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Leon Vatthauer 2bf4655eae
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<html><head><meta charset="utf-8"><title>Categories.Category.Instance.Properties.Setoids.Extensive</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
<a id="37" class="Keyword">module</a> <a id="44" href="Categories.Category.Instance.Properties.Setoids.Extensive.html" class="Module">Categories.Category.Instance.Properties.Setoids.Extensive</a> <a id="102" class="Keyword">where</a>
<a id="109" class="Keyword">open</a> <a id="114" class="Keyword">import</a> <a id="121" href="Level.html" class="Module">Level</a> <a id="127" class="Keyword">using</a> <a id="133" class="Symbol">(</a><a id="134" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="139" class="Symbol">)</a>
<a id="141" class="Keyword">open</a> <a id="146" class="Keyword">import</a> <a id="153" href="Data.Product.html" class="Module">Data.Product</a> <a id="166" class="Keyword">using</a> <a id="172" class="Symbol">(</a><a id="173" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="176" class="Symbol">)</a>
<a id="178" class="Keyword">open</a> <a id="183" class="Keyword">import</a> <a id="190" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a> <a id="204" class="Symbol">as</a> <a id="207" class="Module">Sum</a> <a id="211" class="Keyword">using</a> <a id="217" class="Symbol">(</a><a id="218" href="Data.Sum.Base.html#625" class="Datatype Operator">_⊎_</a><a id="221" class="Symbol">;</a> <a id="223" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a><a id="227" class="Symbol">;</a> <a id="229" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a><a id="233" class="Symbol">)</a>
<a id="235" class="Keyword">open</a> <a id="240" class="Keyword">import</a> <a id="247" href="Data.Sum.Relation.Binary.Pointwise.html" class="Module">Data.Sum.Relation.Binary.Pointwise</a> <a id="282" class="Keyword">using</a> <a id="288" class="Symbol">(</a><a id="289" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a><a id="293" class="Symbol">;</a> <a id="295" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a><a id="299" class="Symbol">;</a> <a id="301" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">_⊎ₛ_</a><a id="305" class="Symbol">;</a> <a id="307" href="Data.Sum.Relation.Binary.Pointwise.html#1666" class="Function">drop-inj₁</a><a id="316" class="Symbol">;</a> <a id="318" href="Data.Sum.Relation.Binary.Pointwise.html#1752" class="Function">drop-inj₂</a><a id="327" class="Symbol">)</a>
<a id="329" class="Keyword">open</a> <a id="334" class="Keyword">import</a> <a id="341" href="Data.Unit.Polymorphic.html" class="Module">Data.Unit.Polymorphic</a> <a id="363" class="Keyword">using</a> <a id="369" class="Symbol">(</a><a id="370" href="Data.Unit.Polymorphic.Base.html#533" class="Function">tt</a><a id="372" class="Symbol">)</a>
<a id="374" class="Keyword">open</a> <a id="379" class="Keyword">import</a> <a id="386" href="Function.Bundles.html" class="Module">Function.Bundles</a> <a id="403" class="Keyword">using</a> <a id="409" class="Symbol">(</a><a id="410" href="Function.Bundles.html#2043" class="Record">Func</a><a id="414" class="Symbol">;</a> <a id="416" href="Function.Bundles.html#15133" class="Function Operator">_⟨$⟩_</a><a id="421" class="Symbol">)</a>
<a id="423" class="Keyword">open</a> <a id="428" class="Keyword">import</a> <a id="435" href="Function.Construct.Composition.html" class="Module">Function.Construct.Composition</a> <a id="466" class="Keyword">using</a> <a id="472" class="Symbol">(</a><a id="473" href="Function.Construct.Composition.html#5240" class="Function">function</a><a id="481" class="Symbol">)</a>
<a id="483" class="Keyword">open</a> <a id="488" class="Keyword">import</a> <a id="495" href="Function.Construct.Setoid.html" class="Module">Function.Construct.Setoid</a> <a id="521" class="Keyword">using</a> <a id="527" class="Symbol">()</a> <a id="530" class="Keyword">renaming</a> <a id="539" class="Symbol">(</a><a id="540" href="Function.Construct.Setoid.html#376" class="Function">setoid</a> <a id="547" class="Symbol">to</a> <a id="550" class="Function">_⇨_</a><a id="553" class="Symbol">)</a>
<a id="555" class="Keyword">open</a> <a id="560" class="Keyword">import</a> <a id="567" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="583" class="Keyword">using</a> <a id="589" class="Symbol">(</a><a id="590" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="596" class="Symbol">)</a>
<a id="598" class="Keyword">import</a> <a id="606" href="Relation.Binary.Reasoning.Setoid.html" class="Module">Relation.Binary.Reasoning.Setoid</a> <a id="639" class="Symbol">as</a> <a id="642" class="Module">SetoidR</a>
<a id="651" class="Keyword">open</a> <a id="656" class="Keyword">import</a> <a id="663" href="Categories.Category.html" class="Module">Categories.Category</a> <a id="683" class="Keyword">using</a> <a id="689" class="Symbol">(</a><a id="690" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="698" class="Symbol">;</a> <a id="700" href="Categories.Category.html#502" class="Function Operator">_[_,_]</a><a id="706" class="Symbol">)</a>
<a id="708" class="Keyword">open</a> <a id="713" class="Keyword">import</a> <a id="720" href="Categories.Category.Instance.Setoids.html" class="Module">Categories.Category.Instance.Setoids</a> <a id="757" class="Keyword">using</a> <a id="763" class="Symbol">(</a><a id="764" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a><a id="771" class="Symbol">)</a>
<a id="773" class="Keyword">open</a> <a id="778" class="Keyword">import</a> <a id="785" href="Categories.Category.Extensive.html" class="Module">Categories.Category.Extensive</a> <a id="815" class="Keyword">using</a> <a id="821" class="Symbol">(</a><a id="822" href="Categories.Category.Extensive.html#599" class="Record">Extensive</a><a id="831" class="Symbol">)</a>
<a id="833" class="Keyword">open</a> <a id="838" class="Keyword">import</a> <a id="845" href="Categories.Category.Cocartesian.html" class="Module">Categories.Category.Cocartesian</a> <a id="877" class="Keyword">using</a> <a id="883" class="Symbol">(</a><a id="884" href="Categories.Category.Cocartesian.html#3385" class="Record">Cocartesian</a><a id="895" class="Symbol">)</a>
<a id="897" class="Keyword">open</a> <a id="902" class="Keyword">import</a> <a id="909" href="Categories.Diagram.Pullback.html" class="Module">Categories.Diagram.Pullback</a> <a id="937" class="Keyword">using</a> <a id="943" class="Symbol">(</a><a id="944" href="Categories.Diagram.Pullback.html#2029" class="Record">Pullback</a><a id="952" class="Symbol">)</a>
<a id="954" class="Keyword">open</a> <a id="959" class="Keyword">import</a> <a id="966" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html" class="Module">Categories.Category.Instance.Properties.Setoids.Limits.Canonical</a> <a id="1031" class="Keyword">using</a> <a id="1037" class="Symbol">(</a><a id="1038" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a><a id="1046" class="Symbol">;</a> <a id="1048" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#905" class="Record">FiberProduct</a><a id="1060" class="Symbol">)</a>
<a id="1062" class="Keyword">open</a> <a id="1067" class="Keyword">import</a> <a id="1074" href="Categories.Category.Monoidal.Instance.Setoids.html" class="Module">Categories.Category.Monoidal.Instance.Setoids</a> <a id="1120" class="Keyword">using</a> <a id="1126" class="Symbol">(</a><a id="1127" href="Categories.Category.Monoidal.Instance.Setoids.html#1968" class="Function">Setoids-Cocartesian</a><a id="1146" class="Symbol">)</a>
<a id="1149" class="Keyword">open</a> <a id="1154" href="Categories.Diagram.Pullback.html#2029" class="Module">Pullback</a>
<a id="1163" class="Keyword">open</a> <a id="1168" href="Function.Bundles.html#2043" class="Module">Func</a>
<a id="1174" class="Comment">-- Note the Setoids is extensive if the two levels coincide. Whether it happens more generally</a>
<a id="1270" class="Comment">-- is unknown at this point.</a>
<a id="Setoids-Extensive"></a><a id="1300" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1300" class="Function">Setoids-Extensive</a> <a id="1318" class="Symbol">:</a> <a id="1320" class="Symbol">(</a><a id="1321" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1321" class="Bound">ℓ</a> <a id="1323" class="Symbol">:</a> <a id="1325" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="1330" class="Symbol">)</a> <a id="1332" class="Symbol">→</a> <a id="1334" href="Categories.Category.Extensive.html#599" class="Record">Extensive</a> <a id="1344" class="Symbol">(</a><a id="1345" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="1353" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1321" class="Bound">ℓ</a> <a id="1355" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1321" class="Bound">ℓ</a><a id="1356" class="Symbol">)</a>
