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<html><head><meta charset="utf-8"><title>Function.Construct.Identity</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
<a id="74" class="Comment">-- The Agda standard library</a>
<a id="103" class="Comment">--</a>
<a id="106" class="Comment">-- The identity function</a>
<a id="131" class="Comment">------------------------------------------------------------------------</a>
<a id="205" class="Symbol">{-#</a> <a id="209" class="Keyword">OPTIONS</a> <a id="217" class="Pragma">--cubical-compatible</a> <a id="238" class="Pragma">--safe</a> <a id="245" class="Symbol">#-}</a>
<a id="250" class="Keyword">module</a> <a id="257" href="Function.Construct.Identity.html" class="Module">Function.Construct.Identity</a> <a id="285" class="Keyword">where</a>
<a id="292" class="Keyword">open</a> <a id="297" class="Keyword">import</a> <a id="304" href="Data.Product.Base.html" class="Module">Data.Product.Base</a> <a id="322" class="Keyword">using</a> <a id="328" class="Symbol">(</a><a id="329" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="332" class="Symbol">)</a>
<a id="334" class="Keyword">open</a> <a id="339" class="Keyword">import</a> <a id="346" href="Function.Base.html" class="Module">Function.Base</a> <a id="360" class="Keyword">using</a> <a id="366" class="Symbol">(</a><a id="367" href="Function.Base.html#704" class="Function">id</a><a id="369" class="Symbol">)</a>
<a id="371" class="Keyword">open</a> <a id="376" class="Keyword">import</a> <a id="383" href="Function.Bundles.html" class="Module">Function.Bundles</a>
<a id="400" class="Keyword">import</a> <a id="407" href="Function.Definitions.html" class="Module">Function.Definitions</a> <a id="428" class="Symbol">as</a> <a id="431" class="Module">Definitions</a>
<a id="443" class="Keyword">import</a> <a id="450" href="Function.Structures.html" class="Module">Function.Structures</a> <a id="470" class="Symbol">as</a> <a id="473" class="Module">Structures</a>
<a id="484" class="Keyword">open</a> <a id="489" class="Keyword">import</a> <a id="496" href="Level.html" class="Module">Level</a> <a id="502" class="Keyword">using</a> <a id="508" class="Symbol">(</a><a id="509" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="514" class="Symbol">)</a>
<a id="516" class="Keyword">open</a> <a id="521" class="Keyword">import</a> <a id="528" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a> <a id="549" class="Keyword">using</a> <a id="555" class="Symbol">(</a><a id="556" href="Relation.Binary.Core.html#896" class="Function">Rel</a><a id="559" class="Symbol">)</a>
<a id="561" class="Keyword">open</a> <a id="566" class="Keyword">import</a> <a id="573" href="Relation.Binary.Bundles.html" class="Module">Relation.Binary.Bundles</a> <a id="597" class="Keyword">using</a> <a id="603" class="Symbol">(</a><a id="604" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="610" class="Symbol">)</a>
<a id="612" class="Keyword">open</a> <a id="617" class="Keyword">import</a> <a id="624" href="Relation.Binary.Structures.html" class="Module">Relation.Binary.Structures</a> <a id="651" class="Symbol">as</a> <a id="654" class="Module">B</a> <a id="656" class="Keyword">hiding</a> <a id="663" class="Symbol">(</a><a id="664" href="Relation.Binary.Structures.html#1550" class="Record">IsEquivalence</a><a id="677" class="Symbol">)</a>
<a id="679" class="Keyword">open</a> <a id="684" class="Keyword">import</a> <a id="691" href="Relation.Binary.Definitions.html" class="Module">Relation.Binary.Definitions</a> <a id="719" class="Keyword">using</a> <a id="725" class="Symbol">(</a><a id="726" href="Relation.Binary.Definitions.html#1428" class="Function">Reflexive</a><a id="735" class="Symbol">)</a>
<a id="737" class="Keyword">open</a> <a id="742" class="Keyword">import</a> <a id="749" href="Relation.Binary.PropositionalEquality.Core.html" class="Module">Relation.Binary.PropositionalEquality.Core</a> <a id="792" class="Keyword">using</a> <a id="798" class="Symbol">(</a><a id="799" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a><a id="802" class="Symbol">)</a>
<a id="804" class="Keyword">open</a> <a id="809" class="Keyword">import</a> <a id="816" href="Relation.Binary.PropositionalEquality.Properties.html" class="Module">Relation.Binary.PropositionalEquality.Properties</a> <a id="865" class="Keyword">using</a> <a id="871" class="Symbol">(</a><a id="872" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a><a id="878" class="Symbol">)</a>
<a id="881" class="Keyword">private</a>
<a id="891" class="Keyword">variable</a>
<a id="904" href="Function.Construct.Identity.html#904" class="Generalizable">a</a> <a id="906" href="Function.Construct.Identity.html#906" class="Generalizable">ℓ</a> <a id="908" class="Symbol">:</a> <a id="910" href="Agda.Primitive.html#742" class="Postulate">Level</a>
<a id="920" href="Function.Construct.Identity.html#920" class="Generalizable">A</a> <a id="922" class="Symbol">:</a> <a id="924" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="928" href="Function.Construct.Identity.html#904" class="Generalizable">a</a>
<a id="931" class="Comment">------------------------------------------------------------------------</a>
<a id="1004" class="Comment">-- Properties</a>
<a id="1019" class="Keyword">module</a> <a id="1026" href="Function.Construct.Identity.html#1026" class="Module">_</a> <a id="1028" class="Symbol">(</a><a id="1029" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1033" class="Symbol">:</a> <a id="1035" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1039" href="Function.Construct.Identity.html#920" class="Generalizable">A</a> <a id="1041" href="Function.Construct.Identity.html#906" class="Generalizable">ℓ</a><a id="1042" class="Symbol">)</a> <a id="1044" class="Keyword">where</a>
