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<html><head><meta charset="utf-8"><title>Function.Consequences.Setoid</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
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<a id="74" class="Comment">-- The Agda standard library</a>
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<a id="103" class="Comment">--</a>
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<a id="106" class="Comment">-- Relationships between properties of functions where the equality</a>
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<a id="174" class="Comment">-- over both the domain and codomain are assumed to be setoids.</a>
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<a id="238" class="Comment">------------------------------------------------------------------------</a>
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<a id="312" class="Symbol">{-#</a> <a id="316" class="Keyword">OPTIONS</a> <a id="324" class="Pragma">--cubical-compatible</a> <a id="345" class="Pragma">--safe</a> <a id="352" class="Symbol">#-}</a>
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<a id="357" class="Keyword">open</a> <a id="362" class="Keyword">import</a> <a id="369" href="Relation.Binary.Bundles.html" class="Module">Relation.Binary.Bundles</a> <a id="393" class="Keyword">using</a> <a id="399" class="Symbol">(</a><a id="400" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="406" class="Symbol">)</a>
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<a id="409" class="Keyword">module</a> <a id="416" href="Function.Consequences.Setoid.html" class="Module">Function.Consequences.Setoid</a>
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<a id="447" class="Symbol">{</a><a id="448" href="Function.Consequences.Setoid.html#448" class="Bound">a</a> <a id="450" href="Function.Consequences.Setoid.html#450" class="Bound">b</a> <a id="452" href="Function.Consequences.Setoid.html#452" class="Bound">ℓ₁</a> <a id="455" href="Function.Consequences.Setoid.html#455" class="Bound">ℓ₂</a><a id="457" class="Symbol">}</a>
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<a id="461" class="Symbol">(</a><a id="462" href="Function.Consequences.Setoid.html#462" class="Bound">S</a> <a id="464" class="Symbol">:</a> <a id="466" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="473" href="Function.Consequences.Setoid.html#448" class="Bound">a</a> <a id="475" href="Function.Consequences.Setoid.html#452" class="Bound">ℓ₁</a><a id="477" class="Symbol">)</a>
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<a id="481" class="Symbol">(</a><a id="482" href="Function.Consequences.Setoid.html#482" class="Bound">T</a> <a id="484" class="Symbol">:</a> <a id="486" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="493" href="Function.Consequences.Setoid.html#450" class="Bound">b</a> <a id="495" href="Function.Consequences.Setoid.html#455" class="Bound">ℓ₂</a><a id="497" class="Symbol">)</a>
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<a id="501" class="Keyword">where</a>
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<a id="508" class="Keyword">open</a> <a id="513" class="Keyword">import</a> <a id="520" href="Function.Definitions.html" class="Module">Function.Definitions</a>
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<a id="541" class="Keyword">open</a> <a id="546" class="Keyword">import</a> <a id="553" href="Relation.Nullary.Negation.Core.html" class="Module">Relation.Nullary.Negation.Core</a>
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<a id="585" class="Keyword">import</a> <a id="592" href="Function.Consequences.html" class="Module">Function.Consequences</a> <a id="614" class="Symbol">as</a> <a id="617" class="Module">C</a>
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<a id="620" class="Keyword">private</a>
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<a id="630" class="Keyword">open</a> <a id="635" class="Keyword">module</a> <a id="S"></a><a id="642" href="Function.Consequences.Setoid.html#642" class="Module">S</a> <a id="644" class="Symbol">=</a> <a id="646" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="653" href="Function.Consequences.Setoid.html#462" class="Bound">S</a> <a id="655" class="Keyword">using</a> <a id="661" class="Symbol">()</a> <a id="664" class="Keyword">renaming</a> <a id="673" class="Symbol">(</a><a id="674" href="Relation.Binary.Bundles.html#1143" class="Function">Carrier</a> <a id="682" class="Symbol">to</a> <a id="685" class="Function">A</a><a id="686" class="Symbol">;</a> <a id="688" href="Relation.Binary.Bundles.html#1169" class="Function Operator">_≈_</a> <a id="692" class="Symbol">to</a> <a id="695" class="Function Operator">≈₁</a><a id="697" class="Symbol">)</a>
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<a id="701" class="Keyword">open</a> <a id="706" class="Keyword">module</a> <a id="T"></a><a id="713" href="Function.Consequences.Setoid.html#713" class="Module">T</a> <a id="715" class="Symbol">=</a> <a id="717" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="724" href="Function.Consequences.Setoid.html#482" class="Bound">T</a> <a id="726" class="Keyword">using</a> <a id="732" class="Symbol">()</a> <a id="735" class="Keyword">renaming</a> <a id="744" class="Symbol">(</a><a id="745" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="753" class="Symbol">to</a> <a id="756" class="Field">B</a><a id="757" class="Symbol">;</a> <a id="759" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="763" class="Symbol">to</a> <a id="766" class="Field Operator">≈₂</a><a id="768" class="Symbol">)</a>
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<a id="773" class="Keyword">variable</a>
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<a id="786" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="788" class="Symbol">:</a> <a id="790" href="Function.Consequences.Setoid.html#685" class="Function">A</a> <a id="792" class="Symbol">→</a> <a id="794" href="Function.Consequences.Setoid.html#756" class="Field">B</a>
