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<html><head><meta charset="utf-8"><title>Categories.Category.Instance.Properties.Setoids.CCC</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.CCC.html" class="Module">Categories.Category.Instance.Properties.Setoids.CCC</a> <a id="96" class="Keyword">where</a>
<a id="103" class="Keyword">open</a> <a id="108" class="Keyword">import</a> <a id="115" href="Level.html" class="Module">Level</a>
<a id="121" class="Keyword">open</a> <a id="126" class="Keyword">import</a> <a id="133" href="Data.Product.html" class="Module">Data.Product</a> <a id="146" class="Keyword">using</a> <a id="152" class="Symbol">(</a><a id="153" href="Agda.Builtin.Sigma.html#165" class="Record">Σ</a> <a id="155" class="Symbol">;</a> <a id="157" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="160" class="Symbol">)</a>
<a id="162" class="Keyword">open</a> <a id="167" class="Keyword">import</a> <a id="174" href="Function.Bundles.html" class="Module">Function.Bundles</a> <a id="191" class="Keyword">using</a> <a id="197" class="Symbol">(</a><a id="198" href="Function.Bundles.html#2043" class="Record">Func</a><a id="202" class="Symbol">;</a> <a id="204" href="Function.Bundles.html#15133" class="Function Operator">_⟨$⟩_</a><a id="209" class="Symbol">)</a>
<a id="211" class="Keyword">open</a> <a id="216" class="Keyword">import</a> <a id="223" href="Function.Construct.Setoid.html" class="Module">Function.Construct.Setoid</a> <a id="249" class="Keyword">using</a> <a id="255" class="Symbol">(</a><a id="256" href="Function.Construct.Setoid.html#376" class="Function">setoid</a><a id="262" class="Symbol">)</a>
<a id="264" class="Keyword">open</a> <a id="269" class="Keyword">import</a> <a id="276" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="292" class="Keyword">using</a> <a id="298" class="Symbol">(</a><a id="299" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="305" class="Symbol">)</a>
<a id="308" class="Keyword">open</a> <a id="313" class="Keyword">import</a> <a id="320" href="Categories.Category.Core.html" class="Module">Categories.Category.Core</a> <a id="345" class="Keyword">using</a> <a id="351" class="Symbol">(</a><a id="352" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="360" class="Symbol">)</a>
<a id="362" class="Keyword">open</a> <a id="367" class="Keyword">import</a> <a id="374" href="Categories.Category.BinaryProducts.html" class="Module">Categories.Category.BinaryProducts</a> <a id="409" class="Keyword">using</a> <a id="415" class="Symbol">(</a><a id="416" href="Categories.Category.BinaryProducts.html#848" class="Record">BinaryProducts</a><a id="430" class="Symbol">)</a>
<a id="432" class="Keyword">open</a> <a id="437" class="Keyword">import</a> <a id="444" href="Categories.Category.CartesianClosed.html" class="Module">Categories.Category.CartesianClosed</a> <a id="480" class="Keyword">using</a> <a id="486" class="Symbol">(</a><a id="487" href="Categories.Category.CartesianClosed.html#1233" class="Record">CartesianClosed</a><a id="502" class="Symbol">)</a>
<a id="504" class="Keyword">open</a> <a id="509" class="Keyword">import</a> <a id="516" href="Categories.Category.CartesianClosed.Canonical.html" class="Module">Categories.Category.CartesianClosed.Canonical</a> <a id="562" class="Keyword">renaming</a> <a id="571" class="Symbol">(</a><a id="572" href="Categories.Category.CartesianClosed.Canonical.html#1539" class="Record">CartesianClosed</a> <a id="588" class="Symbol">to</a> <a id="591" class="Record">CCartesianClosed</a><a id="607" class="Symbol">)</a>
<a id="609" class="Keyword">open</a> <a id="614" class="Keyword">import</a> <a id="621" href="Categories.Category.Monoidal.Instance.Setoids.html" class="Module">Categories.Category.Monoidal.Instance.Setoids</a> <a id="667" class="Keyword">using</a> <a id="673" class="Symbol">(</a><a id="674" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a><a id="691" class="Symbol">)</a>
<a id="693" class="Keyword">open</a> <a id="698" class="Keyword">import</a> <a id="705" href="Categories.Category.Instance.Setoids.html" class="Module">Categories.Category.Instance.Setoids</a> <a id="742" class="Keyword">using</a> <a id="748" class="Symbol">(</a><a id="749" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a><a id="756" class="Symbol">)</a>
<a id="758" class="Keyword">open</a> <a id="763" class="Keyword">import</a> <a id="770" href="Categories.Object.Terminal.html" class="Module">Categories.Object.Terminal</a> <a id="797" class="Keyword">using</a> <a id="803" class="Symbol">(</a><a id="804" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a><a id="812" class="Symbol">)</a>
<a id="815" class="Keyword">module</a> <a id="822" href="Categories.Category.Instance.Properties.Setoids.CCC.html#822" class="Module">_</a> <a id="824" href="Categories.Category.Instance.Properties.Setoids.CCC.html#824" class="Bound">ℓ</a> <a id="826" class="Keyword">where</a>