<a id="1053" class="Keyword">open</a> <a id="1058" href="Function.Definitions.html" class="Module">Definitions</a>
<a id="1073" href="Function.Construct.Identity.html#1073" class="Function">congruent</a> <a id="1083" class="Symbol">:</a> <a id="1085" href="Function.Definitions.html#765" class="Function">Congruent</a> <a id="1095" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1099" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1103" href="Function.Base.html#704" class="Function">id</a>
<a id="1108" href="Function.Construct.Identity.html#1073" class="Function">congruent</a> <a id="1118" class="Symbol">=</a> <a id="1120" href="Function.Base.html#704" class="Function">id</a>
<a id="1126" href="Function.Construct.Identity.html#1126" class="Function">injective</a> <a id="1136" class="Symbol">:</a> <a id="1138" href="Function.Definitions.html#842" class="Function">Injective</a> <a id="1148" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1152" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1156" href="Function.Base.html#704" class="Function">id</a>
<a id="1161" href="Function.Construct.Identity.html#1126" class="Function">injective</a> <a id="1171" class="Symbol">=</a> <a id="1173" href="Function.Base.html#704" class="Function">id</a>
<a id="1179" href="Function.Construct.Identity.html#1179" class="Function">surjective</a> <a id="1190" class="Symbol">:</a> <a id="1192" href="Function.Definitions.html#919" class="Function">Surjective</a> <a id="1203" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1207" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1211" href="Function.Base.html#704" class="Function">id</a>
<a id="1216" href="Function.Construct.Identity.html#1179" class="Function">surjective</a> <a id="1227" href="Function.Construct.Identity.html#1227" class="Bound">x</a> <a id="1229" class="Symbol">=</a> <a id="1231" href="Function.Construct.Identity.html#1227" class="Bound">x</a> <a id="1233" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1235" href="Function.Base.html#704" class="Function">id</a>
<a id="1241" href="Function.Construct.Identity.html#1241" class="Function">bijective</a> <a id="1251" class="Symbol">:</a> <a id="1253" href="Function.Definitions.html#1008" class="Function">Bijective</a> <a id="1263" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1267" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1271" href="Function.Base.html#704" class="Function">id</a>
<a id="1276" href="Function.Construct.Identity.html#1241" class="Function">bijective</a> <a id="1286" class="Symbol">=</a> <a id="1288" href="Function.Construct.Identity.html#1126" class="Function">injective</a> <a id="1298" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1300" href="Function.Construct.Identity.html#1179" class="Function">surjective</a>
<a id="1314" href="Function.Construct.Identity.html#1314" class="Function">inverseˡ</a> <a id="1323" class="Symbol">:</a> <a id="1325" href="Function.Definitions.html#1082" class="Function">Inverseˡ</a> <a id="1334" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1338" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1342" href="Function.Base.html#704" class="Function">id</a> <a id="1345" href="Function.Base.html#704" class="Function">id</a>
<a id="1350" href="Function.Construct.Identity.html#1314" class="Function">inverseˡ</a> <a id="1359" class="Symbol">=</a> <a id="1361" href="Function.Base.html#704" class="Function">id</a>
<a id="1367" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a> <a id="1376" class="Symbol">:</a> <a id="1378" href="Function.Definitions.html#1169" class="Function">Inverseʳ</a> <a id="1387" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1391" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1395" href="Function.Base.html#704" class="Function">id</a> <a id="1398" href="Function.Base.html#704" class="Function">id</a>
<a id="1403" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a> <a id="1412" class="Symbol">=</a> <a id="1414" href="Function.Base.html#704" class="Function">id</a>
<a id="1420" href="Function.Construct.Identity.html#1420" class="Function">inverseᵇ</a> <a id="1429" class="Symbol">:</a> <a id="1431" href="Function.Definitions.html#1256" class="Function">Inverseᵇ</a> <a id="1440" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1444" href="Function.Construct.Identity.html#1029" class="Bound Operator">_≈_</a> <a id="1448" href="Function.Base.html#704" class="Function">id</a> <a id="1451" href="Function.Base.html#704" class="Function">id</a>
<a id="1456" href="Function.Construct.Identity.html#1420" class="Function">inverseᵇ</a> <a id="1465" class="Symbol">=</a> <a id="1467" href="Function.Construct.Identity.html#1314" class="Function">inverseˡ</a> <a id="1476" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1478" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a>
<a id="1488" class="Comment">------------------------------------------------------------------------</a>
<a id="1561" class="Comment">-- Structures</a>
