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<html><head><meta charset="utf-8"><title>Categories.Utils.Product</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="Keyword">module</a> <a id="43" href="Categories.Utils.Product.html" class="Module">Categories.Utils.Product</a> <a id="68" class="Keyword">where</a>
<a id="75" class="Keyword">open</a> <a id="80" class="Keyword">import</a> <a id="87" href="Level.html" class="Module">Level</a>
<a id="93" class="Keyword">open</a> <a id="98" class="Keyword">import</a> <a id="105" href="Data.Product.html" class="Module">Data.Product</a> <a id="118" class="Keyword">using</a> <a id="124" class="Symbol">(</a><a id="125" href="Data.Product.html#1176" class="Function Operator">_×_</a><a id="128" class="Symbol">;</a> <a id="130" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a><a id="131" class="Symbol">;</a> <a id="133" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">_,_</a><a id="136" class="Symbol">;</a> <a id="138" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a><a id="143" class="Symbol">;</a> <a id="145" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a><a id="150" class="Symbol">)</a>
<a id="152" class="Keyword">open</a> <a id="157" class="Keyword">import</a> <a id="164" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a>
<a id="203" class="Comment">-- &quot;very dependent&quot; versions of map and zipWith</a>
<a id="map⁎"></a><a id="251" href="Categories.Utils.Product.html#251" class="Function">map⁎</a> <a id="256" class="Symbol">:</a> <a id="258" class="Symbol">∀</a> <a id="260" class="Symbol">{</a><a id="261" href="Categories.Utils.Product.html#261" class="Bound">a</a> <a id="263" href="Categories.Utils.Product.html#263" class="Bound">b</a> <a id="265" href="Categories.Utils.Product.html#265" class="Bound">p</a> <a id="267" href="Categories.Utils.Product.html#267" class="Bound">q</a><a id="268" class="Symbol">}</a> <a id="270" class="Symbol">{</a><a id="271" href="Categories.Utils.Product.html#271" class="Bound">A</a> <a id="273" class="Symbol">:</a> <a id="275" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="279" href="Categories.Utils.Product.html#261" class="Bound">a</a><a id="280" class="Symbol">}</a> <a id="282" class="Symbol">{</a><a id="283" href="Categories.Utils.Product.html#283" class="Bound">B</a> <a id="285" class="Symbol">:</a> <a id="287" href="Categories.Utils.Product.html#271" class="Bound">A</a> <a id="289" class="Symbol">→</a> <a id="291" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="295" href="Categories.Utils.Product.html#263" class="Bound">b</a><a id="296" class="Symbol">}</a> <a id="298" class="Symbol">{</a><a id="299" href="Categories.Utils.Product.html#299" class="Bound">P</a> <a id="301" class="Symbol">:</a> <a id="303" href="Categories.Utils.Product.html#271" class="Bound">A</a> <a id="305" class="Symbol">→</a> <a id="307" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="311" href="Categories.Utils.Product.html#265" class="Bound">p</a><a id="312" class="Symbol">}</a> <a id="314" class="Symbol">{</a><a id="315" href="Categories.Utils.Product.html#315" class="Bound">Q</a> <a id="317" class="Symbol">:</a> <a id="319" class="Symbol">{</a><a id="320" href="Categories.Utils.Product.html#320" class="Bound">x</a> <a id="322" class="Symbol">:</a> <a id="324" href="Categories.Utils.Product.html#271" class="Bound">A</a><a id="325" class="Symbol">}</a> <a id="327" class="Symbol">→</a> <a id="329" href="Categories.Utils.Product.html#299" class="Bound">P</a> <a id="331" href="Categories.Utils.Product.html#320" class="Bound">x</a> <a id="333" class="Symbol">→</a> <a id="335" href="Categories.Utils.Product.html#283" class="Bound">B</a> <a id="337" href="Categories.Utils.Product.html#320" class="Bound">x</a> <a id="339" class="Symbol">→</a> <a id="341" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="345" href="Categories.Utils.Product.html#267" class="Bound">q</a><a id="346" class="Symbol">}</a> <a id="348" class="Symbol">→</a>