<a id="1358" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1300" class="Function">Setoids-Extensive</a> <a id="1376" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="1378" class="Symbol">=</a> <a id="1380" class="Keyword">record</a>
<a id="1390" class="Symbol">{</a> <a id="1392" href="Categories.Category.Extensive.html#734" class="Field">cocartesian</a> <a id="1404" class="Symbol">=</a> <a id="1406" class="Keyword">record</a> <a id="1413" class="Symbol">{</a> <a id="1415" href="Categories.Category.Cocartesian.html#3437" class="Field">initial</a> <a id="1423" class="Symbol">=</a> <a id="1425" href="Categories.Category.Cocartesian.html#3437" class="Function">initial</a> <a id="1433" class="Symbol">;</a> <a id="1435" href="Categories.Category.Cocartesian.html#3462" class="Field">coproducts</a> <a id="1446" class="Symbol">=</a> <a id="1448" href="Categories.Category.Cocartesian.html#3462" class="Function">coproducts</a> <a id="1459" class="Symbol">}</a>
<a id="1464" class="Symbol">;</a> <a id="1466" href="Categories.Category.Extensive.html#847" class="Field">pullback₁</a> <a id="1476" class="Symbol">=</a> <a id="1478" class="Symbol">λ</a> <a id="1480" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1480" class="Bound">f</a> <a id="1482" class="Symbol">→</a> <a id="1484" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="1493" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="1495" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="1497" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1480" class="Bound">f</a> <a id="1499" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a>
<a id="1505" class="Symbol">;</a> <a id="1507" href="Categories.Category.Extensive.html#911" class="Field">pullback₂</a> <a id="1517" class="Symbol">=</a> <a id="1519" class="Symbol">λ</a> <a id="1521" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1521" class="Bound">f</a> <a id="1523" class="Symbol">→</a> <a id="1525" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="1534" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="1536" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="1538" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1521" class="Bound">f</a> <a id="1540" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a>
<a id="1546" class="Symbol">;</a> <a id="1548" href="Categories.Category.Extensive.html#975" class="Field">pullback-of-cp-is-cp</a> <a id="1569" class="Symbol">=</a> <a id="1571" class="Symbol">λ</a> <a id="1573" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1573" class="Bound">f</a> <a id="1575" class="Symbol">→</a> <a id="1577" class="Keyword">record</a>
<a id="1592" class="Symbol">{</a> <a id="1594" href="Categories.Object.Coproduct.html#1233" class="Field Operator">[_,_]</a> <a id="1600" class="Symbol">=</a> <a id="1602" class="Symbol">λ</a> <a id="1604" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1604" class="Bound">g</a> <a id="1606" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1606" class="Bound">h</a> <a id="1608" class="Symbol">→</a> <a id="1610" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="1617" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1573" class="Bound">f</a> <a id="1619" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1604" class="Bound">g</a> <a id="1621" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1606" class="Bound">h</a>
<a id="1631" class="Symbol">;</a> <a id="1633" href="Categories.Object.Coproduct.html#1270" class="Field">inject₁</a> <a id="1641" class="Symbol">=</a> <a id="1643" class="Symbol">λ</a> <a id="1645" class="Symbol">{</a><a id="1646" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1646" class="Bound">X</a> <a id="1648" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1648" class="Bound">g</a> <a id="1650" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1650" class="Bound">h</a> <a id="1652" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1652" class="Bound">z</a><a id="1653" class="Symbol">}</a> <a id="1655" class="Symbol">→</a> <a id="1657" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6096" class="Function">copair-inject₁</a> <a id="1672" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1573" class="Bound">f</a> <a id="1674" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1648" class="Bound">g</a> <a id="1676" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1650" class="Bound">h</a> <a id="1678" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1652" class="Bound">z</a>
<a id="1688" class="Symbol">;</a> <a id="1690" href="Categories.Object.Coproduct.html#1303" class="Field">inject₂</a> <a id="1698" class="Symbol">=</a> <a id="1700" class="Symbol">λ</a> <a id="1702" class="Symbol">{</a><a id="1703" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1703" class="Bound">X</a> <a id="1705" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1705" class="Bound">g</a> <a id="1707" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1707" class="Bound">h</a> <a id="1709" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1709" class="Bound">z</a><a id="1710" class="Symbol">}</a> <a id="1712" class="Symbol">→</a> <a id="1714" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6306" class="Function">copair-inject₂</a> <a id="1729" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1573" class="Bound">f</a> <a id="1731" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1705" class="Bound">g</a> <a id="1733" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1707" class="Bound">h</a> <a id="1735" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1709" class="Bound">z</a>
<a id="1745" class="Symbol">;</a> <a id="1747" href="Categories.Object.Coproduct.html#1336" class="Field">unique</a> <a id="1754" class="Symbol">=</a> <a id="1756" class="Symbol">λ</a> <a id="1758" class="Symbol">{</a><a id="1759" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1759" class="Bound">X</a> <a id="1761" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1761" class="Bound">u</a> <a id="1763" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1763" class="Bound">g</a> <a id="1765" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1765" class="Bound">h</a><a id="1766" class="Symbol">}</a> <a id="1768" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1768" class="Bound">feq₁</a> <a id="1773" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1773" class="Bound">feq₂</a> <a id="1778" class="Symbol">{</a><a id="1779" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1779" class="Bound">z</a><a id="1780" class="Symbol">}</a> <a id="1782" class="Symbol">→</a> <a id="1784" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7893" class="Function">copair-unique</a> <a id="1798" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1573" class="Bound">f</a> <a id="1800" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1763" class="Bound">g</a> <a id="1802" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1765" class="Bound">h</a> <a id="1804" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1761" class="Bound">u</a> <a id="1806" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1779" class="Bound">z</a> <a id="1808" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1768" class="Bound">feq₁</a> <a id="1813" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1773" class="Bound">feq₂</a>
<a id="1826" class="Symbol">}</a>
<a id="1831" class="Symbol">;</a> <a id="1833" href="Categories.Category.Extensive.html#1091" class="Field">pullback₁-is-mono</a> <a id="1851" class="Symbol">=</a> <a id="1853" class="Symbol">λ</a> <a id="1855" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1855" class="Bound">_</a> <a id="1857" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1857" class="Bound">_</a> <a id="1859" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1859" class="Bound">eq</a> <a id="1862" class="Symbol">→</a> <a id="1864" href="Data.Sum.Relation.Binary.Pointwise.html#1666" class="Function">drop-inj₁</a> <a id="1874" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1859" class="Bound">eq</a>
<a id="1880" class="Symbol">;</a> <a id="1882" href="Categories.Category.Extensive.html#1158" class="Field">pullback₂-is-mono</a> <a id="1900" class="Symbol">=</a> <a id="1902" class="Symbol">λ</a> <a id="1904" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1904" class="Bound">_</a> <a id="1906" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1906" class="Bound">_</a> <a id="1908" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1908" class="Bound">eq</a> <a id="1911" class="Symbol">→</a> <a id="1913" href="Data.Sum.Relation.Binary.Pointwise.html#1752" class="Function">drop-inj₂</a> <a id="1923" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1908" class="Bound">eq</a>
<a id="1929" class="Symbol">;</a> <a id="1931" href="Categories.Category.Extensive.html#1226" class="Field">disjoint</a> <a id="1940" class="Symbol">=</a> <a id="1942" class="Symbol">λ</a> <a id="1944" class="Symbol">{</a><a id="1945" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1945" class="Bound">A</a> <a id="1947" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1947" class="Bound">B</a><a id="1948" class="Symbol">}</a> <a id="1950" class="Symbol">→</a> <a id="1952" class="Keyword">record</a>
