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221 lines
83 KiB
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<html><head><meta charset="utf-8"><title>Relation.Binary.Construct.On</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">-- Many properties which hold for `_∼_` also hold for `_∼_ on f`</a>
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<a id="171" class="Comment">------------------------------------------------------------------------</a>
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<a id="245" class="Symbol">{-#</a> <a id="249" class="Keyword">OPTIONS</a> <a id="257" class="Pragma">--cubical-compatible</a> <a id="278" class="Pragma">--safe</a> <a id="285" class="Symbol">#-}</a>
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<a id="290" class="Keyword">module</a> <a id="297" href="Relation.Binary.Construct.On.html" class="Module">Relation.Binary.Construct.On</a> <a id="326" class="Keyword">where</a>
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<a id="333" class="Keyword">open</a> <a id="338" class="Keyword">import</a> <a id="345" href="Data.Product.html" class="Module">Data.Product</a>
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<a id="358" class="Keyword">open</a> <a id="363" class="Keyword">import</a> <a id="370" href="Function.Base.html" class="Module">Function.Base</a> <a id="384" class="Keyword">using</a> <a id="390" class="Symbol">(</a><a id="391" href="Function.Base.html#6294" class="Function Operator">_on_</a><a id="395" class="Symbol">;</a> <a id="397" href="Function.Base.html#1040" class="Function Operator">_∘_</a><a id="400" class="Symbol">)</a>
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<a id="402" class="Keyword">open</a> <a id="407" class="Keyword">import</a> <a id="414" href="Induction.WellFounded.html" class="Module">Induction.WellFounded</a> <a id="436" class="Keyword">using</a> <a id="442" class="Symbol">(</a><a id="443" href="Induction.WellFounded.html#1257" class="Function">WellFounded</a><a id="454" class="Symbol">;</a> <a id="456" href="Induction.WellFounded.html#1009" class="Datatype">Acc</a><a id="459" class="Symbol">;</a> <a id="461" href="Induction.WellFounded.html#1071" class="InductiveConstructor">acc</a><a id="464" class="Symbol">)</a>
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<a id="466" class="Keyword">open</a> <a id="471" class="Keyword">import</a> <a id="478" href="Level.html" class="Module">Level</a> <a id="484" class="Keyword">using</a> <a id="490" class="Symbol">(</a><a id="491" href="Agda.Primitive.html#591" class="Postulate">Level</a><a id="496" class="Symbol">)</a>
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<a id="498" class="Keyword">open</a> <a id="503" class="Keyword">import</a> <a id="510" href="Relation.Binary.html" class="Module">Relation.Binary</a>
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<a id="527" class="Keyword">private</a>
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<a id="537" class="Keyword">variable</a>
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<a id="550" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="552" href="Relation.Binary.Construct.On.html#552" class="Generalizable">b</a> <a id="554" href="Relation.Binary.Construct.On.html#554" class="Generalizable">p</a> <a id="556" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a> <a id="558" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="561" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a> <a id="564" class="Symbol">:</a> <a id="566" href="Agda.Primitive.html#591" class="Postulate">Level</a>
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<a id="576" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a> <a id="578" class="Symbol">:</a> <a id="580" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="584" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a>
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<a id="590" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="592" class="Symbol">:</a> <a id="594" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="598" href="Relation.Binary.Construct.On.html#552" class="Generalizable">b</a>
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<a id="601" class="Comment">------------------------------------------------------------------------</a>
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<a id="674" class="Comment">-- Definitions</a>
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<a id="690" class="Keyword">module</a> <a id="697" href="Relation.Binary.Construct.On.html#697" class="Module">_</a> <a id="699" class="Symbol">(</a><a id="700" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="702" class="Symbol">:</a> <a id="704" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="706" class="Symbol">→</a> <a id="708" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a><a id="709" class="Symbol">)</a> <a id="711" class="Keyword">where</a>
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<a id="720" href="Relation.Binary.Construct.On.html#720" class="Function">implies</a> <a id="728" class="Symbol">:</a> <a id="730" class="Symbol">(</a><a id="731" href="Relation.Binary.Construct.On.html#731" class="Bound">≈</a> <a id="733" class="Symbol">:</a> <a id="735" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="739" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="741" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="743" class="Symbol">)</a> <a id="745" class="Symbol">(</a><a id="746" href="Relation.Binary.Construct.On.html#746" class="Bound">∼</a> <a id="748" class="Symbol">:</a> <a id="750" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="754" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="756" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="758" class="Symbol">)</a> <a id="760" class="Symbol">→</a>