<a id="356" class="Symbol">(</a><a id="357" href="Categories.Utils.Product.html#357" class="Bound">f</a> <a id="359" class="Symbol">:</a> <a id="361" class="Symbol">(</a><a id="362" href="Categories.Utils.Product.html#362" class="Bound">x</a> <a id="364" class="Symbol">:</a> <a id="366" href="Categories.Utils.Product.html#271" class="Bound">A</a><a id="367" class="Symbol">)</a> <a id="369" class="Symbol">→</a> <a id="371" href="Categories.Utils.Product.html#283" class="Bound">B</a> <a id="373" href="Categories.Utils.Product.html#362" class="Bound">x</a><a id="374" class="Symbol">)</a> <a id="376" class="Symbol">→</a> <a id="378" class="Symbol">(∀</a> <a id="381" class="Symbol">{</a><a id="382" href="Categories.Utils.Product.html#382" class="Bound">x</a><a id="383" class="Symbol">}</a> <a id="385" class="Symbol">→</a> <a id="387" class="Symbol">(</a><a id="388" href="Categories.Utils.Product.html#388" class="Bound">y</a> <a id="390" class="Symbol">:</a> <a id="392" href="Categories.Utils.Product.html#299" class="Bound">P</a> <a id="394" href="Categories.Utils.Product.html#382" class="Bound">x</a><a id="395" class="Symbol">)</a> <a id="397" class="Symbol">→</a> <a id="399" href="Categories.Utils.Product.html#315" class="Bound">Q</a> <a id="401" href="Categories.Utils.Product.html#388" class="Bound">y</a> <a id="403" class="Symbol">(</a><a id="404" href="Categories.Utils.Product.html#357" class="Bound">f</a> <a id="406" href="Categories.Utils.Product.html#382" class="Bound">x</a><a id="407" class="Symbol">))</a> <a id="410" class="Symbol">→</a> <a id="412" class="Symbol">(</a><a id="413" href="Categories.Utils.Product.html#413" class="Bound">v</a> <a id="415" class="Symbol">:</a> <a id="417" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="419" href="Categories.Utils.Product.html#271" class="Bound">A</a> <a id="421" href="Categories.Utils.Product.html#299" class="Bound">P</a><a id="422" class="Symbol">)</a> <a id="424" class="Symbol">→</a> <a id="426" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="428" class="Symbol">(</a><a id="429" href="Categories.Utils.Product.html#283" class="Bound">B</a> <a id="431" class="Symbol">(</a><a id="432" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="438" href="Categories.Utils.Product.html#413" class="Bound">v</a><a id="439" class="Symbol">))</a> <a id="442" class="Symbol">(</a><a id="443" href="Categories.Utils.Product.html#315" class="Bound">Q</a> <a id="445" class="Symbol">(</a><a id="446" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="452" href="Categories.Utils.Product.html#413" class="Bound">v</a><a id="453" class="Symbol">))</a>
<a id="456" href="Categories.Utils.Product.html#251" class="Function">map⁎</a> <a id="461" href="Categories.Utils.Product.html#461" class="Bound">f</a> <a id="463" href="Categories.Utils.Product.html#463" class="Bound">g</a> <a id="465" class="Symbol">(</a><a id="466" href="Categories.Utils.Product.html#466" class="Bound">x</a> <a id="468" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="470" href="Categories.Utils.Product.html#470" class="Bound">y</a><a id="471" class="Symbol">)</a> <a id="473" class="Symbol">=</a> <a id="475" class="Symbol">(</a><a id="476" href="Categories.Utils.Product.html#461" class="Bound">f</a> <a id="478" href="Categories.Utils.Product.html#466" class="Bound">x</a> <a id="480" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="482" href="Categories.Utils.Product.html#463" class="Bound">g</a> <a id="484" href="Categories.Utils.Product.html#470" class="Bound">y</a><a id="485" class="Symbol">)</a>