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<a id="800" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="804" class="Symbol">:</a> <a id="806" href="Function.Consequences.Setoid.html#756" class="Field">B</a> <a id="808" class="Symbol">→</a> <a id="810" href="Function.Consequences.Setoid.html#685" class="Function">A</a>
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<a id="813" class="Comment">------------------------------------------------------------------------</a>
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<a id="886" class="Comment">-- Injective</a>
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<a id="contraInjective"></a><a id="900" href="Function.Consequences.Setoid.html#900" class="Function">contraInjective</a> <a id="916" class="Symbol">:</a> <a id="918" href="Function.Definitions.html#842" class="Function">Injective</a> <a id="928" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="931" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="934" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="936" class="Symbol">→</a>
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<a id="956" class="Symbol">∀</a> <a id="958" class="Symbol">{</a><a id="959" href="Function.Consequences.Setoid.html#959" class="Bound">x</a> <a id="961" href="Function.Consequences.Setoid.html#961" class="Bound">y</a><a id="962" class="Symbol">}</a> <a id="964" class="Symbol">→</a> <a id="966" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬</a> <a id="968" class="Symbol">(</a><a id="969" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="972" href="Function.Consequences.Setoid.html#959" class="Bound">x</a> <a id="974" href="Function.Consequences.Setoid.html#961" class="Bound">y</a><a id="975" class="Symbol">)</a> <a id="977" class="Symbol">→</a> <a id="979" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬</a> <a id="981" class="Symbol">(</a><a id="982" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="985" class="Symbol">(</a><a id="986" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="988" href="Function.Consequences.Setoid.html#959" class="Bound">x</a><a id="989" class="Symbol">)</a> <a id="991" class="Symbol">(</a><a id="992" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="994" href="Function.Consequences.Setoid.html#961" class="Bound">y</a><a id="995" class="Symbol">))</a>
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<a id="998" href="Function.Consequences.Setoid.html#900" class="Function">contraInjective</a> <a id="1014" class="Symbol">=</a> <a id="1016" href="Function.Consequences.html#941" class="Function">C.contraInjective</a> <a id="1034" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a>
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<a id="1038" class="Comment">------------------------------------------------------------------------</a>
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<a id="1111" class="Comment">-- Inverseˡ</a>
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<a id="inverseˡ⇒surjective"></a><a id="1124" href="Function.Consequences.Setoid.html#1124" class="Function">inverseˡ⇒surjective</a> <a id="1144" class="Symbol">:</a> <a id="1146" href="Function.Definitions.html#1082" class="Function">Inverseˡ</a> <a id="1155" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1158" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1161" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="1163" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="1167" class="Symbol">→</a> <a id="1169" href="Function.Definitions.html#919" class="Function">Surjective</a> <a id="1180" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1183" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1186" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a>
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<a id="1188" href="Function.Consequences.Setoid.html#1124" class="Function">inverseˡ⇒surjective</a> <a id="1208" class="Symbol">=</a> <a id="1210" href="Function.Consequences.html#1193" class="Function">C.inverseˡ⇒surjective</a> <a id="1232" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a>
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<a id="1236" class="Comment">------------------------------------------------------------------------</a>
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<a id="1309" class="Comment">-- Inverseʳ</a>
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<a id="inverseʳ⇒injective"></a><a id="1322" href="Function.Consequences.Setoid.html#1322" class="Function">inverseʳ⇒injective</a> <a id="1341" class="Symbol">:</a> <a id="1343" class="Symbol">∀</a> <a id="1345" href="Function.Consequences.Setoid.html#1345" class="Bound">f</a> <a id="1347" class="Symbol">→</a> <a id="1349" href="Function.Definitions.html#1169" class="Function">Inverseʳ</a> <a id="1358" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1361" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1364" href="Function.Consequences.Setoid.html#1345" class="Bound">f</a> <a id="1366" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="1370" class="Symbol">→</a> <a id="1372" href="Function.Definitions.html#842" class="Function">Injective</a> <a id="1382" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1385" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1388" href="Function.Consequences.Setoid.html#1345" class="Bound">f</a>
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<a id="1390" href="Function.Consequences.Setoid.html#1322" class="Function">inverseʳ⇒injective</a> <a id="1409" href="Function.Consequences.Setoid.html#1409" class="Bound">f</a> <a id="1411" class="Symbol">=</a> <a id="1413" href="Function.Consequences.html#1451" class="Function">C.inverseʳ⇒injective</a> <a id="1434" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1437" href="Function.Consequences.Setoid.html#1409" class="Bound">f</a> <a id="1439" href="Relation.Binary.Structures.html#1596" class="Function">T.refl</a> <a id="1446" href="Relation.Binary.Structures.html#1200" class="Function">S.sym</a> <a id="1452" href="Relation.Binary.Structures.html#1226" class="Function">S.trans</a>