<a id="834" class="Keyword">private</a>
<a id="846" href="Categories.Category.Instance.Properties.Setoids.CCC.html#846" class="Function">S</a> <a id="848" class="Symbol">=</a> <a id="850" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="858" href="Categories.Category.Instance.Properties.Setoids.CCC.html#824" class="Bound">ℓ</a> <a id="860" href="Categories.Category.Instance.Properties.Setoids.CCC.html#824" class="Bound">ℓ</a>
<a id="866" class="Keyword">module</a> <a id="873" href="Categories.Category.Instance.Properties.Setoids.CCC.html#873" class="Module">S</a> <a id="875" class="Symbol">=</a> <a id="877" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="886" href="Categories.Category.Instance.Properties.Setoids.CCC.html#846" class="Function">S</a>
<a id="891" href="Categories.Category.Instance.Properties.Setoids.CCC.html#891" class="Function">Setoids-Canonical</a> <a id="909" class="Symbol">:</a> <a id="911" href="Categories.Category.Instance.Properties.Setoids.CCC.html#591" class="Record">CCartesianClosed</a> <a id="928" href="Categories.Category.Instance.Properties.Setoids.CCC.html#846" class="Function">S</a>
<a id="932" href="Categories.Category.Instance.Properties.Setoids.CCC.html#891" class="Function">Setoids-Canonical</a> <a id="950" class="Symbol">=</a> <a id="952" class="Keyword">record</a>
<a id="963" class="Symbol">{</a> <a id="965" href="Categories.Category.CartesianClosed.Canonical.html#1671" class="Field">⊤</a> <a id="978" class="Symbol">=</a> <a id="980" href="Categories.Object.Terminal.html#905" class="Function">⊤</a>
<a id="986" class="Symbol">;</a> <a id="988" href="Categories.Category.CartesianClosed.Canonical.html#1686" class="Field Operator">_×_</a> <a id="1001" class="Symbol">=</a> <a id="1003" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">_×_</a>
<a id="1011" class="Symbol">;</a> <a id="1013" href="Categories.Category.CartesianClosed.Canonical.html#1714" class="Field">!</a> <a id="1026" class="Symbol">=</a> <a id="1028" href="Categories.Object.Terminal.html#577" class="Function">!</a>
<a id="1034" class="Symbol">;</a> <a id="1036" href="Categories.Category.CartesianClosed.Canonical.html#1732" class="Field">π₁</a> <a id="1049" class="Symbol">=</a> <a id="1051" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a>
<a id="1058" class="Symbol">;</a> <a id="1060" href="Categories.Category.CartesianClosed.Canonical.html#1754" class="Field">π₂</a> <a id="1073" class="Symbol">=</a> <a id="1075" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a>
<a id="1082" class="Symbol">;</a> <a id="1084" href="Categories.Category.CartesianClosed.Canonical.html#1776" class="Field Operator">⟨_,_⟩</a> <a id="1097" class="Symbol">=</a> <a id="1099" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨_,_⟩</a>
<a id="1109" class="Symbol">;</a> <a id="1111" href="Categories.Category.CartesianClosed.Canonical.html#1815" class="Field">!-unique</a> <a id="1124" class="Symbol">=</a> <a id="1126" href="Categories.Object.Terminal.html#605" class="Function">!-unique</a>
<a id="1139" class="Symbol">;</a> <a id="1141" href="Categories.Category.CartesianClosed.Canonical.html#1851" class="Field">π₁-comp</a> <a id="1154" class="Symbol">=</a> <a id="1156" class="Symbol">λ</a> <a id="1158" class="Symbol">{</a><a id="1159" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1159" class="Bound">_</a> <a id="1161" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1161" class="Bound">_</a> <a id="1163" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1163" class="Bound">f</a> <a id="1165" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1165" class="Bound">_</a> <a id="1167" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1167" class="Bound">g</a><a id="1168" class="Symbol">}</a> <a id="1170" class="Symbol">→</a> <a id="1172" href="Categories.Object.Product.Core.html#603" class="Function">project₁</a> <a id="1181" class="Symbol">{</a><a id="1182" class="Argument">h</a> <a id="1184" class="Symbol">=</a> <a id="1186" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1163" class="Bound">f</a><a id="1187" class="Symbol">}</a> <a id="1189" class="Symbol">{</a><a id="1190" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1167" class="Bound">g</a><a id="1191" class="Symbol">}</a>