<a id="1967" class="Symbol">{</a> <a id="1969" href="Categories.Diagram.Pullback.html#854" class="Field">commute</a> <a id="1977" class="Symbol">=</a> <a id="1979" class="Symbol">λ</a> <a id="1981" class="Symbol">{</a> <a id="1983" class="Symbol">{()}}</a>
<a id="1997" class="Symbol">;</a> <a id="1999" href="Categories.Diagram.Pullback.html#886" class="Field">universal</a> <a id="2009" class="Symbol">=</a> <a id="2011" class="Symbol">λ</a> <a id="2013" class="Symbol">{</a><a id="2014" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2014" class="Bound">C</a> <a id="2016" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2016" class="Bound">f</a> <a id="2018" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2018" class="Bound">g</a><a id="2019" class="Symbol">}</a> <a id="2021" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2021" class="Bound">eq</a> <a id="2024" class="Symbol">→</a> <a id="2026" class="Keyword">record</a>
<a id="2044" class="Symbol">{</a> <a id="2046" href="Function.Bundles.html#2094" class="Field">to</a> <a id="2049" class="Symbol">=</a> <a id="2051" class="Symbol">λ</a> <a id="2053" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2053" class="Bound">z</a> <a id="2055" class="Symbol">→</a> <a id="2057" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2744" class="Function">conflict</a> <a id="2066" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1945" class="Bound">A</a> <a id="2068" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1947" class="Bound">B</a> <a id="2070" class="Symbol">(</a><a id="2071" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2021" class="Bound">eq</a> <a id="2074" class="Symbol">{</a><a id="2075" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2053" class="Bound">z</a><a id="2076" class="Symbol">})</a>
<a id="2090" class="Symbol">;</a> <a id="2092" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="2097" class="Symbol">=</a> <a id="2099" class="Symbol">λ</a> <a id="2101" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2101" class="Bound">z</a> <a id="2103" class="Symbol">→</a> <a id="2105" href="Data.Unit.Polymorphic.Base.html#533" class="Function">tt</a>
<a id="2119" class="Symbol">}</a>
<a id="2129" class="Symbol">;</a> <a id="2131" href="Categories.Diagram.Pullback.html#956" class="Field">unique</a> <a id="2138" class="Symbol">=</a> <a id="2140" class="Symbol">λ</a> <a id="2142" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2142" class="Bound">_</a> <a id="2144" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2144" class="Bound">_</a> <a id="2146" class="Symbol">→</a> <a id="2148" href="Data.Unit.Polymorphic.Base.html#533" class="Function">tt</a>
<a id="2159" class="Symbol">;</a> <a id="2161" href="Categories.Diagram.Pullback.html#1081" class="Field">p₁∘universal≈h₁</a> <a id="2177" class="Symbol">=</a> <a id="2179" class="Symbol">λ</a> <a id="2181" class="Symbol">{</a><a id="2182" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2182" class="Bound">_</a> <a id="2184" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2184" class="Bound">_</a> <a id="2186" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2186" class="Bound">_</a> <a id="2188" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2188" class="Bound">eq</a> <a id="2191" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2191" class="Bound">x</a><a id="2192" class="Symbol">}</a> <a id="2194" class="Symbol">→</a> <a id="2196" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2744" class="Function">conflict</a> <a id="2205" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1945" class="Bound">A</a> <a id="2207" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1947" class="Bound">B</a> <a id="2209" class="Symbol">(</a><a id="2210" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2188" class="Bound">eq</a> <a id="2213" class="Symbol">{</a><a id="2214" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2191" class="Bound">x</a><a id="2215" class="Symbol">})</a>
<a id="2226" class="Symbol">;</a> <a id="2228" href="Categories.Diagram.Pullback.html#1179" class="Field">p₂∘universal≈h₂</a> <a id="2244" class="Symbol">=</a> <a id="2246" class="Symbol">λ</a> <a id="2248" class="Symbol">{</a><a id="2249" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2249" class="Bound">_</a> <a id="2251" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2251" class="Bound">_</a> <a id="2253" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2253" class="Bound">_</a> <a id="2255" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2255" class="Bound">eq</a> <a id="2258" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2258" class="Bound">y</a><a id="2259" class="Symbol">}</a> <a id="2261" class="Symbol">→</a> <a id="2263" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2744" class="Function">conflict</a> <a id="2272" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1945" class="Bound">A</a> <a id="2274" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1947" class="Bound">B</a> <a id="2276" class="Symbol">(</a><a id="2277" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2255" class="Bound">eq</a> <a id="2280" class="Symbol">{</a><a id="2281" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2258" class="Bound">y</a><a id="2282" class="Symbol">})</a>
<a id="2293" class="Symbol">}</a>
<a id="2298" class="Symbol">}</a>
<a id="2305" class="Keyword">where</a>
<a id="2318" class="Keyword">infixr</a> <a id="2325" class="Number">9</a> <a id="2327" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">_∙_</a>
<a id="2338" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">_∙_</a> <a id="2342" class="Symbol">:</a> <a id="2344" class="Symbol">{</a><a id="2345" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2345" class="Bound">a₁</a> <a id="2348" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2348" class="Bound">a₂</a> <a id="2351" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2351" class="Bound">b₁</a> <a id="2354" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2354" class="Bound">b₂</a> <a id="2357" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2357" class="Bound">c₁</a> <a id="2360" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2360" class="Bound">c₂</a> <a id="2363" class="Symbol">:</a> <a id="2365" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="2370" class="Symbol">}</a> <a id="2372" class="Symbol">{</a><a id="2373" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2373" class="Bound">A</a> <a id="2375" class="Symbol">:</a> <a id="2377" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2384" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2345" class="Bound">a₁</a> <a id="2387" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2348" class="Bound">a₂</a><a id="2389" class="Symbol">}</a> <a id="2391" class="Symbol">{</a><a id="2392" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2392" class="Bound">B</a> <a id="2394" class="Symbol">:</a> <a id="2396" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2403" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2351" class="Bound">b₁</a> <a id="2406" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2354" class="Bound">b₂</a><a id="2408" class="Symbol">}</a>
<a id="2419" class="Symbol">{</a><a id="2420" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2420" class="Bound">C</a> <a id="2422" class="Symbol">:</a> <a id="2424" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2431" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2357" class="Bound">c₁</a> <a id="2434" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2360" class="Bound">c₂</a><a id="2436" class="Symbol">}</a> <a id="2438" class="Symbol">→</a> <a id="2440" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2445" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2392" class="Bound">B</a> <a id="2447" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2420" class="Bound">C</a> <a id="2449" class="Symbol">→</a> <a id="2451" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2456" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2373" class="Bound">A</a> <a id="2458" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2392" class="Bound">B</a> <a id="2460" class="Symbol">→</a> <a id="2462" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2467" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2373" class="Bound">A</a> <a id="2469" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2420" class="Bound">C</a>