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<a id="1461" class="Comment">------------------------------------------------------------------------</a>
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<a id="1534" class="Comment">-- Inverseᵇ</a>
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<a id="inverseᵇ⇒bijective"></a><a id="1547" href="Function.Consequences.Setoid.html#1547" class="Function">inverseᵇ⇒bijective</a> <a id="1566" class="Symbol">:</a> <a id="1568" href="Function.Definitions.html#1256" class="Function">Inverseᵇ</a> <a id="1577" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1580" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1583" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="1585" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="1589" class="Symbol">→</a> <a id="1591" href="Function.Definitions.html#1008" class="Function">Bijective</a> <a id="1601" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1604" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1607" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a>
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<a id="1609" href="Function.Consequences.Setoid.html#1547" class="Function">inverseᵇ⇒bijective</a> <a id="1628" class="Symbol">=</a> <a id="1630" href="Function.Consequences.html#1872" class="Function">C.inverseᵇ⇒bijective</a> <a id="1651" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1654" href="Relation.Binary.Structures.html#1596" class="Function">T.refl</a> <a id="1661" href="Relation.Binary.Structures.html#1200" class="Function">S.sym</a> <a id="1667" href="Relation.Binary.Structures.html#1226" class="Function">S.trans</a>
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<a id="1676" class="Comment">------------------------------------------------------------------------</a>
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<a id="1749" class="Comment">-- StrictlySurjective</a>
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<a id="surjective⇒strictlySurjective"></a><a id="1772" href="Function.Consequences.Setoid.html#1772" class="Function">surjective⇒strictlySurjective</a> <a id="1802" class="Symbol">:</a> <a id="1804" href="Function.Definitions.html#919" class="Function">Surjective</a> <a id="1815" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="1818" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1821" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="1823" class="Symbol">→</a>
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<a id="1858" href="Function.Definitions.html#1522" class="Function">StrictlySurjective</a> <a id="1877" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1880" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a>
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<a id="1882" href="Function.Consequences.Setoid.html#1772" class="Function">surjective⇒strictlySurjective</a> <a id="1912" class="Symbol">=</a>
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<a id="1916" href="Function.Consequences.html#2341" class="Function">C.surjective⇒strictlySurjective</a> <a id="1948" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="1951" href="Relation.Binary.Structures.html#1596" class="Function">S.refl</a>
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<a id="strictlySurjective⇒surjective"></a><a id="1959" href="Function.Consequences.Setoid.html#1959" class="Function">strictlySurjective⇒surjective</a> <a id="1989" class="Symbol">:</a> <a id="1991" href="Function.Definitions.html#765" class="Function">Congruent</a> <a id="2001" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2004" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2007" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2009" class="Symbol">→</a>
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<a id="2044" href="Function.Definitions.html#1522" class="Function">StrictlySurjective</a> <a id="2063" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2066" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2068" class="Symbol">→</a>
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<a id="2103" href="Function.Definitions.html#919" class="Function">Surjective</a> <a id="2114" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2117" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2120" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a>
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<a id="2122" href="Function.Consequences.Setoid.html#1959" class="Function">strictlySurjective⇒surjective</a> <a id="2152" class="Symbol">=</a>
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<a id="2156" href="Function.Consequences.html#2635" class="Function">C.strictlySurjective⇒surjective</a> <a id="2188" href="Relation.Binary.Structures.html#1226" class="Function">T.trans</a>
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<a id="2197" class="Comment">------------------------------------------------------------------------</a>
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<a id="2270" class="Comment">-- StrictlyInverseˡ</a>
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<a id="inverseˡ⇒strictlyInverseˡ"></a><a id="2291" href="Function.Consequences.Setoid.html#2291" class="Function">inverseˡ⇒strictlyInverseˡ</a> <a id="2317" class="Symbol">:</a> <a id="2319" href="Function.Definitions.html#1082" class="Function">Inverseˡ</a> <a id="2328" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2331" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2334" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2336" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="2340" class="Symbol">→</a>