<a id="map⁎′"></a><a id="488" href="Categories.Utils.Product.html#488" class="Function">map⁎′</a> <a id="494" class="Symbol">:</a> <a id="496" class="Symbol">∀</a> <a id="498" class="Symbol">{</a><a id="499" href="Categories.Utils.Product.html#499" class="Bound">a</a> <a id="501" href="Categories.Utils.Product.html#501" class="Bound">b</a> <a id="503" href="Categories.Utils.Product.html#503" class="Bound">p</a> <a id="505" href="Categories.Utils.Product.html#505" class="Bound">q</a><a id="506" class="Symbol">}</a> <a id="508" class="Symbol">{</a><a id="509" href="Categories.Utils.Product.html#509" class="Bound">A</a> <a id="511" class="Symbol">:</a> <a id="513" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="517" href="Categories.Utils.Product.html#499" class="Bound">a</a><a id="518" class="Symbol">}</a> <a id="520" class="Symbol">{</a><a id="521" href="Categories.Utils.Product.html#521" class="Bound">B</a> <a id="523" class="Symbol">:</a> <a id="525" href="Categories.Utils.Product.html#509" class="Bound">A</a> <a id="527" class="Symbol">→</a> <a id="529" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="533" href="Categories.Utils.Product.html#501" class="Bound">b</a><a id="534" class="Symbol">}</a> <a id="536" class="Symbol">{</a><a id="537" href="Categories.Utils.Product.html#537" class="Bound">P</a> <a id="539" class="Symbol">:</a> <a id="541" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="545" href="Categories.Utils.Product.html#503" class="Bound">p</a><a id="546" class="Symbol">}</a> <a id="548" class="Symbol">{</a><a id="549" href="Categories.Utils.Product.html#549" class="Bound">Q</a> <a id="551" class="Symbol">:</a> <a id="553" href="Categories.Utils.Product.html#537" class="Bound">P</a> <a id="555" class="Symbol">→</a> <a id="557" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="561" href="Categories.Utils.Product.html#505" class="Bound">q</a><a id="562" class="Symbol">}</a> <a id="564" class="Symbol">→</a> <a id="566" class="Symbol">(</a><a id="567" href="Categories.Utils.Product.html#567" class="Bound">f</a> <a id="569" class="Symbol">:</a> <a id="571" class="Symbol">(</a><a id="572" href="Categories.Utils.Product.html#572" class="Bound">x</a> <a id="574" class="Symbol">:</a> <a id="576" href="Categories.Utils.Product.html#509" class="Bound">A</a><a id="577" class="Symbol">)</a> <a id="579" class="Symbol">→</a> <a id="581" href="Categories.Utils.Product.html#521" class="Bound">B</a> <a id="583" href="Categories.Utils.Product.html#572" class="Bound">x</a><a id="584" class="Symbol">)</a> <a id="586" class="Symbol">→</a> <a id="588" class="Symbol">((</a><a id="590" href="Categories.Utils.Product.html#590" class="Bound">x</a> <a id="592" class="Symbol">:</a> <a id="594" href="Categories.Utils.Product.html#537" class="Bound">P</a><a id="595" class="Symbol">)</a> <a id="597" class="Symbol">→</a> <a id="599" href="Categories.Utils.Product.html#549" class="Bound">Q</a> <a id="601" href="Categories.Utils.Product.html#590" class="Bound">x</a><a id="602" class="Symbol">)</a> <a id="604" class="Symbol">→</a> <a id="606" class="Symbol">(</a><a id="607" href="Categories.Utils.Product.html#607" class="Bound">v</a> <a id="609" class="Symbol">:</a> <a id="611" href="Categories.Utils.Product.html#509" class="Bound">A</a> <a id="613" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="615" href="Categories.Utils.Product.html#537" class="Bound">P</a><a id="616" class="Symbol">)</a> <a id="618" class="Symbol">→</a> <a id="620" href="Categories.Utils.Product.html#521" class="Bound">B</a> <a id="622" class="Symbol">(</a><a id="623" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="629" href="Categories.Utils.Product.html#607" class="Bound">v</a><a id="630" class="Symbol">)</a> <a id="632" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="634" href="Categories.Utils.Product.html#549" class="Bound">Q</a> <a id="636" class="Symbol">(</a><a id="637" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="643" href="Categories.Utils.Product.html#607" class="Bound">v</a><a id="644" class="Symbol">)</a>