<a id="1576" class="Keyword">module</a> <a id="1583" href="Function.Construct.Identity.html#1583" class="Module">_</a> <a id="1585" class="Symbol">{</a><a id="1586" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a> <a id="1590" class="Symbol">:</a> <a id="1592" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1596" href="Function.Construct.Identity.html#920" class="Generalizable">A</a> <a id="1598" href="Function.Construct.Identity.html#906" class="Generalizable">ℓ</a><a id="1599" class="Symbol">}</a> <a id="1601" class="Symbol">(</a><a id="1602" href="Function.Construct.Identity.html#1602" class="Bound">isEq</a> <a id="1607" class="Symbol">:</a> <a id="1609" href="Relation.Binary.Structures.html#1550" class="Record">B.IsEquivalence</a> <a id="1625" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a><a id="1628" class="Symbol">)</a> <a id="1630" class="Keyword">where</a>
<a id="1639" class="Keyword">open</a> <a id="1644" href="Function.Structures.html" class="Module">Structures</a> <a id="1655" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a> <a id="1659" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="1665" class="Keyword">open</a> <a id="1670" href="Relation.Binary.Structures.html#1550" class="Module">B.IsEquivalence</a> <a id="1686" href="Function.Construct.Identity.html#1602" class="Bound">isEq</a>
<a id="1694" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a> <a id="1706" class="Symbol">:</a> <a id="1708" href="Function.Structures.html#995" class="Record">IsCongruent</a> <a id="1720" href="Function.Base.html#704" class="Function">id</a>
<a id="1725" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a> <a id="1737" class="Symbol">=</a> <a id="1739" class="Keyword">record</a>
<a id="1750" class="Symbol">{</a> <a id="1752" href="Function.Structures.html#1062" class="Field">cong</a> <a id="1767" class="Symbol">=</a> <a id="1769" href="Function.Base.html#704" class="Function">id</a>
<a id="1776" class="Symbol">;</a> <a id="1778" href="Function.Structures.html#1106" class="Field">isEquivalence₁</a> <a id="1793" class="Symbol">=</a> <a id="1795" href="Function.Construct.Identity.html#1602" class="Bound">isEq</a>
<a id="1804" class="Symbol">;</a> <a id="1806" href="Function.Structures.html#1146" class="Field">isEquivalence₂</a> <a id="1821" class="Symbol">=</a> <a id="1823" href="Function.Construct.Identity.html#1602" class="Bound">isEq</a>
<a id="1832" class="Symbol">}</a>
<a id="1837" href="Function.Construct.Identity.html#1837" class="Function">isInjection</a> <a id="1849" class="Symbol">:</a> <a id="1851" href="Function.Structures.html#1479" class="Record">IsInjection</a> <a id="1863" href="Function.Base.html#704" class="Function">id</a>
<a id="1868" href="Function.Construct.Identity.html#1837" class="Function">isInjection</a> <a id="1880" class="Symbol">=</a> <a id="1882" class="Keyword">record</a>
<a id="1893" class="Symbol">{</a> <a id="1895" href="Function.Structures.html#1546" class="Field">isCongruent</a> <a id="1907" class="Symbol">=</a> <a id="1909" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a>
<a id="1925" class="Symbol">;</a> <a id="1927" href="Function.Structures.html#1579" class="Field">injective</a> <a id="1939" class="Symbol">=</a> <a id="1941" href="Function.Construct.Identity.html#1126" class="Function">injective</a> <a id="1951" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="1959" class="Symbol">}</a>
<a id="1964" href="Function.Construct.Identity.html#1964" class="Function">isSurjection</a> <a id="1977" class="Symbol">:</a> <a id="1979" href="Function.Structures.html#1664" class="Record">IsSurjection</a> <a id="1992" href="Function.Base.html#704" class="Function">id</a>
<a id="1997" href="Function.Construct.Identity.html#1964" class="Function">isSurjection</a> <a id="2010" class="Symbol">=</a> <a id="2012" class="Keyword">record</a>
<a id="2023" class="Symbol">{</a> <a id="2025" href="Function.Structures.html#1731" class="Field">isCongruent</a> <a id="2037" class="Symbol">=</a> <a id="2039" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a>
<a id="2055" class="Symbol">;</a> <a id="2057" href="Function.Structures.html#1763" class="Field">surjective</a> <a id="2069" class="Symbol">=</a> <a id="2071" href="Function.Construct.Identity.html#1179" class="Function">surjective</a> <a id="2082" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="2090" class="Symbol">}</a>
<a id="2095" href="Function.Construct.Identity.html#2095" class="Function">isBijection</a> <a id="2107" class="Symbol">:</a> <a id="2109" href="Function.Structures.html#1970" class="Record">IsBijection</a> <a id="2121" href="Function.Base.html#704" class="Function">id</a>
<a id="2126" href="Function.Construct.Identity.html#2095" class="Function">isBijection</a> <a id="2138" class="Symbol">=</a> <a id="2140" class="Keyword">record</a>
<a id="2151" class="Symbol">{</a> <a id="2153" href="Function.Structures.html#2036" class="Field">isInjection</a> <a id="2165" class="Symbol">=</a> <a id="2167" href="Function.Construct.Identity.html#1837" class="Function">isInjection</a>
<a id="2183" class="Symbol">;</a> <a id="2185" href="Function.Structures.html#2068" class="Field">surjective</a> <a id="2197" class="Symbol">=</a> <a id="2199" href="Function.Construct.Identity.html#1179" class="Function">surjective</a> <a id="2210" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="2218" class="Symbol">}</a>
<a id="2223" href="Function.Construct.Identity.html#2223" class="Function">isLeftInverse</a> <a id="2237" class="Symbol">:</a> <a id="2239" href="Function.Structures.html#2598" class="Record">IsLeftInverse</a> <a id="2253" href="Function.Base.html#704" class="Function">id</a> <a id="2256" href="Function.Base.html#704" class="Function">id</a>