<a id="2478" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2478" class="Bound">f</a> <a id="2480" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="2482" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2482" class="Bound">g</a> <a id="2484" class="Symbol">=</a> <a id="2486" href="Function.Construct.Composition.html#5240" class="Function">function</a> <a id="2495" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2482" class="Bound">g</a> <a id="2497" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2478" class="Bound">f</a>
<a id="2507" class="Keyword">open</a> <a id="2512" href="Categories.Category.Cocartesian.html#3385" class="Module">Cocartesian</a> <a id="2524" class="Symbol">(</a><a id="2525" href="Categories.Category.Monoidal.Instance.Setoids.html#1968" class="Function">Setoids-Cocartesian</a> <a id="2545" class="Symbol">{</a><a id="2546" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a><a id="2547" class="Symbol">}</a> <a id="2549" class="Symbol">{</a><a id="2550" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a><a id="2551" class="Symbol">})</a>
<a id="2561" class="Keyword">open</a> <a id="2566" href="Relation.Binary.Structures.html#1550" class="Module">Relation.Binary.IsEquivalence</a>
<a id="2603" class="Keyword">open</a> <a id="2608" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="2615" class="Keyword">renaming</a> <a id="2624" class="Symbol">(</a><a id="2625" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="2629" class="Symbol">to</a> <a id="2632" class="Field Operator">[_][_≈_]</a><a id="2640" class="Symbol">;</a> <a id="2642" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="2650" class="Symbol">to</a> <a id="2653" class="Field">∣_∣</a><a id="2656" class="Symbol">)</a> <a id="2658" class="Keyword">using</a> <a id="2664" class="Symbol">(</a><a id="2665" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a><a id="2678" class="Symbol">)</a>
<a id="2688" class="Comment">-- must be in the standard library. Maybe it is?</a>
<a id="2744" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2744" class="Function">conflict</a> <a id="2753" class="Symbol">:</a> <a id="2755" class="Symbol">∀</a> <a id="2757" class="Symbol">{</a><a id="2758" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2758" class="Bound">ℓ</a> <a id="2760" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2760" class="Bound">ℓ&#39;</a> <a id="2763" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2763" class="Bound">ℓ&#39;&#39;</a><a id="2766" class="Symbol">}</a> <a id="2768" class="Symbol">(</a><a id="2769" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2769" class="Bound">X</a> <a id="2771" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2771" class="Bound">Y</a> <a id="2773" class="Symbol">:</a> <a id="2775" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2782" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2758" class="Bound">ℓ</a> <a id="2784" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2760" class="Bound">ℓ&#39;</a><a id="2786" class="Symbol">)</a> <a id="2788" class="Symbol">{</a><a id="2789" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2789" class="Bound">Z</a> <a id="2791" class="Symbol">:</a> <a id="2793" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2797" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2763" class="Bound">ℓ&#39;&#39;</a><a id="2800" class="Symbol">}</a>
<a id="2811" class="Symbol">{</a><a id="2812" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2812" class="Bound">x</a> <a id="2814" class="Symbol">:</a> <a id="2816" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="2818" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2769" class="Bound">X</a> <a id="2820" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="2821" class="Symbol">}</a> <a id="2823" class="Symbol">{</a><a id="2824" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2824" class="Bound">y</a> <a id="2826" class="Symbol">:</a> <a id="2828" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="2830" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2771" class="Bound">Y</a> <a id="2832" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="2833" class="Symbol">}</a> <a id="2835" class="Symbol">→</a> <a id="2837" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="2839" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2769" class="Bound">X</a> <a id="2841" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="2844" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2771" class="Bound">Y</a> <a id="2846" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="2849" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="2854" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2812" class="Bound">x</a> <a id="2856" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="2858" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="2863" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2824" class="Bound">y</a> <a id="2865" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="2867" class="Symbol">→</a> <a id="2869" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2789" class="Bound">Z</a>
<a id="2878" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2744" class="Function">conflict</a> <a id="2887" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2887" class="Bound">X</a> <a id="2889" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2889" class="Bound">Y</a> <a id="2891" class="Symbol">()</a>
<a id="2902" class="Keyword">module</a> <a id="2909" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2909" class="Module">Diagram</a> <a id="2917" class="Symbol">{</a><a id="2918" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2918" class="Bound">A</a> <a id="2920" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2920" class="Bound">B</a> <a id="2922" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="2924" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="2926" class="Symbol">:</a> <a id="2928" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2935" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="2937" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a><a id="2938" class="Symbol">}</a> <a id="2940" class="Symbol">(</a><a id="2941" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="2943" class="Symbol">:</a> <a id="2945" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2950" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="2952" class="Symbol">(</a><a id="2953" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2918" class="Bound">A</a> <a id="2955" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="2958" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2920" class="Bound">B</a><a id="2959" class="Symbol">))</a>
<a id="2971" class="Symbol">(</a><a id="2972" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="2974" class="Symbol">:</a> <a id="2976" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2981" class="Symbol">(</a><a id="2982" href="Categories.Diagram.Pullback.html#2099" class="Field">P</a> <a id="2984" class="Symbol">(</a><a id="2985" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="2994" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="2996" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="2998" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="3000" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="3002" class="Symbol">))</a> <a id="3005" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a><a id="3006" class="Symbol">)</a> <a id="3008" class="Symbol">(</a><a id="3009" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="3011" class="Symbol">:</a> <a id="3013" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="3018" class="Symbol">(</a><a id="3019" href="Categories.Diagram.Pullback.html#2099" class="Field">P</a> <a id="3021" class="Symbol">(</a><a id="3022" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="3031" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="3033" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="3035" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="3037" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a><a id="3039" class="Symbol">))</a> <a id="3042" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a><a id="3043" class="Symbol">)</a> <a id="3045" class="Keyword">where</a>
<a id="3061" class="Keyword">private</a>
<a id="3080" class="Keyword">module</a> <a id="3087" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3087" class="Module">A</a> <a id="3089" class="Symbol">=</a> <a id="3091" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="3098" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2918" class="Bound">A</a>
<a id="3111" class="Keyword">module</a> <a id="3118" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3118" class="Module">B</a> <a id="3120" class="Symbol">=</a> <a id="3122" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="3129" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2920" class="Bound">B</a>
<a id="3142" class="Keyword">module</a> <a id="3149" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3149" class="Module">C</a> <a id="3151" class="Symbol">=</a> <a id="3153" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="3160" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a>