<a id="646" href="Categories.Utils.Product.html#488" class="Function">map⁎′</a> <a id="652" href="Categories.Utils.Product.html#652" class="Bound">f</a> <a id="654" href="Categories.Utils.Product.html#654" class="Bound">g</a> <a id="656" class="Symbol">(</a><a id="657" href="Categories.Utils.Product.html#657" class="Bound">x</a> <a id="659" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="661" href="Categories.Utils.Product.html#661" class="Bound">y</a><a id="662" class="Symbol">)</a> <a id="664" class="Symbol">=</a> <a id="666" class="Symbol">(</a><a id="667" href="Categories.Utils.Product.html#652" class="Bound">f</a> <a id="669" href="Categories.Utils.Product.html#657" class="Bound">x</a> <a id="671" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="673" href="Categories.Utils.Product.html#654" class="Bound">g</a> <a id="675" href="Categories.Utils.Product.html#661" class="Bound">y</a><a id="676" class="Symbol">)</a>
<a id="zipWith"></a><a id="679" href="Categories.Utils.Product.html#679" class="Function">zipWith</a> <a id="687" class="Symbol">:</a> <a id="689" class="Symbol">∀</a> <a id="691" class="Symbol">{</a><a id="692" href="Categories.Utils.Product.html#692" class="Bound">a</a> <a id="694" href="Categories.Utils.Product.html#694" class="Bound">b</a> <a id="696" href="Categories.Utils.Product.html#696" class="Bound">c</a> <a id="698" href="Categories.Utils.Product.html#698" class="Bound">p</a> <a id="700" href="Categories.Utils.Product.html#700" class="Bound">q</a> <a id="702" href="Categories.Utils.Product.html#702" class="Bound">r</a> <a id="704" href="Categories.Utils.Product.html#704" class="Bound">s</a><a id="705" class="Symbol">}</a> <a id="707" class="Symbol">{</a><a id="708" href="Categories.Utils.Product.html#708" class="Bound">A</a> <a id="710" class="Symbol">:</a> <a id="712" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="716" href="Categories.Utils.Product.html#692" class="Bound">a</a><a id="717" class="Symbol">}</a> <a id="719" class="Symbol">{</a><a id="720" href="Categories.Utils.Product.html#720" class="Bound">B</a> <a id="722" class="Symbol">:</a> <a id="724" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="728" href="Categories.Utils.Product.html#694" class="Bound">b</a><a id="729" class="Symbol">}</a> <a id="731" class="Symbol">{</a><a id="732" href="Categories.Utils.Product.html#732" class="Bound">C</a> <a id="734" class="Symbol">:</a> <a id="736" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="740" href="Categories.Utils.Product.html#696" class="Bound">c</a><a id="741" class="Symbol">}</a> <a id="743" class="Symbol">{</a><a id="744" href="Categories.Utils.Product.html#744" class="Bound">P</a> <a id="746" class="Symbol">:</a> <a id="748" href="Categories.Utils.Product.html#708" class="Bound">A</a> <a id="750" class="Symbol">→</a> <a id="752" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="756" href="Categories.Utils.Product.html#698" class="Bound">p</a><a id="757" class="Symbol">}</a> <a id="759" class="Symbol">{</a><a id="760" href="Categories.Utils.Product.html#760" class="Bound">Q</a> <a id="762" class="Symbol">:</a> <a id="764" href="Categories.Utils.Product.html#720" class="Bound">B</a> <a id="766" class="Symbol">→</a> <a id="768" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="772" href="Categories.Utils.Product.html#700" class="Bound">q</a><a id="773" class="Symbol">}</a> <a id="775" class="Symbol">{</a><a id="776" href="Categories.Utils.Product.html#776" class="Bound">R</a> <a