="6237" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6239" href="Categories.Object.Product.Morphisms.html#6072" class="Bound">p₁</a> <a id="6242" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6244" href="Categories.Object.Product.Morphisms.html#6078" class="Bound">p₃</a> <a id="6247" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6252" class="Symbol">(</a><a id="6253" href="Categories.Object.Product.Morphisms.html#6061" class="Bound">f</a> <a id="6255" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6257" href="Categories.Object.Product.Morphisms.html#6069" class="Bound">g</a><a id="6258" class="Symbol">)</a> <a id="6273" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="[_⇒_,_⇒_]first↔second"></a><a id="6276" href="Categories.Object.Product.Morphisms.html#6276" class="Function Operator">[_⇒_,_⇒_]first↔second</a> <a id="6298" class="Symbol">:</a> <a id="6300" class="Symbol">∀</a> <a id="6302" class="Symbol">(</a><a id="6303" href="Categories.Object.Product.Morphisms.html#6303" class="Bound">p₁</a> <a id="6306" class="Symbol">:</a> <a id="6308" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="6316" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="6318" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="6319" class="Symbol">)</a> <a id="6321" class="Symbol">(</a><a id="6322" href="Categories.Object.Product.Morphisms.html#6322" class="Bound">p₂</a> <a id="6325" class="Symbol">:</a> <a id="6327" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="6335" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="6337" href="Categories.Object.Product.Morphisms.html#470" class="Generalizable">D</a><a id="6338" class="Symbol">)</a>
<a id="6366" class="Symbol">(</a><a id="6367" href="Categories.Object.Product.Morphisms.html#6367" class="Bound">p₃</a> <a id="6370" class="Symbol">:</a> <a id="6372" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="6380" href="Categories.Object.Product.Morphisms.html#464" class="Generalizable">A</a> <a id="6382" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="6383" class="Symbol">)</a> <a id="6385" class="Symbol">(</a><a id="6386" href="Categories.Object.Product.Morphisms.html#6386" class="Bound">p₄</a> <a id="6389" class="Symbol">:</a> <a id="6391" href="Categories.Object.Product.Core.html#435" class="Record">Product</a> <a id="6399" href="Categories.Object.Product.Morphisms.html#466" class="Generalizable">B</a> <a id="6401" href="Categories.Object.Product.Morphisms.html#468" class="Generalizable">C</a><a id="6402" class="Symbol">)</a> <a id="6404" class="Symbol">→</a>
<a id="6432" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="6434" href="Categories.Object.Product.Morphisms.html#6303" class="Bound">p₁</a> <a id="6437" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="6439" href="Categories.Object.Product.Morphisms.html#6322" class="Bound">p₂</a> <a id="6442" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="6444" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="6446" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="6450" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6452" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6454" href="Categories.Object.Product.Morphisms.html#6367" class="Bound">p₃</a> <a id="6457" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6459" href="Categories.Object.Product.Morphisms.html#6303" class="Bound">p₁</a> <a id="6462" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6467" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="6469" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="6471" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6473" href="Categories.Object.Product.Morphisms.html#6386" class="Bound">p₄</a> <a id="6476" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6478" href="Categories.Object.Product.Morphisms.html#6322" class="Bound">p₂</a> <a id="6481" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6486" href="Categories.Object.Product.Morphisms.html#491" class="Generalizable">g</a> <a id="6488" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6490" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="6492" href="Categories.Object.Product.Morphisms.html#6367" class="Bound">p₃</a> <a id="6495" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="6497" href="Categories.Object.Product.Morphisms.html#6386" class="Bound">p₄</a> <a id="6500" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="6502" href="Categories.Object.Product.Morphisms.html#486" class="Generalizable">f</a> <a id="6504" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a>
<a id="6508" href="Categories.Object.Product.Morphisms.html#6276" class="Function Operator">[_⇒_,_⇒_]first↔second</a> <a id="6530" class="Symbol">{</a><a id="6531" class="Argument">f</a> <a id="6533" class="Symbol">=</a> <a id="6535" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a><a id="6536" class="Symbol">}</a> <a id="6538" class="Symbol">{</a><a id="6539" class="Argument">g</a> <a id="6541" class="Symbol">=</a> <a id="6543" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a><a id="6544" class="Symbol">}</a> <a id="6546" href="Categories.Object.Product.Morphisms.html#6546" class="Bound">p₁</a> <a id="6549" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6552" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6555" href="Categories.Object.Product.Morphisms.html#6555" class="Bound">p₄</a> <a id="6558" class="Symbol">=</a> <a id="6560" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="6568" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="6570" href="Categories.Object.Product.Morphisms.html#6546" class="Bound">p₁</a> <a id="6573" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="6575" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6578" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="6580" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a> <a id="6582" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="6586" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6588" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6590" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6593" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6595" href="Categories.Object.Product.Morphisms.html#6546" class="Bound">p₁</a> <a