<a id="3173" class="Keyword">module</a> <a id="3180" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3180" class="Module">X</a> <a id="3182" class="Symbol">=</a> <a id="3184" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="3191" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a>
<a id="3204" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3204" class="Function">A⊎B</a> <a id="3208" class="Symbol">=</a> <a id="3210" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2918" class="Bound">A</a> <a id="3212" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="3215" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2920" class="Bound">B</a>
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<a id="3593" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3593" class="Bound">f₁</a> <a id="3596" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="3599" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3599" class="Bound">f₂</a> <a id="3602" class="Symbol">=</a> <a id="3604" class="Keyword">record</a>
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<a id="5703" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5703" class="Function">f⟨$⟩-cong</a> <a id="5713" class="Symbol">:</a> <a id="5715" class="Symbol">{</a><a id="5716" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5716" class="Bound">i</a> <a id="5718" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5718" class="Bound">j</a> <a id="5720" class="Symbol">:</a> <a id="5722" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="5724" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="5726" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="5727" class="Symbol">}</a> <a id="5729" class="Symbol">→</a> <a id="5731" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5716" class="Bound">i</a> <a id="5733" href="Relation.Binary.Bundles.html#1169" class="Function Operator">C.≈</a> <a id="5737" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5718" class="Bound">j</a> <a id="5739" class="Symbol">→</a> <a id="5741" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="5743" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3269" class="Function">A′</a> <a id="5746" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="5749" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3307" class="Function">B′</a> <a id="5752" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="5755" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4310" class="Function">f⟨$⟩→</a> <a id="5761" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5716" class="Bound">i</a> <a id="5763" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="5765" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4310" class="Function">f⟨$⟩→</a> <a id="5771" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5718" class="Bound">j</a> <a id="5773" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a>
<a id="5784" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5703" class="Function">f⟨$⟩-cong</a> <a id="5794" class="Symbol">{</a><a id="5795" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5795" class="Bound">i</a><a id="5796" class="Symbol">}</a> <a id="5798" class="Symbol">{</a><a id="5799" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5799" class="Bound">j</a><a id="5800" class="Symbol">}</a> <a id="5802" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5802" class="Bound">i≈j</a> <a id="5806" class="Symbol">=</a> <a id="5808" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4401" class="Function">f⟨$⟩-cong′</a> <a id="5819" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5802" class="Bound">i≈j</a> <a id="5823" class="Symbol">(</a><a id="5824" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="5826" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="5830" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5795" class="Bound">i</a><a id="5831" class="Symbol">)</a> <a id="5833" class="Symbol">(</a><a id="5834" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="5836" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="5840" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5799" class="Bound">j</a><a id="5841" class="Symbol">)</a> <a id="5843" href="Relation.Binary.Structures.html#1596" class="Function">A⊎B.refl</a> <a id="5852" href="Relation.Binary.Structures.html#1596" class="Function">A⊎B.refl</a>
<a id="5871" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5871" class="Function">f⟨$⟩</a> <a id="5876" class="Symbol">:</a> <a id="5878" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="5883" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="5885" class="Symbol">(</a><a id="5886" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3269" class="Function">A′</a> <a id="5889" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="5892" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3307" class="Function">B′</a><a id="5894" class="Symbol">)</a>
<a id="5905" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5871" class="Function">f⟨$⟩</a> <a id="5910" class="Symbol">=</a> <a id="5912" class="Keyword">record</a> <a id="5919" class="Symbol">{</a> <a id="5921" href="Function.Bundles.html#2094" class="Field">to</a> <a id="5924" class="Symbol">=</a> <a id="5926" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4310" class="Function">f⟨$⟩→</a> <a id="5932" class="Symbol">;</a> <a id="5934" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="5939" class="Symbol">=</a> <a id="5941" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5703" class="Function">f⟨$⟩-cong</a> <a id="5951" class="Symbol">}</a>
<a id="5963" class="Comment">-- copairing of g : A′ → X and h : B′ → X, resulting in C → X</a>
<a id="6034" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6041" class="Symbol">:</a> <a id="6043" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="6048" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="6050" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a>
<a id="6061" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6068" class="Symbol">=</a> <a id="6070" class="Symbol">(</a><a id="6071" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6073" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="6076" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a><a id="6077" class="Symbol">)</a> <a id="6079" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="6081" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#5871" class="Function">f⟨$⟩</a>
<a id="6096" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6096" class="Function">copair-inject₁</a> <a id="6111" class="Symbol">:</a> <a id="6113" class="Symbol">(</a><a id="6114" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6114" class="Bound">z</a> <a id="6116" class="Symbol">:</a> <a id="6118" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#905" class="Record">FiberProduct</a> <a id="6131" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6133" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="6135" class="Symbol">)</a> <a id="6137" class="Symbol">→</a> <a id="6139" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6141" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="6143" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6146" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6153" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6157" class="Symbol">(</a><a id="6158" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">FiberProduct.elem₁</a> <a id="6177" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6114" class="Bound">z</a><a id="6178" class="Symbol">)</a> <a id="6180" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6182" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6184" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6188" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6114" class="Bound">z</a> <a id="6190" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a>
<a id="6201" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6096" class="Function">copair-inject₁</a> <a id="6216" class="Keyword">record</a> <a id="6223" class="Symbol">{</a> <a id="6225" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">elem₁</a> <a id="6231" class="Symbol">=</a> <a id="6233" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6233" class="Bound">z</a> <a id="6235" class="Symbol">;</a> <a id="6237" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1048" class="Field">elem₂</a> <a id="6243" class="Symbol">=</a> <a id="6245" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6245" class="Bound">x</a> <a id="6247" class="Symbol">;</a> <a id="6249" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1070" class="Field">commute</a> <a id="6257" class="Symbol">=</a> <a id="6259" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6259" class="Bound">eq</a> <a id="6262" class="Symbol">}</a> <a id="6264" class="Symbol">=</a> <a id="6266" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="6271" class="Symbol">(</a><a id="6272" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6274" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="6277" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a><a id="6278" class="Symbol">)</a> <a id="6280" class="Symbol">(</a><a id="6281" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4015" class="Function">to-⊎ₛ-cong</a> <a id="6292" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6259" class="Bound">eq</a><a id="6294" class="Symbol">)</a>