id="778" class="Symbol">:</a> <a id="780" href="Categories.Utils.Product.html#732" class="Bound">C</a> <a id="782" class="Symbol">→</a> <a id="784" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="788" href="Categories.Utils.Product.html#702" class="Bound">r</a><a id="789" class="Symbol">}</a> <a id="791" class="Symbol">{</a><a id="792" href="Categories.Utils.Product.html#792" class="Bound">S</a> <a id="794" class="Symbol">:</a> <a id="796" class="Symbol">(</a><a id="797" href="Categories.Utils.Product.html#797" class="Bound">x</a> <a id="799" class="Symbol">:</a> <a id="801" href="Categories.Utils.Product.html#732" class="Bound">C</a><a id="802" class="Symbol">)</a> <a id="804" class="Symbol">→</a> <a id="806" href="Categories.Utils.Product.html#776" class="Bound">R</a> <a id="808" href="Categories.Utils.Product.html#797" class="Bound">x</a> <a id="810" class="Symbol">→</a> <a id="812" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="816" href="Categories.Utils.Product.html#704" class="Bound">s</a><a id="817" class="Symbol">}</a> <a id="819" class="Symbol">(</a><a id="820" href="Categories.Utils.Product.html#820" class="Bound Operator">_∙_</a> <a id="824" class="Symbol">:</a> <a id="826" href="Categories.Utils.Product.html#708" class="Bound">A</a> <a id="828" class="Symbol">→</a> <a id="830" href="Categories.Utils.Product.html#720" class="Bound">B</a> <a id="832" class="Symbol">→</a> <a id="834" href="Categories.Utils.Product.html#732" class="Bound">C</a><a id="835" class="Symbol">)</a> <a id="837" class="Symbol">→</a> <a id="839" class="Symbol">(</a><a id="840" href="Categories.Utils.Product.html#840" class="Bound Operator">_∘_</a> <a id="844" class="Symbol">:</a> <a id="846" class="Symbol">∀</a> <a id="848" class="Symbol">{</a><a id="849" href="Categories.Utils.Product.html#849" class="Bound">x</a> <a id="851" href="Categories.Utils.Product.html#851" class="Bound">y</a><a id="852" class="Symbol">}</a> <a id="854" class="Symbol">→</a> <a id="856" href="Categories.Utils.Product.html#744" class="Bound">P</a> <a id="858" href="Categories.Utils.Product.html#849" class="Bound">x</a> <a id="860" class="Symbol">→</a> <a id="862" href="Categories.Utils.Product.html#760" class="Bound">Q</a> <a id="864" href="Categories.Utils.Product.html#851" class="Bound">y</a> <a id="866" class="Symbol">→</a> <a id="868" href="Categories.Utils.Product.html#776" class="Bound">R</a> <a id="870" class="Symbol">(</a><a id="871" href="Categories.Utils.Product.html#849" class="Bound">x</a> <a id="873" href="Categories.Utils.Product.html#820" class="Bound Operator">∙</a> <a id="875" href="Categories.Utils.Product.html#851" class="Bound">y</a><a id="876" class="Symbol">))</a> <a id="879" class="Symbol">→</a> <a id="881" class="Symbol">(</a><a id="882" href="Categories.Utils.Product.html#882" class="Bound Operator">_*_</a> <a id="886" class="Symbol">:</a> <a id="888" class="Symbol">(</a><a id="889" href="Categories.Utils.Product.html#889" class="Bound">x</a> <a id="891" class="Symbol">:</a> <a id="893" href="Categories.Utils.Product.html#732" class="Bound">C</a><a id="894" class="Symbol">)</a> <a id="896" class="Symbol">→</a> <a id="898" class="Symbol">(</a><a id="899" href="Categories.Utils.Product.html#899" class="Bound">y</a> <a id="901" class="Symbol">:</a> <a id="903" href="Categories.Utils.Product.html#776" class="Bound">R</a> <a id="905" href="Categories.Utils.Product.html#889" class="Bound">x</a><a id="906" class="Symbol">)</a> <a id="908" class="Symbol">→</a> <a id="910" href="Categories.Utils.Product.html#792" class="Bound">S</a> <a id="912" href="Categories.Utils.Product.html#889" class="Bound">x</a> <a id="914" href="Categories.Utils.Product.html#899" class="Bound">y</a><a id="915" class="Symbol">)</a> <a id="917" class="Symbol">→</a> <a