<a id="1197" class="Symbol">;</a> <a id="1199" href="Categories.Category.CartesianClosed.Canonical.html#1885" class="Field">π₂-comp</a> <a id="1212" class="Symbol">=</a> <a id="1214" class="Symbol">λ</a> <a id="1216" class="Symbol">{</a><a id="1217" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1217" class="Bound">_</a> <a id="1219" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1219" class="Bound">_</a> <a id="1221" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1221" class="Bound">f</a> <a id="1223" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1223" class="Bound">_</a> <a id="1225" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1225" class="Bound">g</a><a id="1226" class="Symbol">}</a> <a id="1228" class="Symbol">→</a> <a id="1230" href="Categories.Object.Product.Core.html#637" class="Function">project₂</a> <a id="1239" class="Symbol">{</a><a id="1240" class="Argument">h</a> <a id="1242" class="Symbol">=</a> <a id="1244" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1221" class="Bound">f</a><a id="1245" class="Symbol">}</a> <a id="1247" class="Symbol">{</a><a id="1248" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1225" class="Bound">g</a><a id="1249" class="Symbol">}</a>
<a id="1255" class="Symbol">;</a> <a id="1257" href="Categories.Category.CartesianClosed.Canonical.html#1920" class="Field">⟨,⟩-unique</a> <a id="1270" class="Symbol">=</a> <a id="1272" class="Symbol">λ</a> <a id="1274" class="Symbol">{</a><a id="1275" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1275" class="Bound">_</a> <a id="1277" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1277" class="Bound">_</a> <a id="1279" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1279" class="Bound">_</a> <a id="1281" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1281" class="Bound">f</a> <a id="1283" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1283" class="Bound">g</a> <a id="1285" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1285" class="Bound">h</a><a id="1286" class="Symbol">}</a> <a id="1288" class="Symbol">→</a> <a id="1290" href="Categories.Object.Product.Core.html#671" class="Function">unique</a> <a id="1297" class="Symbol">{</a><a id="1298" class="Argument">h</a> <a id="1300" class="Symbol">=</a> <a id="1302" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1285" class="Bound">h</a><a id="1303" class="Symbol">}</a> <a id="1305" class="Symbol">{</a><a id="1306" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1281" class="Bound">f</a><a id="1307" class="Symbol">}</a> <a id="1309" class="Symbol">{</a><a id="1310" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1283" class="Bound">g</a><a id="1311" class="Symbol">}</a>
<a id="1317" class="Symbol">;</a> <a id="1319" href="Categories.Category.CartesianClosed.Canonical.html#2601" class="Field Operator">_^_</a> <a id="1332" class="Symbol">=</a> <a id="1334" class="Symbol">λ</a> <a id="1336" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1336" class="Bound">X</a> <a id="1338" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1338" class="Bound">Y</a> <a id="1340" class="Symbol">→</a> <a id="1342" href="Function.Construct.Setoid.html#376" class="Function">setoid</a> <a id="1349" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1338" class="Bound">Y</a> <a id="1351" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1336" class="Bound">X</a>
<a id="1357" class="Symbol">;</a> <a id="1359" href="Categories.Category.CartesianClosed.Canonical.html#2629" class="Field">eval</a> <a id="1372" class="Symbol">=</a> <a id="1374" class="Symbol">λ</a> <a id="1376" class="Symbol">{</a><a id="1377" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1377" class="Bound">X</a> <a id="1379" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1379" class="Bound">Y</a><a id="1380" class="Symbol">}</a> <a id="1382" class="Symbol">→</a>
<a id="1390" class="Keyword">let</a> <a id="1394" class="Keyword">module</a> <a id="1401" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1401" class="Module">X</a> <a id="1403" class="Symbol">=</a> <a id="1405" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="1412" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1377" class="Bound">X</a> <a id="1414" class="Keyword">in</a> <a id="1417" class="Keyword">record</a>
<a id="1430" class="Symbol">{</a> <a id="1432" href="Function.Bundles.html#2094" class="Field">to</a> <a id="1435" class="Symbol">=</a> <a id="1437" class="Symbol">λ</a> <a id="1439" class="Symbol">{</a> <a id="1441" class="Symbol">(</a><a id="1442" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1442" class="Bound">f</a> <a id="1444" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1446" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1446" class="Bound">x</a><a id="1447" class="Symbol">)</a> <a id="1449" class="Symbol">→</a> <a id="1451" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1442" class="Bound">f</a> <a id="1453" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="1457" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1446" class="Bound">x</a> <a id="1459" class="Symbol">}</a>