<a id="2261" href="Function.Construct.Identity.html#2223" class="Function">isLeftInverse</a> <a id="2275" class="Symbol">=</a> <a id="2277" class="Keyword">record</a>
<a id="2288" class="Symbol">{</a> <a id="2290" href="Function.Structures.html#2682" class="Field">isCongruent</a> <a id="2302" class="Symbol">=</a> <a id="2304" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a>
<a id="2320" class="Symbol">;</a> <a id="2322" href="Function.Structures.html#2716" class="Field">from-cong</a> <a id="2334" class="Symbol">=</a> <a id="2336" href="Function.Base.html#704" class="Function">id</a>
<a id="2343" class="Symbol">;</a> <a id="2345" href="Function.Structures.html#2760" class="Field">inverseˡ</a> <a id="2357" class="Symbol">=</a> <a id="2359" href="Function.Construct.Identity.html#1314" class="Function">inverseˡ</a> <a id="2368" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="2376" class="Symbol">}</a>
<a id="2381" href="Function.Construct.Identity.html#2381" class="Function">isRightInverse</a> <a id="2396" class="Symbol">:</a> <a id="2398" href="Function.Structures.html#3113" class="Record">IsRightInverse</a> <a id="2413" href="Function.Base.html#704" class="Function">id</a> <a id="2416" href="Function.Base.html#704" class="Function">id</a>
<a id="2421" href="Function.Construct.Identity.html#2381" class="Function">isRightInverse</a> <a id="2436" class="Symbol">=</a> <a id="2438" class="Keyword">record</a>
<a id="2449" class="Symbol">{</a> <a id="2451" href="Function.Structures.html#3198" class="Field">isCongruent</a> <a id="2463" class="Symbol">=</a> <a id="2465" href="Function.Construct.Identity.html#1694" class="Function">isCongruent</a>
<a id="2481" class="Symbol">;</a> <a id="2483" href="Function.Structures.html#3231" class="Field">from-cong</a> <a id="2495" class="Symbol">=</a> <a id="2497" href="Function.Base.html#704" class="Function">id</a>
<a id="2504" class="Symbol">;</a> <a id="2506" href="Function.Structures.html#3274" class="Field">inverseʳ</a> <a id="2518" class="Symbol">=</a> <a id="2520" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a> <a id="2529" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="2537" class="Symbol">}</a>
<a id="2542" href="Function.Construct.Identity.html#2542" class="Function">isInverse</a> <a id="2552" class="Symbol">:</a> <a id="2554" href="Function.Structures.html#3487" class="Record">IsInverse</a> <a id="2564" href="Function.Base.html#704" class="Function">id</a> <a id="2567" href="Function.Base.html#704" class="Function">id</a>
<a id="2572" href="Function.Construct.Identity.html#2542" class="Function">isInverse</a> <a id="2582" class="Symbol">=</a> <a id="2584" class="Keyword">record</a>
<a id="2595" class="Symbol">{</a> <a id="2597" href="Function.Structures.html#3567" class="Field">isLeftInverse</a> <a id="2611" class="Symbol">=</a> <a id="2613" href="Function.Construct.Identity.html#2223" class="Function">isLeftInverse</a>
<a id="2631" class="Symbol">;</a> <a id="2633" href="Function.Structures.html#3609" class="Field">inverseʳ</a> <a id="2647" class="Symbol">=</a> <a id="2649" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a> <a id="2658" href="Function.Construct.Identity.html#1586" class="Bound Operator">_≈_</a>
<a id="2666" class="Symbol">}</a>
<a id="2669" class="Comment">------------------------------------------------------------------------</a>
<a id="2742" class="Comment">-- Setoid bundles</a>
<a id="2761" class="Keyword">module</a> <a id="2768" href="Function.Construct.Identity.html#2768" class="Module">_</a> <a id="2770" class="Symbol">(</a><a id="2771" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="2773" class="Symbol">:</a> <a id="2775" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2782" href="Function.Construct.Identity.html#904" class="Generalizable">a</a> <a id="2784" href="Function.Construct.Identity.html#906" class="Generalizable">ℓ</a><a id="2785" class="Symbol">)</a> <a id="2787" class="Keyword">where</a>
<a id="2796" class="Keyword">open</a> <a id="2801" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="2808" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="2813" href="Function.Construct.Identity.html#2813" class="Function">function</a> <a id="2822" class="Symbol">:</a> <a id="2824" href="Function.Bundles.html#2043" class="Record">Func</a> <a id="2829" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="2831" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="2835" href="Function.Construct.Identity.html#2813" class="Function">function</a> <a id="2844" class="Symbol">=</a> <a id="2846" class="Keyword">record</a>
<a id="2857" class="Symbol">{</a> <a id="2859" href="Function.Bundles.html#2094" class="Field">to</a> <a id="2864" class="Symbol">=</a> <a id="2866" href="Function.Base.html#704" class="Function">id</a>
<a id="2873" class="Symbol">;</a> <a id="2875" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="2880" class="Symbol">=</a> <a id="2882" href="Function.Base.html#704" class="Function">id</a>
<a id="2889" class="Symbol">}</a>
<a id="2894" href="Function.Construct.Identity.html#2894" class="Function">injection</a> <a id="2904" class="Symbol">:</a> <a id="2906" href="Function.Bundles.html#2415" class="Record">Injection</a> <a id="2916" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="2918" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="2922" href="Function.Construct.Identity.html#2894" class="Function">injection</a> <a id="2932" class="Symbol">=</a> <a id="2934" class="Keyword">record</a>