id="6598" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6603" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a> <a id="6605" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="6608" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[</a> <a id="6610" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6613" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6615" href="Categories.Object.Product.Morphisms.html#6546" class="Bound">p₁</a> <a id="6618" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6620" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6623" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">]×∘×</a> <a id="6628" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="6632" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="6634" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6637" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="6639" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6642" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="6644" class="Symbol">(</a><a id="6645" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a> <a id="6647" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6649" href="Categories.Category.Core.html#630" class="Field">id</a><a id="6651" class="Symbol">)</a> <a id="6653" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="6655" class="Symbol">(</a><a id="6656" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="6659" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6661" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a><a id="6662" class="Symbol">)</a> <a id="6669" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="6672" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[</a> <a id="6674" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6677" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">⇒</a> <a id="6679" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6682" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">]×-cong₂</a> <a id="6691" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="6701" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="6711" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="6715" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="6717" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6720" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="6722" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6725" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="6727" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a> <a id="6729" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="6731" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a> <a id="6752" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="6756" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">[</a> <a id="6758" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6761" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">⇒</a> <a id="6763" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6766" href="Categories.Object.Product.Morphisms.html#1731" class="Function Operator">]×-cong₂</a> <a id="6775" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="6785" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="6795" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="6799" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">[</a> <a id="6801" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6804" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">⇒</a> <a id="6806" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6809" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">]</a> <a id="6811" class="Symbol">(</a><a id="6812" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="6815" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6817" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a><a id="6818" class="Symbol">)</a> <a id="6820" href="Categories.Object.Product.Morphisms.html#838" class="Function Operator">×</a> <a id="6822" class="Symbol">(</a><a id="6823" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a> <a id="6825" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6827" href="Categories.Category.Core.html#630" class="Field">id</a><a id="6829" class="Symbol">)</a> <a id="6836" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="6840" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">[</a> <a id="6842" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6845" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6847" href="Categories.Object.Product.Morphisms.html#6555" class="Bound">p₄</a> <a id="6850" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">⇒</a> <a id="6852" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6855" href="Categories.Object.Product.Morphisms.html#3079" class="Function Operator">]×∘×</a> <a id="6860" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="6864" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">[</a> <a id="6866" href="Categories.Object.Product.Morphisms.html#6555" class="Bound">p₄</a> <a id="6869" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">⇒</a> <a id="6871" href="Categories.Object.Product.Morphisms.html#6549" class="Bound">p₂</a> <a id="6874" href="Categories.Object.Product.Morphisms.html#4398" class="Function Operator">]id×</a> <a id="6879" href="Categories.Object.Product.Morphisms.html#6543" class="Bound">g</a> <a id="6881" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6883" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">[</a> <a id="6885" href="Categories.Object.Product.Morphisms.html#6552" class="Bound">p₃</a> <a id="6888" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">⇒</a> <a id="6890" href="Categories.Object.Product.Morphisms.html#6555" class="Bound">p₄</a> <a id="6893" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">]</a> <a id="6895" href="Categories.Object.Product.Morphisms.html#6535" class="Bound">f</a> <a id="6897" href="Categories.Object.Product.Morphisms.html#4276" class="Function Operator">×id</a> <a id="6901" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
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