<a id="1467" class="Symbol">;</a> <a id="1469" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="1475" class="Symbol">=</a> <a id="1477" class="Symbol">λ</a> <a id="1479" class="Symbol">{</a> <a id="1481" class="Symbol">{(</a> <a id="1484" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1484" class="Bound">f₁</a> <a id="1487" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1489" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1489" class="Bound">x₁</a><a id="1491" class="Symbol">)}</a> <a id="1494" class="Symbol">{(</a><a id="1496" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1496" class="Bound">f₂</a> <a id="1499" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1501" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1501" class="Bound">x₂</a><a id="1503" class="Symbol">)}</a> <a id="1506" class="Symbol">(</a><a id="1507" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1507" class="Bound">eq₁</a> <a id="1511" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1513" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1513" class="Bound">eq₂</a><a id="1516" class="Symbol">)</a> <a id="1518" class="Symbol">→</a>
<a id="1531" href="Relation.Binary.Structures.html#1226" class="Function">X.trans</a> <a id="1539" class="Symbol">(</a><a id="1540" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1507" class="Bound">eq₁</a> <a id="1544" class="Symbol">{</a><a id="1545" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1489" class="Bound">x₁</a><a id="1547" class="Symbol">})</a> <a id="1550" class="Symbol">(</a><a id="1551" href="Function.Bundles.html#2113" class="Field">Func.cong</a> <a id="1561" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1496" class="Bound">f₂</a> <a id="1564" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1513" class="Bound">eq₂</a><a id="1567" class="Symbol">)}</a>
<a id="1576" class="Symbol">}</a>
<a id="1582" class="Symbol">;</a> <a id="1584" href="Categories.Category.CartesianClosed.Canonical.html#2655" class="Field">curry</a> <a id="1597" class="Symbol">=</a> <a id="1599" class="Symbol">λ</a> <a id="1601" class="Symbol">{</a><a id="1602" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1602" class="Bound">C</a> <a id="1604" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1604" class="Bound">A</a> <a id="1606" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1606" class="Bound">B</a><a id="1607" class="Symbol">}</a> <a id="1609" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1609" class="Bound">f</a> <a id="1611" class="Symbol">→</a> <a id="1613" class="Keyword">record</a>
<a id="1626" class="Symbol">{</a> <a id="1628" href="Function.Bundles.html#2094" class="Field">to</a> <a id="1631" class="Symbol">=</a> <a id="1633" class="Symbol">λ</a> <a id="1635" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1635" class="Bound">c</a> <a id="1637" class="Symbol">→</a> <a id="1639" class="Keyword">record</a>
<a id="1654" class="Symbol">{</a> <a id="1656" href="Function.Bundles.html#2094" class="Field">to</a> <a id="1659" class="Symbol">=</a> <a id="1661" class="Symbol">λ</a> <a id="1663" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1663" class="Bound">a</a> <a id="1665" class="Symbol">→</a> <a id="1667" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1609" class="Bound">f</a> <a id="1669" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="1673" class="Symbol">(</a><a id="1674" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1635" class="Bound">c</a> <a id="1676" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1678" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1663" class="Bound">a</a><a id="1679" class="Symbol">)</a>
<a id="1689" class="Symbol">;</a> <a id="1691" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="1697" class="Symbol">=</a> <a id="1699" class="Symbol">λ</a> <a id="1701" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1701" class="Bound">eq</a> <a id="1704" class="Symbol">→</a> <a id="1706" href="Function.Bundles.html#2113" class="Field">Func.cong</a> <a id="1716" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1609" class="Bound">f</a> <a id="1718" class="Symbol">(</a><a id="1719" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="1731" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1602" class="Bound">C</a> <a id="1733" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1735" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1701" class="Bound">eq</a><a id="1737" class="Symbol">)</a>
<a id="1747" class="Symbol">}</a>
<a id="1755" class="Symbol">;</a> <a id="1757" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="1763" class="Symbol">=</a> <a id="1765" class="Symbol">λ</a> <a id="1767" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1767" class="Bound">eq₁</a> <a id="1771" class="Symbol">→</a> <a id="1773" href="Function.Bundles.html#2113" class="Field">Func.cong</a> <a id="1783" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1609" class="Bound">f</a> <a id="1785" class="Symbol">(</a><a id="1786" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1767" class="Bound">eq₁</a> <a id="1790" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1792" class="Symbol">(</a><a id="1793" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="1805" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1604" class="Bound">A</a><a id="1806" class="Symbol">))</a>