<a id="2945" class="Symbol">{</a> <a id="2947" href="Function.Bundles.html#2471" class="Field">to</a> <a id="2957" class="Symbol">=</a> <a id="2959" href="Function.Base.html#704" class="Function">id</a>
<a id="2966" class="Symbol">;</a> <a id="2968" href="Function.Bundles.html#2497" class="Field">cong</a> <a id="2978" class="Symbol">=</a> <a id="2980" href="Function.Base.html#704" class="Function">id</a>
<a id="2987" class="Symbol">;</a> <a id="2989" href="Function.Bundles.html#2540" class="Field">injective</a> <a id="2999" class="Symbol">=</a> <a id="3001" href="Function.Construct.Identity.html#1126" class="Function">injective</a> <a id="3011" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3019" class="Symbol">}</a>
<a id="3024" href="Function.Construct.Identity.html#3024" class="Function">surjection</a> <a id="3035" class="Symbol">:</a> <a id="3037" href="Function.Bundles.html#2865" class="Record">Surjection</a> <a id="3048" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3050" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3054" href="Function.Construct.Identity.html#3024" class="Function">surjection</a> <a id="3065" class="Symbol">=</a> <a id="3067" class="Keyword">record</a>
<a id="3078" class="Symbol">{</a> <a id="3080" href="Function.Bundles.html#2922" class="Field">to</a> <a id="3091" class="Symbol">=</a> <a id="3093" href="Function.Base.html#704" class="Function">id</a>
<a id="3100" class="Symbol">;</a> <a id="3102" href="Function.Bundles.html#2947" class="Field">cong</a> <a id="3113" class="Symbol">=</a> <a id="3115" href="Function.Base.html#704" class="Function">id</a>
<a id="3122" class="Symbol">;</a> <a id="3124" href="Function.Bundles.html#2989" class="Field">surjective</a> <a id="3135" class="Symbol">=</a> <a id="3137" href="Function.Construct.Identity.html#1179" class="Function">surjective</a> <a id="3148" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3156" class="Symbol">}</a>
<a id="3161" href="Function.Construct.Identity.html#3161" class="Function">bijection</a> <a id="3171" class="Symbol">:</a> <a id="3173" href="Function.Bundles.html#3530" class="Record">Bijection</a> <a id="3183" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3185" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3189" href="Function.Construct.Identity.html#3161" class="Function">bijection</a> <a id="3199" class="Symbol">=</a> <a id="3201" class="Keyword">record</a>
<a id="3212" class="Symbol">{</a> <a id="3214" href="Function.Bundles.html#3586" class="Field">to</a> <a id="3224" class="Symbol">=</a> <a id="3226" href="Function.Base.html#704" class="Function">id</a>
<a id="3233" class="Symbol">;</a> <a id="3235" href="Function.Bundles.html#3610" class="Field">cong</a> <a id="3245" class="Symbol">=</a> <a id="3247" href="Function.Base.html#704" class="Function">id</a>
<a id="3254" class="Symbol">;</a> <a id="3256" href="Function.Bundles.html#3651" class="Field">bijective</a> <a id="3266" class="Symbol">=</a> <a id="3268" href="Function.Construct.Identity.html#1241" class="Function">bijective</a> <a id="3278" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3286" class="Symbol">}</a>
<a id="3291" href="Function.Construct.Identity.html#3291" class="Function">equivalence</a> <a id="3303" class="Symbol">:</a> <a id="3305" href="Function.Bundles.html#4752" class="Record">Equivalence</a> <a id="3317" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3319" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3323" href="Function.Construct.Identity.html#3291" class="Function">equivalence</a> <a id="3335" class="Symbol">=</a> <a id="3337" class="Keyword">record</a>
<a id="3348" class="Symbol">{</a> <a id="3350" href="Function.Bundles.html#4810" class="Field">to</a> <a id="3360" class="Symbol">=</a> <a id="3362" href="Function.Base.html#704" class="Function">id</a>
<a id="3369" class="Symbol">;</a> <a id="3371" href="Function.Bundles.html#4834" class="Field">from</a> <a id="3381" class="Symbol">=</a> <a id="3383" href="Function.Base.html#704" class="Function">id</a>
<a id="3390" class="Symbol">;</a> <a id="3392" href="Function.Bundles.html#4858" class="Field">to-cong</a> <a id="3402" class="Symbol">=</a> <a id="3404" href="Function.Base.html#704" class="Function">id</a>
<a id="3411" class="Symbol">;</a> <a id="3413" href="Function.Bundles.html#4899" class="Field">from-cong</a> <a id="3423" class="Symbol">=</a> <a id="3425" href="Function.Base.html#704" class="Function">id</a>
<a id="3432" class="Symbol">}</a>
<a id="3437" href="Function.Construct.Identity.html#3437" class="Function">leftInverse</a> <a id="3449" class="Symbol">:</a> <a id="3451" href="Function.Bundles.html#5375" class="Record">LeftInverse</a> <a id="3463" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3465" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3469" href="Function.Construct.Identity.html#3437" class="Function">leftInverse</a> <a id="3481" class="Symbol">=</a> <a id="3483" class="Keyword">record</a>
<a id="3494" class="Symbol">{</a> <a id="3496" href="Function.Bundles.html#5433" class="Field">to</a> <a id="3506" class="Symbol">=</a> <a id="3508" href="Function.Base.html#704" class="Function">id</a>
<a id="3515" class="Symbol">;</a> <a id="3517" href="Function.Bundles.html#5457" class="Field">from</a> <a id="3527" class="Symbol">=</a> <a id="3529" href="Function.Base.html#704" class="Function">id</a>
<a id="3536" class="Symbol">;</a> <a id="3538" href="Function.Bundles.html#5481" class="Field">to-cong</a> <a id="3548" class="Symbol">=</a> <a id="3550" href="Function.Base.html#704" class="Function">id</a>