<a id="6306" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6306" class="Function">copair-inject₂</a> <a id="6321" class="Symbol">:</a> <a id="6323" class="Symbol">(</a><a id="6324" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6324" class="Bound">z</a> <a id="6326" class="Symbol">:</a> <a id="6328" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#905" class="Record">FiberProduct</a> <a id="6341" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6343" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a><a id="6345" class="Symbol">)</a> <a id="6347" class="Symbol">→</a> <a id="6349" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6351" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="6353" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6356" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6363" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6367" class="Symbol">(</a><a id="6368" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">FiberProduct.elem₁</a> <a id="6387" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6324" class="Bound">z</a><a id="6388" class="Symbol">)</a> <a id="6390" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6392" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="6394" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6398" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6324" class="Bound">z</a> <a id="6400" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a>
<a id="6411" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6306" class="Function">copair-inject₂</a> <a id="6426" class="Keyword">record</a> <a id="6433" class="Symbol">{</a> <a id="6435" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">elem₁</a> <a id="6441" class="Symbol">=</a> <a id="6443" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6443" class="Bound">z</a> <a id="6445" class="Symbol">;</a> <a id="6447" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1048" class="Field">elem₂</a> <a id="6453" class="Symbol">=</a> <a id="6455" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6455" class="Bound">y</a> <a id="6457" class="Symbol">;</a> <a id="6459" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1070" class="Field">commute</a> <a id="6467" class="Symbol">=</a> <a id="6469" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6469" class="Bound">eq</a> <a id="6472" class="Symbol">}</a> <a id="6474" class="Symbol">=</a> <a id="6476" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="6481" class="Symbol">(</a><a id="6482" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6484" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="6487" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a><a id="6488" class="Symbol">)</a> <a id="6490" class="Symbol">(</a><a id="6491" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4015" class="Function">to-⊎ₛ-cong</a> <a id="6502" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6469" class="Bound">eq</a><a id="6504" class="Symbol">)</a>
<a id="6516" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6516" class="Function">copair-unique′</a> <a id="6531" class="Symbol">:</a> <a id="6533" class="Symbol">(</a><a id="6534" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6534" class="Bound">u</a> <a id="6536" class="Symbol">:</a> <a id="6538" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="6543" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="6545" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a><a id="6546" class="Symbol">)</a> <a id="6548" class="Symbol">(</a><a id="6549" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6549" class="Bound">z</a> <a id="6551" class="Symbol">:</a> <a id="6553" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="6555" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="6557" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="6558" class="Symbol">)</a> <a id="6560" class="Symbol">→</a>
<a id="6573" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6575" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3269" class="Function">A′</a> <a id="6578" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#550" class="Function Operator">⇨</a> <a id="6580" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="6582" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6585" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6534" class="Bound">u</a> <a id="6587" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="6589" href="Categories.Diagram.Pullback.html#2112" class="Field">p₁</a> <a id="6592" class="Symbol">(</a><a id="6593" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="6602" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="6604" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="6606" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6608" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="6610" class="Symbol">)</a> <a id="6612" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6614" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6616" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="6618" class="Symbol">→</a>
<a id="6631" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6633" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3307" class="Function">B′</a> <a id="6636" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#550" class="Function Operator">⇨</a> <a id="6638" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="6640" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6643" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6534" class="Bound">u</a> <a id="6645" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="6647" href="Categories.Diagram.Pullback.html#2112" class="Field">p₁</a> <a id="6650" class="Symbol">(</a><a id="6651" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="6660" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="6662" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="6664" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6666" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a><a id="6668" class="Symbol">)</a> <a id="6670" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6672" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="6674" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="6676" class="Symbol">→</a>
<a id="6689" class="Symbol">(</a><a id="6690" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6690" class="Bound">w</a> <a id="6692" class="Symbol">:</a> <a id="6694" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="6696" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3204" class="Function">A⊎B</a> <a id="6700" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="6701" class="Symbol">)</a> <a id="6703" class="Symbol">→</a> <a id="6705" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6707" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3204" class="Function">A⊎B</a> <a id="6711" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6714" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6716" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6720" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6549" class="Bound">z</a> <a id="6722" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6724" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6690" class="Bound">w</a> <a id="6726" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="6728" class="Symbol">→</a>
<a id="6741" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="6743" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="6745" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="6748" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6755" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6759" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6549" class="Bound">z</a> <a id="6761" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="6763" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6534" class="Bound">u</a> <a id="6765" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6769" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6549" class="Bound">z</a> <a id="6771" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a>