<a id="1815" class="Symbol">}</a>
<a id="1821" class="Symbol">;</a> <a id="1823" href="Categories.Category.CartesianClosed.Canonical.html#2690" class="Field">eval-comp</a> <a id="1836" class="Symbol">=</a> <a id="1838" class="Symbol">λ</a> <a id="1840" class="Symbol">{</a><a id="1841" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1841" class="Bound">C</a> <a id="1843" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1843" class="Bound">A</a> <a id="1845" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1845" class="Bound">B</a> <a id="1847" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1847" class="Bound">f</a><a id="1848" class="Symbol">}</a> <a id="1850" class="Symbol">→</a> <a id="1852" href="Function.Bundles.html#2113" class="Field">Func.cong</a> <a id="1862" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1847" class="Bound">f</a> <a id="1864" class="Symbol">(</a><a id="1865" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="1877" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1845" class="Bound">B</a> <a id="1879" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1881" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="1893" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1843" class="Bound">A</a><a id="1894" class="Symbol">)</a>
<a id="1900" class="Symbol">;</a> <a id="1902" href="Categories.Category.CartesianClosed.Canonical.html#2734" class="Field">curry-unique</a> <a id="1915" class="Symbol">=</a> <a id="1917" class="Symbol">λ</a> <a id="1919" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1919" class="Bound">eq</a> <a id="1922" class="Symbol">→</a> <a id="1924" href="Categories.Category.Instance.Properties.Setoids.CCC.html#1919" class="Bound">eq</a>
<a id="1931" class="Symbol">}</a>
<a id="1937" class="Keyword">where</a>
<a id="1949" class="Keyword">open</a> <a id="1954" href="Categories.Category.Monoidal.Instance.Setoids.html#1732" class="Module">Setoids-Cartesian</a>
<a id="1978" class="Keyword">open</a> <a id="1983" href="Categories.Category.BinaryProducts.html#848" class="Module">BinaryProducts</a> <a id="1998" href="Categories.Category.Cartesian.html#801" class="Function">products</a> <a id="2007" class="Keyword">using</a> <a id="2013" class="Symbol">(</a><a id="2014" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">_×_</a><a id="2017" class="Symbol">;</a> <a id="2019" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="2021" class="Symbol">;</a> <a id="2023" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="2025" class="Symbol">;</a> <a id="2027" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨_,_⟩</a><a id="2032" class="Symbol">;</a> <a id="2034" href="Categories.Object.Product.Core.html#603" class="Function">project₁</a><a id="2042" class="Symbol">;</a> <a id="2044" href="Categories.Object.Product.Core.html#637" class="Function">project₂</a><a id="2052" class="Symbol">;</a> <a id="2054" href="Categories.Object.Product.Core.html#671" class="Function">unique</a><a id="2060" class="Symbol">)</a>
<a id="2068" class="Keyword">open</a> <a id="2073" href="Categories.Object.Terminal.html#860" class="Module">Terminal</a> <a id="2082" href="Categories.Category.Cartesian.html#777" class="Function">terminal</a> <a id="2091" class="Keyword">using</a> <a id="2097" class="Symbol">(</a><a id="2098" href="Categories.Object.Terminal.html#905" class="Field">⊤</a><a id="2099" class="Symbol">;</a> <a id="2101" href="Categories.Object.Terminal.html#577" class="Function">!</a><a id="2102" class="Symbol">;</a> <a id="2104" href="Categories.Object.Terminal.html#605" class="Function">!-unique</a><a id="2112" class="Symbol">)</a>
<a id="2117" href="Categories.Category.Instance.Properties.Setoids.CCC.html#2117" class="Function">Setoids-CCC</a> <a id="2129" class="Symbol">:</a> <a id="2131" href="Categories.Category.CartesianClosed.html#1233" class="Record">CartesianClosed</a> <a id="2147" href="Categories.Category.Instance.Properties.Setoids.CCC.html#846" class="Function">S</a>
<a id="2151" href="Categories.Category.Instance.Properties.Setoids.CCC.html#2117" class="Function">Setoids-CCC</a> <a id="2163" class="Symbol">=</a> <a id="2165" href="Categories.Category.CartesianClosed.Canonical.html#4055" class="Function">Equivalence.fromCanonical</a> <a id="2191" href="Categories.Category.Instance.Properties.Setoids.CCC.html#846" class="Function">S</a> <a id="2193" href="Categories.Category.Instance.Properties.Setoids.CCC.html#891" class="Function">Setoids-Canonical</a>
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