id="919" class="Symbol">(</a><a id="920" href="Categories.Utils.Product.html#920" class="Bound">x</a> <a id="922" class="Symbol">:</a> <a id="924" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="926" href="Categories.Utils.Product.html#708" class="Bound">A</a> <a id="928" href="Categories.Utils.Product.html#744" class="Bound">P</a><a id="929" class="Symbol">)</a> <a id="931" class="Symbol">→</a> <a id="933" class="Symbol">(</a><a id="934" href="Categories.Utils.Product.html#934" class="Bound">y</a> <a id="936" class="Symbol">:</a> <a id="938" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="940" href="Categories.Utils.Product.html#720" class="Bound">B</a> <a id="942" href="Categories.Utils.Product.html#760" class="Bound">Q</a><a id="943" class="Symbol">)</a> <a id="945" class="Symbol">→</a> <a id="947" href="Categories.Utils.Product.html#792" class="Bound">S</a> <a id="949" class="Symbol">(</a><a id="950" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="956" href="Categories.Utils.Product.html#920" class="Bound">x</a> <a id="958" href="Categories.Utils.Product.html#820" class="Bound Operator">∙</a> <a id="960" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="966" href="Categories.Utils.Product.html#934" class="Bound">y</a><a id="967" class="Symbol">)</a> <a id="969" class="Symbol">(</a><a id="970" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="976" href="Categories.Utils.Product.html#920" class="Bound">x</a> <a id="978" href="Categories.Utils.Product.html#840" class="Bound Operator">∘</a> <a id="980" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="986" href="Categories.Utils.Product.html#934" class="Bound">y</a><a id="987" class="Symbol">)</a>
<a id="989" href="Categories.Utils.Product.html#679" class="Function">zipWith</a> <a id="997" href="Categories.Utils.Product.html#997" class="Bound Operator">_∙_</a> <a id="1001" href="Categories.Utils.Product.html#1001" class="Bound Operator">_∘_</a> <a id="1005" href="Categories.Utils.Product.html#1005" class="Bound Operator">_*_</a> <a id="1009" class="Symbol">(</a><a id="1010" href="Categories.Utils.Product.html#1010" class="Bound">a</a> <a id="1012" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1014" href="Categories.Utils.Product.html#1014" class="Bound">p</a><a id="1015" class="Symbol">)</a> <a id="1017" class="Symbol">(</a><a id="1018" href="Categories.Utils.Product.html#1018" class="Bound">b</a> <a id="1020" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1022" href="Categories.Utils.Product.html#1022" class="Bound">q</a><a id="1023" class="Symbol">)</a> <a id="1025" class="Symbol">=</a> <a id="1027" class="Symbol">(</a><a id="1028" href="Categories.Utils.Product.html#1010" class="Bound">a</a> <a id="1030" href="Categories.Utils.Product.html#997" class="Bound Operator">∙</a> <a id="1032" href="Categories.Utils.Product.html#1018" class="Bound">b</a><a id="1033" class="Symbol">)</a> <a id="1035" href="Categories.Utils.Product.html#1005" class="Bound Operator">*</a> <a id="1037" class="Symbol">(</a><a id="1038" href="Categories.Utils.Product.html#1014" class="Bound">p</a> <a id="1040" href="Categories.Utils.Product.html#1001" class="Bound Operator">∘</a> <a id="1042" href="Categories.Utils.Product.html#1022" class="Bound">q</a><a id="1043" class="Symbol">)</a>
<a id="1045" class="Keyword">syntax</a> <a id="1052" href="Categories.Utils.Product.html#679" class="Function">zipWith</a> <a id="1060" class="Bound">f</a> <a id="1062" class="Bound">g</a> <a id="1064" class="Bound">h</a> <a id="1066" class="Symbol">=</a> <a id="1068" class="Bound">f</a> <a id="1070" class="Function">-&lt;</a> <a id="1073" class="Bound">h</a> <a id="1075" class="Function">&gt;-</a> <a id="1078" class="Bound">g</a>
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