<a id="6782" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6516" class="Function">copair-unique′</a> <a id="6797" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6797" class="Bound">u</a> <a id="6799" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="6801" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6801" class="Bound">feq₁</a> <a id="6806" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6806" class="Bound">feq₂</a> <a id="6811" class="Symbol">(</a><a id="6812" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="6817" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6817" class="Bound">x</a><a id="6818" class="Symbol">)</a> <a id="6820" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6820" class="Bound">fz≈w</a> <a id="6825" class="Symbol">=</a> <a id="6827" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">XR.begin</a>
<a id="6847" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="6854" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6858" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="6891" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="6897" href="Relation.Binary.Structures.html#1596" class="Function">X.refl</a> <a id="6904" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="6917" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6919" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="6922" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="6924" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6928" class="Symbol">(</a><a id="6929" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3747" class="Function">to-⊎ₛ</a> <a id="6935" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="6937" class="Symbol">(</a><a id="6938" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="6940" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="6944" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a><a id="6945" class="Symbol">)</a> <a id="6947" href="Relation.Binary.Structures.html#1596" class="Function">A⊎B.refl</a><a id="6955" class="Symbol">)</a> <a id="6961" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="6967" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="6972" class="Symbol">(</a><a id="6973" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="6975" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="6978" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a><a id="6979" class="Symbol">)</a> <a id="6981" class="Symbol">(</a><a id="6982" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4015" class="Function">to-⊎ₛ-cong</a> <a id="6993" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6820" class="Bound">fz≈w</a><a id="6997" class="Symbol">)</a> <a id="6999" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7012" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7014" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="7017" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="7019" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7023" class="Symbol">(</a><a id="7024" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3747" class="Function">to-⊎ₛ</a> <a id="7030" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="7032" class="Symbol">(</a><a id="7033" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="7038" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6817" class="Bound">x</a><a id="7039" class="Symbol">)</a> <a id="7041" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6820" class="Bound">fz≈w</a><a id="7045" class="Symbol">)</a> <a id="7055" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7061" href="Relation.Binary.Structures.html#1596" class="Function">X.refl</a> <a id="7068" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7081" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7083" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7087" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7281" class="Function">fb</a> <a id="7125" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7131" href="Relation.Binary.Structures.html#1200" class="Function">X.sym</a> <a id="7137" class="Symbol">(</a><a id="7138" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6801" class="Bound">feq₁</a> <a id="7143" class="Symbol">{</a><a id="7144" class="Argument">x</a> <a id="7146" class="Symbol">=</a> <a id="7148" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7281" class="Function">fb</a><a id="7150" class="Symbol">})</a> <a id="7153" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7166" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6797" class="Bound">u</a> <a id="7168" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7172" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="7210" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">XR.∎</a>
<a id="7227" class="Keyword">where</a>
<a id="7246" class="Keyword">module</a> <a id="7253" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7253" class="Module">XR</a> <a id="7256" class="Symbol">=</a> <a id="7258" href="Relation.Binary.Reasoning.Setoid.html" class="Module">SetoidR</a> <a id="7266" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a>
<a id="7281" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7281" class="Function">fb</a> <a id="7284" class="Symbol">=</a> <a id="7286" class="Keyword">record</a> <a id="7293" class="Symbol">{</a><a id="7294" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">elem₁</a> <a id="7300" class="Symbol">=</a> <a id="7302" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6799" class="Bound">z</a> <a id="7304" class="Symbol">;</a> <a id="7306" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1048" class="Field">elem₂</a> <a id="7312" class="Symbol">=</a> <a id="7314" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6817" class="Bound">x</a><a id="7315" class="Symbol">;</a> <a id="7317" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1070" class="Field">commute</a> <a id="7325" class="Symbol">=</a> <a id="7327" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6820" class="Bound">fz≈w</a> <a id="7332" class="Symbol">}</a>
<a id="7343" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6516" class="Function">copair-unique′</a> <a id="7358" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7358" class="Bound">u</a> <a id="7360" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7362" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7362" class="Bound">feq₁</a> <a id="7367" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7367" class="Bound">feq₂</a> <a id="7372" class="Symbol">(</a><a id="7373" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="7378" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7378" class="Bound">y</a><a id="7379" class="Symbol">)</a> <a id="7381" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7381" class="Bound">fz≈w</a> <a id="7386" class="Symbol">=</a> <a id="7388" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">XR.begin</a>
<a id="7408" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="7415" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7419" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7452" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7458" href="Relation.Binary.Structures.html#1596" class="Function">X.refl</a> <a id="7465" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7478" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7480" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="7483" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="7485" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7489" class="Symbol">(</a><a id="7490" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3747" class="Function">to-⊎ₛ</a> <a id="7496" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7498" class="Symbol">(</a><a id="7499" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="7501" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7505" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a><a id="7506" class="Symbol">)</a> <a id="7508" href="Relation.Binary.Structures.html#1596" class="Function">A⊎B.refl</a><a id="7516" class="Symbol">)</a> <a id="7522" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7528" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="7533" class="Symbol">(</a><a id="7534" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7536" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="7539" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a><a id="7540" class="Symbol">)</a> <a id="7542" class="Symbol">(</a><a id="7543" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#4015" class="Function">to-⊎ₛ-cong</a> <a id="7554" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7381" class="Bound">fz≈w</a><a id="7558" class="Symbol">)</a> <a id="7560" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7573" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7575" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3437" class="Function Operator">⊎⟶</a> <a id="7578" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="7580" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7584" class="Symbol">(</a><a id="7585" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3747" class="Function">to-⊎ₛ</a> <a id="7591" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7593" class="Symbol">(</a><a id="7594" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="7599" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7378" class="Bound">y</a><a id="7600" class="Symbol">)</a> <a id="7602" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7381" class="Bound">fz≈w</a><a id="7606" class="Symbol">)</a> <a id="7616" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7622" href="Relation.Binary.Structures.html#1596" class="Function">X.refl</a> <a id="7629" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7642" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="7644" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7648" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7830" class="Function">fb</a> <a id="7686" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">XR.