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<a id="2370" href="Function.Definitions.html#1622" class="Function">StrictlyInverseˡ</a> <a id="2387" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2390" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2392" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a>
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<a id="2396" href="Function.Consequences.Setoid.html#2291" class="Function">inverseˡ⇒strictlyInverseˡ</a> <a id="2422" class="Symbol">=</a> <a id="2424" href="Function.Consequences.html#3050" class="Function">C.inverseˡ⇒strictlyInverseˡ</a> <a id="2452" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2455" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2458" href="Relation.Binary.Structures.html#1596" class="Function">S.refl</a>
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<a id="strictlyInverseˡ⇒inverseˡ"></a><a id="2466" href="Function.Consequences.Setoid.html#2466" class="Function">strictlyInverseˡ⇒inverseˡ</a> <a id="2492" class="Symbol">:</a> <a id="2494" href="Function.Definitions.html#765" class="Function">Congruent</a> <a id="2504" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2507" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2510" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2512" class="Symbol">→</a>
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<a id="2542" href="Function.Definitions.html#1622" class="Function">StrictlyInverseˡ</a> <a id="2559" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2562" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2564" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="2568" class="Symbol">→</a>
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<a id="2598" href="Function.Definitions.html#1082" class="Function">Inverseˡ</a> <a id="2607" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2610" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2613" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2615" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a>
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<a id="2619" href="Function.Consequences.Setoid.html#2466" class="Function">strictlyInverseˡ⇒inverseˡ</a> <a id="2645" class="Symbol">=</a> <a id="2647" href="Function.Consequences.html#3317" class="Function">C.strictlyInverseˡ⇒inverseˡ</a> <a id="2675" href="Relation.Binary.Structures.html#1226" class="Function">T.trans</a>
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<a id="2684" class="Comment">------------------------------------------------------------------------</a>
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<a id="2757" class="Comment">-- StrictlyInverseʳ</a>
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<a id="inverseʳ⇒strictlyInverseʳ"></a><a id="2778" href="Function.Consequences.Setoid.html#2778" class="Function">inverseʳ⇒strictlyInverseʳ</a> <a id="2804" class="Symbol">:</a> <a id="2806" href="Function.Definitions.html#1169" class="Function">Inverseʳ</a> <a id="2815" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2818" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2821" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2823" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="2827" class="Symbol">→</a>
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<a id="2857" href="Function.Definitions.html#1726" class="Function">StrictlyInverseʳ</a> <a id="2874" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2877" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="2879" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a>
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<a id="2883" href="Function.Consequences.Setoid.html#2778" class="Function">inverseʳ⇒strictlyInverseʳ</a> <a id="2909" class="Symbol">=</a> <a id="2911" href="Function.Consequences.html#3695" class="Function">C.inverseʳ⇒strictlyInverseʳ</a> <a id="2939" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2942" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2945" href="Relation.Binary.Structures.html#1596" class="Function">T.refl</a>
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<a id="strictlyInverseʳ⇒inverseʳ"></a><a id="2953" href="Function.Consequences.Setoid.html#2953" class="Function">strictlyInverseʳ⇒inverseʳ</a> <a id="2979" class="Symbol">:</a> <a id="2981" href="Function.Definitions.html#765" class="Function">Congruent</a> <a id="2991" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="2994" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="2997" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="3001" class="Symbol">→</a>
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<a id="3031" href="Function.Definitions.html#1726" class="Function">StrictlyInverseʳ</a> <a id="3048" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="3051" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="3053" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a> <a id="3057" class="Symbol">→</a>
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<a id="3087" href="Function.Definitions.html#1169" class="Function">Inverseʳ</a> <a id="3096" href="Function.Consequences.Setoid.html#695" class="Function">≈₁</a> <a id="3099" href="Function.Consequences.Setoid.html#766" class="Field">≈₂</a> <a id="3102" href="Function.Consequences.Setoid.html#786" class="Generalizable">f</a> <a id="3104" href="Function.Consequences.Setoid.html#800" class="Generalizable">f⁻¹</a>
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<a id="3108" href="Function.Consequences.Setoid.html#2953" class="Function">strictlyInverseʳ⇒inverseʳ</a> <a id="3134" class="Symbol">=</a> <a id="3136" href="Function.Consequences.html#3962" class="Function">C.strictlyInverseʳ⇒inverseʳ</a> <a id="3164" href="Relation.Binary.Structures.html#1226" class="Function">S.trans</a>
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