<a id="3557" class="Symbol">;</a> <a id="3559" href="Function.Bundles.html#5522" class="Field">from-cong</a> <a id="3569" class="Symbol">=</a> <a id="3571" href="Function.Base.html#704" class="Function">id</a>
<a id="3578" class="Symbol">;</a> <a id="3580" href="Function.Bundles.html#5565" class="Field">inverseˡ</a> <a id="3590" class="Symbol">=</a> <a id="3592" href="Function.Construct.Identity.html#1314" class="Function">inverseˡ</a> <a id="3601" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3609" class="Symbol">}</a>
<a id="3614" href="Function.Construct.Identity.html#3614" class="Function">rightInverse</a> <a id="3627" class="Symbol">:</a> <a id="3629" href="Function.Bundles.html#6509" class="Record">RightInverse</a> <a id="3642" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3644" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3648" href="Function.Construct.Identity.html#3614" class="Function">rightInverse</a> <a id="3661" class="Symbol">=</a> <a id="3663" class="Keyword">record</a>
<a id="3674" class="Symbol">{</a> <a id="3676" href="Function.Bundles.html#6568" class="Field">to</a> <a id="3686" class="Symbol">=</a> <a id="3688" href="Function.Base.html#704" class="Function">id</a>
<a id="3695" class="Symbol">;</a> <a id="3697" href="Function.Bundles.html#6592" class="Field">from</a> <a id="3707" class="Symbol">=</a> <a id="3709" href="Function.Base.html#704" class="Function">id</a>
<a id="3716" class="Symbol">;</a> <a id="3718" href="Function.Bundles.html#6616" class="Field">to-cong</a> <a id="3728" class="Symbol">=</a> <a id="3730" href="Function.Base.html#704" class="Function">id</a>
<a id="3737" class="Symbol">;</a> <a id="3739" href="Function.Bundles.html#6657" class="Field">from-cong</a> <a id="3749" class="Symbol">=</a> <a id="3751" href="Function.Base.html#704" class="Function">id</a>
<a id="3758" class="Symbol">;</a> <a id="3760" href="Function.Bundles.html#6702" class="Field">inverseʳ</a> <a id="3770" class="Symbol">=</a> <a id="3772" href="Function.Construct.Identity.html#1367" class="Function">inverseʳ</a> <a id="3781" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3789" class="Symbol">}</a>
<a id="3794" href="Function.Construct.Identity.html#3794" class="Function">inverse</a> <a id="3802" class="Symbol">:</a> <a id="3804" href="Function.Bundles.html#7340" class="Record">Inverse</a> <a id="3812" href="Function.Construct.Identity.html#2771" class="Bound">S</a> <a id="3814" href="Function.Construct.Identity.html#2771" class="Bound">S</a>
<a id="3818" href="Function.Construct.Identity.html#3794" class="Function">inverse</a> <a id="3826" class="Symbol">=</a> <a id="3828" class="Keyword">record</a>
<a id="3839" class="Symbol">{</a> <a id="3841" href="Function.Bundles.html#7394" class="Field">to</a> <a id="3851" class="Symbol">=</a> <a id="3853" href="Function.Base.html#704" class="Function">id</a>
<a id="3860" class="Symbol">;</a> <a id="3862" href="Function.Bundles.html#7418" class="Field">from</a> <a id="3872" class="Symbol">=</a> <a id="3874" href="Function.Base.html#704" class="Function">id</a>
<a id="3881" class="Symbol">;</a> <a id="3883" href="Function.Bundles.html#7442" class="Field">to-cong</a> <a id="3893" class="Symbol">=</a> <a id="3895" href="Function.Base.html#704" class="Function">id</a>
<a id="3902" class="Symbol">;</a> <a id="3904" href="Function.Bundles.html#7483" class="Field">from-cong</a> <a id="3914" class="Symbol">=</a> <a id="3916" href="Function.Base.html#704" class="Function">id</a>
<a id="3923" class="Symbol">;</a> <a id="3925" href="Function.Bundles.html#7526" class="Field">inverse</a> <a id="3935" class="Symbol">=</a> <a id="3937" href="Function.Construct.Identity.html#1420" class="Function">inverseᵇ</a> <a id="3946" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="3954" class="Symbol">}</a>
<a id="3957" class="Comment">------------------------------------------------------------------------</a>
<a id="4030" class="Comment">-- Propositional bundles</a>
<a id="4056" class="Keyword">module</a> <a id="4063" href="Function.Construct.Identity.html#4063" class="Module">_</a> <a id="4065" class="Symbol">(</a><a id="4066" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4068" class="Symbol">:</a> <a id="4070" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4074" href="Function.Construct.Identity.html#904" class="Generalizable">a</a><a id="4075" class="Symbol">)</a> <a id="4077" class="Keyword">where</a>
<a id="4086" href="Function.Construct.Identity.html#4086" class="Function">⟶-id</a> <a id="4091" class="Symbol">:</a> <a id="4093" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4095" href="Function.Bundles.html#11751" class="Function Operator">⟶</a> <a id="4097" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4101" href="Function.Construct.Identity.html#4086" class="Function">⟶-id</a> <a id="4106" class="Symbol">=</a> <a id="4108" href="Function.Construct.Identity.html#2813" class="Function">function</a> <a id="4117" class="Symbol">(</a><a id="4118" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4125" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4126" class="Symbol">)</a>