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<a id="774" href="Relation.Binary.Construct.On.html#731" class="Bound">≈</a> <a id="776" href="Relation.Binary.Core.html#1263" class="Function Operator">⇒</a> <a id="778" href="Relation.Binary.Construct.On.html#746" class="Bound">∼</a> <a id="780" class="Symbol">→</a> <a id="782" class="Symbol">(</a><a id="783" href="Relation.Binary.Construct.On.html#731" class="Bound">≈</a> <a id="785" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="788" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="789" class="Symbol">)</a> <a id="791" href="Relation.Binary.Core.html#1263" class="Function Operator">⇒</a> <a id="793" class="Symbol">(</a><a id="794" href="Relation.Binary.Construct.On.html#746" class="Bound">∼</a> <a id="796" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="799" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="800" class="Symbol">)</a>
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<a id="804" href="Relation.Binary.Construct.On.html#720" class="Function">implies</a> <a id="812" class="Symbol">_</a> <a id="814" class="Symbol">_</a> <a id="816" href="Relation.Binary.Construct.On.html#816" class="Bound">impl</a> <a id="821" class="Symbol">=</a> <a id="823" href="Relation.Binary.Construct.On.html#816" class="Bound">impl</a>
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<a id="831" href="Relation.Binary.Construct.On.html#831" class="Function">reflexive</a> <a id="841" class="Symbol">:</a> <a id="843" class="Symbol">(</a><a id="844" href="Relation.Binary.Construct.On.html#844" class="Bound">∼</a> <a id="846" class="Symbol">:</a> <a id="848" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="852" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="854" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="855" class="Symbol">)</a> <a id="857" class="Symbol">→</a> <a id="859" href="Relation.Binary.Definitions.html#1348" class="Function">Reflexive</a> <a id="869" href="Relation.Binary.Construct.On.html#844" class="Bound">∼</a> <a id="871" class="Symbol">→</a> <a id="873" href="Relation.Binary.Definitions.html#1348" class="Function">Reflexive</a> <a id="883" class="Symbol">(</a><a id="884" href="Relation.Binary.Construct.On.html#844" class="Bound">∼</a> <a id="886" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="889" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="890" class="Symbol">)</a>
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<a id="894" href="Relation.Binary.Construct.On.html#831" class="Function">reflexive</a> <a id="904" class="Symbol">_</a> <a id="906" href="Relation.Binary.Construct.On.html#906" class="Bound">refl</a> <a id="911" class="Symbol">=</a> <a id="913" href="Relation.Binary.Construct.On.html#906" class="Bound">refl</a>
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<a id="921" href="Relation.Binary.Construct.On.html#921" class="Function">irreflexive</a> <a id="933" class="Symbol">:</a> <a id="935" class="Symbol">(</a><a id="936" href="Relation.Binary.Construct.On.html#936" class="Bound">≈</a> <a id="938" class="Symbol">:</a> <a id="940" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="944" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="946" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="948" class="Symbol">)</a> <a id="950" class="Symbol">(</a><a id="951" href="Relation.Binary.Construct.On.html#951" class="Bound">∼</a> <a id="953" class="Symbol">:</a> <a id="955" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="959" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="961" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="963" class="Symbol">)</a> <a id="965" class="Symbol">→</a>
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<a id="983" href="Relation.Binary.Definitions.html#2250" class="Function">Irreflexive</a> <a id="995" href="Relation.Binary.Construct.On.html#936" class="Bound">≈</a> <a id="997" href="Relation.Binary.Construct.On.html#951" class="Bound">∼</a> <a id="999" class="Symbol">→</a> <a id="1001" href="Relation.Binary.Definitions.html#2250" class="Function">Irreflexive</a> <a id="1013" class="Symbol">(</a><a id="1014" href="Relation.Binary.Construct.On.html#936" class="Bound">≈</a> <a id="1016" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1019" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1020" class="Symbol">)</a> <a id="1022" class="Symbol">(</a><a id="1023" href="Relation.Binary.Construct.On.html#951" class="Bound">∼</a> <a id="1025" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1028" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1029" class="Symbol">)</a>
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<a id="1033" href="Relation.Binary.Construct.On.html#921" class="Function">irreflexive</a> <a id="1045" class="Symbol">_</a> <a id="1047" class="Symbol">_</a> <a id="1049" href="Relation.Binary.Construct.On.html#1049" class="Bound">irrefl</a> <a id="1056" class="Symbol">=</a> <a id="1058" href="Relation.Binary.Construct.On.html#1049" class="Bound">irrefl</a>