≈⟨</a> <a id="7692" href="Relation.Binary.Structures.html#1200" class="Function">X.sym</a> <a id="7698" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7367" class="Bound">feq₂</a> <a id="7703" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="7716" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7358" class="Bound">u</a> <a id="7718" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="7722" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7760" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">XR.∎</a>
<a id="7776" class="Keyword">where</a>
<a id="7795" class="Keyword">module</a> <a id="7802" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7802" class="Module">XR</a> <a id="7805" class="Symbol">=</a> <a id="7807" href="Relation.Binary.Reasoning.Setoid.html" class="Module">SetoidR</a> <a id="7815" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a>
<a id="7830" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7830" class="Function">fb</a> <a id="7833" class="Symbol">=</a> <a id="7835" class="Keyword">record</a> <a id="7842" class="Symbol">{</a><a id="7843" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1026" class="Field">elem₁</a> <a id="7849" class="Symbol">=</a> <a id="7851" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7360" class="Bound">z</a> <a id="7853" class="Symbol">;</a> <a id="7855" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1048" class="Field">elem₂</a> <a id="7861" class="Symbol">=</a> <a id="7863" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7378" class="Bound">y</a><a id="7864" class="Symbol">;</a> <a id="7866" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1070" class="Field">commute</a> <a id="7874" class="Symbol">=</a> <a id="7876" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7381" class="Bound">fz≈w</a> <a id="7881" class="Symbol">}</a>
<a id="7893" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7893" class="Function">copair-unique</a> <a id="7907" class="Symbol">:</a> <a id="7909" class="Symbol">(</a><a id="7910" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7910" class="Bound">u</a> <a id="7912" class="Symbol">:</a> <a id="7914" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="7919" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="7921" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a><a id="7922" class="Symbol">)</a> <a id="7924" class="Symbol">(</a><a id="7925" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7925" class="Bound">z</a> <a id="7927" class="Symbol">:</a> <a id="7929" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a> <a id="7931" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2922" class="Bound">C</a> <a id="7933" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2653" class="Field Operator">∣</a><a id="7934" class="Symbol">)</a> <a id="7936" class="Symbol">→</a>
<a id="7949" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="7951" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3269" class="Function">A′</a> <a id="7954" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#550" class="Function Operator">⇨</a> <a id="7956" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="7958" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="7961" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7910" class="Bound">u</a> <a id="7963" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="7965" href="Categories.Diagram.Pullback.html#2112" class="Field">p₁</a> <a id="7968" class="Symbol">(</a><a id="7969" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="7978" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="7980" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="7982" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="7984" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="7986" class="Symbol">)</a> <a id="7988" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="7990" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2972" class="Bound">g</a> <a id="7992" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="7994" class="Symbol">→</a>
<a id="8007" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="8009" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3307" class="Function">B′</a> <a id="8012" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#550" class="Function Operator">⇨</a> <a id="8014" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="8016" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="8019" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7910" class="Bound">u</a> <a id="8021" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2338" class="Function Operator">∙</a> <a id="8023" href="Categories.Diagram.Pullback.html#2112" class="Field">p₁</a> <a id="8026" class="Symbol">(</a><a id="8027" href="Categories.Category.Instance.Properties.Setoids.Limits.Canonical.html#1320" class="Function">pullback</a> <a id="8036" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="8038" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#1376" class="Bound">ℓ</a> <a id="8040" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="8042" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a><a id="8044" class="Symbol">)</a> <a id="8046" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="8048" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#3009" class="Bound">h</a> <a id="8050" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a> <a id="8052" class="Symbol">→</a>
<a id="8065" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">[</a> <a id="8067" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2924" class="Bound">X</a> <a id="8069" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">][</a> <a id="8072" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6034" class="Function">copair</a> <a id="8079" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="8083" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7925" class="Bound">z</a> <a id="8085" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">≈</a> <a id="8087" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7910" class="Bound">u</a> <a id="8089" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="8093" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7925" class="Bound">z</a> <a id="8095" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2632" class="Field Operator">]</a>
<a id="8106" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#7893" class="Function">copair-unique</a> <a id="8120" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8120" class="Bound">u</a> <a id="8122" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8122" class="Bound">z</a> <a id="8124" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8124" class="Bound">feq₁</a> <a id="8129" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8129" class="Bound">feq₂</a> <a id="8134" class="Symbol">=</a> <a id="8136" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#6516" class="Function">copair-unique′</a> <a id="8151" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8120" class="Bound">u</a> <a id="8153" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8122" class="Bound">z</a> <a id="8155" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8124" class="Bound">feq₁</a> <a id="8160" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8129" class="Bound">feq₂</a> <a id="8165" class="Symbol">(</a><a id="8166" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2941" class="Bound">f</a> <a id="8168" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="8172" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#8122" class="Bound">z</a><a id="8173" class="Symbol">)</a> <a id="8175" href="Relation.Binary.Structures.html#1596" class="Function">A⊎B.refl</a>
<a id="8192" class="Keyword">open</a> <a id="8197" href="Categories.Category.Instance.Properties.Setoids.Extensive.html#2909" class="Module">Diagram</a>
</pre></body></html>
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