<a id="4131" href="Function.Construct.Identity.html#4131" class="Function">↣-id</a> <a id="4136" class="Symbol">:</a> <a id="4138" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4140" href="Function.Bundles.html#11819" class="Function Operator">↣</a> <a id="4142" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4146" href="Function.Construct.Identity.html#4131" class="Function">↣-id</a> <a id="4151" class="Symbol">=</a> <a id="4153" href="Function.Construct.Identity.html#2894" class="Function">injection</a> <a id="4163" class="Symbol">(</a><a id="4164" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4171" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4172" class="Symbol">)</a>
<a id="4177" href="Function.Construct.Identity.html#4177" class="Function">↠-id</a> <a id="4182" class="Symbol">:</a> <a id="4184" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4186" href="Function.Bundles.html#11892" class="Function Operator">↠</a> <a id="4188" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4192" href="Function.Construct.Identity.html#4177" class="Function">↠-id</a> <a id="4197" class="Symbol">=</a> <a id="4199" href="Function.Construct.Identity.html#3024" class="Function">surjection</a> <a id="4210" class="Symbol">(</a><a id="4211" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4218" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4219" class="Symbol">)</a>
<a id="4224" href="Function.Construct.Identity.html#4224" class="Function">⤖-id</a> <a id="4229" class="Symbol">:</a> <a id="4231" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4233" href="Function.Bundles.html#11966" class="Function Operator">⤖</a> <a id="4235" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4239" href="Function.Construct.Identity.html#4224" class="Function">⤖-id</a> <a id="4244" class="Symbol">=</a> <a id="4246" href="Function.Construct.Identity.html#3161" class="Function">bijection</a> <a id="4256" class="Symbol">(</a><a id="4257" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4264" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4265" class="Symbol">)</a>
<a id="4270" href="Function.Construct.Identity.html#4270" class="Function">⇔-id</a> <a id="4275" class="Symbol">:</a> <a id="4277" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4279" href="Function.Bundles.html#12039" class="Function Operator">⇔</a> <a id="4281" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4285" href="Function.Construct.Identity.html#4270" class="Function">⇔-id</a> <a id="4290" class="Symbol">=</a> <a id="4292" href="Function.Construct.Identity.html#3291" class="Function">equivalence</a> <a id="4304" class="Symbol">(</a><a id="4305" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4312" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4313" class="Symbol">)</a>
<a id="4318" href="Function.Construct.Identity.html#4318" class="Function">↩-id</a> <a id="4323" class="Symbol">:</a> <a id="4325" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4327" href="Function.Bundles.html#12114" class="Function Operator">↩</a> <a id="4329" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4333" href="Function.Construct.Identity.html#4318" class="Function">↩-id</a> <a id="4338" class="Symbol">=</a> <a id="4340" href="Function.Construct.Identity.html#3437" class="Function">leftInverse</a> <a id="4352" class="Symbol">(</a><a id="4353" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4360" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4361" class="Symbol">)</a>
<a id="4366" href="Function.Construct.Identity.html#4366" class="Function">↪-id</a> <a id="4371" class="Symbol">:</a> <a id="4373" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4375" href="Function.Bundles.html#12189" class="Function Operator">↪</a> <a id="4377" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4381" href="Function.Construct.Identity.html#4366" class="Function">↪-id</a> <a id="4386" class="Symbol">=</a> <a id="4388" href="Function.Construct.Identity.html#3614" class="Function">rightInverse</a> <a id="4401" class="Symbol">(</a><a id="4402" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4409" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4410" class="Symbol">)</a>
<a id="4415" href="Function.Construct.Identity.html#4415" class="Function">↔-id</a> <a id="4420" class="Symbol">:</a> <a id="4422" href="Function.Construct.Identity.html#4066" class="Bound">A</a> <a id="4424" href="Function.Bundles.html#12340" class="Function Operator">↔</a> <a id="4426" href="Function.Construct.Identity.html#4066" class="Bound">A</a>
<a id="4430" href="Function.Construct.Identity.html#4415" class="Function">↔-id</a> <a id="4435" class="Symbol">=</a> <a id="4437" href="Function.Construct.Identity.html#3794" class="Function">inverse</a> <a id="4445" class="Symbol">(</a><a id="4446" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="4453" href="Function.Construct.Identity.html#4066" class="Bound">A</a><a id="4454" class="Symbol">)</a>
<a id="4458" class="Comment">------------------------------------------------------------------------</a>
<a id="4531" class="Comment">-- DEPRECATED NAMES</a>
<a id="4551" class="Comment">------------------------------------------------------------------------</a>
<a id="4624" class="Comment">-- Please use the new names as continuing support for the old names is</a>
<a id="4695" class="Comment">-- not guaranteed.</a>
<a id="4715" class="Comment">-- Version v2.0</a>
<a id="id-⟶"></a><a id="4732" href="Function.Construct.Identity.html#4732" class="Function">id-⟶</a> <a id="4737" class="Symbol">=</a> <a id="4739" href="Function.Construct.Identity.html#4086" class="Function">⟶-id</a>
<a id="4744" class="Symbol">{-#</a> <a id="4748" class="Keyword">WARNING_ON_USAGE</a> <a id="4765" class="Pragma">id-⟶</a>
<a id="4770" class="String">&quot;Warning: id-⟶ was deprecated in v2.0.
Please use ⟶-id instead.&quot;</a>
<a id="4835" class="Symbol">#-}</a>
<a id="id-↣"></a><a id="4840" href="Function.Construct.Identity.html#4840" class="Function">id-↣</a> <a id="4845" class="Symbol">=</a> <a id="4847" href="Function.Construct.Identity.html#4131" class="Function">↣-id</a>
<a id="4852" class="Symbol">{-#</a> <a id="4856" class="Keyword">WARNING_ON_USAGE</a> <a id="4873" class="Pragma">id-↣</a>
<a id="4878" class="String">&quot;Warning: id-↣ was deprecated in v2.0.
Please use ↣-id instead.&quot;</a>
<a id="4943" class="Symbol">#-}</a>
<a id="id-↠"></a><a id="4948" href="Function.Construct.Identity.html#4948" class="Function">id-↠</a> <a id="4953" class="Symbol">=</a> <a id="4955" href="Function.Construct.Identity.html#4177" class="Function">↠-id</a>
<a id="4960" class="Symbol">{-#</a> <a id="4964" class="Keyword">WARNING_ON_USAGE</a> <a id="4981" class="Pragma">id-↠</a>
<a id="4986" class="String">&quot;Warning: id-↠ was deprecated in v2.0.
Please use ↠-id instead.&quot;</a>
<a id="5051" class="Symbol">#-}</a>
<a id="id-⤖"></a><a id="5056" href="Function.Construct.Identity.html#5056" class="Function">id-⤖</a> <a id="5061" class="Symbol">=</a> <a id="5063" href="Function.Construct.Identity.html#4224" class="Function">⤖-id</a>
<a id="5068" class="Symbol">{-#</a> <a id="5072" class="Keyword">WARNING_ON_USAGE</a> <a id="5089" class="Pragma">id-⤖</a>
<a id="5094" class="String">&quot;Warning: id-⤖ was deprecated in v2.0.
Please use ⤖-id instead.&quot;</a>
<a id="5159" class="Symbol">#-}</a>
<a id="id-⇔"></a><a id="5164" href="Function.Construct.Identity.html#5164" class="Function">id-⇔</a> <a id="5169" class="Symbol">=</a> <a id="5171" href="Function.Construct.Identity.html#4270" class="Function">⇔-id</a>
<a id="5176" class="Symbol">{-#</a> <a id="5180" class="Keyword">WARNING_ON_USAGE</a> <a id="5197" class="Pragma">id-⇔</a>
<a id="5202" class="String">&quot;Warning: id-⇔ was deprecated in v2.0.
Please use ⇔-id instead.&quot;</a>
<a id="5267" class="Symbol">#-}</a>
<a id="id-↩"></a><a id="5272" href="Function.Construct.Identity.html#5272" class="Function">id-↩</a> <a id="5277" class="Symbol">=</a> <a id="5279" href="Function.Construct.Identity.html#4318" class="Function">↩-id</a>
<a id="5284" class="Symbol">{-#</a> <a id="5288" class="Keyword">WARNING_ON_USAGE</a> <a id="5305" class="Pragma">id-↩</a>
<a id="5310" class="String">&quot;Warning: id-↩ was deprecated in v2.0.
Please use ↩-id instead.&quot;</a>
<a id="5375" class="Symbol">#-}</a>
<a id="id-↪"></a><a id="5380" href="Function.Construct.Identity.html#5380" class="Function">id-↪</a> <a id="5385" class="Symbol">=</a> <a id="5387" href="Function.Construct.Identity.html#4366" class="Function">↪-id</a>
<a id="5392" class="Symbol">{-#</a> <a id="5396" class="Keyword">WARNING_ON_USAGE</a> <a id="5413" class="Pragma">id-↪</a>
<a id="5418" class="String">&quot;Warning: id-↪ was deprecated in v2.0.
Please use ↪-id instead.&quot;</a>
<a id="5483" class="Symbol">#-}</a>
<a id="id-↔"></a><a id="5488" href="Function.Construct.Identity.html#5488" class="Function">id-↔</a> <a id="5493" class="Symbol">=</a> <a id="5495" href="Function.Construct.Identity.html#4415" class="Function">↔-id</a>
<a id="5500" class="Symbol">{-#</a> <a id="5504" class="Keyword">WARNING_ON_USAGE</a> <a id="5521" class="Pragma">id-↔</a>
<a id="5526" class="String">&quot;Warning: id-↔ was deprecated in v2.0.
Please use ↔-id instead.&quot;</a>
<a id="5591" class="Symbol">#-}</a>
</pre></body></html>
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