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<a id="1068" href="Relation.Binary.Construct.On.html#1068" class="Function">symmetric</a> <a id="1078" class="Symbol">:</a> <a id="1080" class="Symbol">(</a><a id="1081" href="Relation.Binary.Construct.On.html#1081" class="Bound">∼</a> <a id="1083" class="Symbol">:</a> <a id="1085" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1089" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1091" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1092" class="Symbol">)</a> <a id="1094" class="Symbol">→</a> <a id="1096" href="Relation.Binary.Definitions.html#1507" class="Function">Symmetric</a> <a id="1106" href="Relation.Binary.Construct.On.html#1081" class="Bound">∼</a> <a id="1108" class="Symbol">→</a> <a id="1110" href="Relation.Binary.Definitions.html#1507" class="Function">Symmetric</a> <a id="1120" class="Symbol">(</a><a id="1121" href="Relation.Binary.Construct.On.html#1081" class="Bound">∼</a> <a id="1123" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1126" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1127" class="Symbol">)</a>
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<a id="1131" href="Relation.Binary.Construct.On.html#1068" class="Function">symmetric</a> <a id="1141" class="Symbol">_</a> <a id="1143" href="Relation.Binary.Construct.On.html#1143" class="Bound">sym</a> <a id="1147" class="Symbol">=</a> <a id="1149" href="Relation.Binary.Construct.On.html#1143" class="Bound">sym</a>
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<a id="1156" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="1167" class="Symbol">:</a> <a id="1169" class="Symbol">(</a><a id="1170" href="Relation.Binary.Construct.On.html#1170" class="Bound">∼</a> <a id="1172" class="Symbol">:</a> <a id="1174" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1178" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1180" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1181" class="Symbol">)</a> <a id="1183" class="Symbol">→</a> <a id="1185" href="Relation.Binary.Definitions.html#1875" class="Function">Transitive</a> <a id="1196" href="Relation.Binary.Construct.On.html#1170" class="Bound">∼</a> <a id="1198" class="Symbol">→</a> <a id="1200" href="Relation.Binary.Definitions.html#1875" class="Function">Transitive</a> <a id="1211" class="Symbol">(</a><a id="1212" href="Relation.Binary.Construct.On.html#1170" class="Bound">∼</a> <a id="1214" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1217" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1218" class="Symbol">)</a>
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<a id="1222" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="1233" class="Symbol">_</a> <a id="1235" href="Relation.Binary.Construct.On.html#1235" class="Bound">trans</a> <a id="1241" class="Symbol">=</a> <a id="1243" href="Relation.Binary.Construct.On.html#1235" class="Bound">trans</a>
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<a id="1252" href="Relation.Binary.Construct.On.html#1252" class="Function">antisymmetric</a> <a id="1266" class="Symbol">:</a> <a id="1268" class="Symbol">(</a><a id="1269" href="Relation.Binary.Construct.On.html#1269" class="Bound">≈</a> <a id="1271" class="Symbol">:</a> <a id="1273" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1277" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1279" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="1281" class="Symbol">)</a> <a id="1283" class="Symbol">(</a><a id="1284" href="Relation.Binary.Construct.On.html#1284" class="Bound">≤</a> <a id="1286" class="Symbol">:</a> <a id="1288" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1292" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1294" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="1296" class="Symbol">)</a> <a id="1298" class="Symbol">→</a>
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<a id="1318" href="Relation.Binary.Definitions.html#2091" class="Function">Antisymmetric</a> <a id="1332" href="Relation.Binary.Construct.On.html#1269" class="Bound">≈</a> <a id="1334" href="Relation.Binary.Construct.On.html#1284" class="Bound">≤</a> <a id="1336" class="Symbol">→</a> <a id="1338" href="Relation.Binary.Definitions.html#2091" class="Function">Antisymmetric</a> <a id="1352" class="Symbol">(</a><a id="1353" href="Relation.Binary.Construct.On.html#1269" class="Bound">≈</a> <a id="1355" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1358" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1359" class="Symbol">)</a> <a id="1361" class="Symbol">(</a><a id="1362" href="Relation.Binary.Construct.On.html#1284" class="Bound">≤</a> <a id="1364" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1367" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1368" class="Symbol">)</a>
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<a id="1372" href="Relation.Binary.Construct.On.html#1252" class="Function">antisymmetric</a> <a id="1386" class="Symbol">_</a> <a id="1388" class="Symbol">_</a> <a id="1390" href="Relation.Binary.Construct.On.html#1390" class="Bound">antisym</a> <a id="1398" class="Symbol">=</a> <a id="1400" href="Relation.Binary.Construct.On.html#1390" class="Bound">antisym</a>
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<a id="1411" href="Relation.Binary.Construct.On.html#1411" class="Function">asymmetric</a> <a id="1422" class="Symbol">:</a> <a id="1424" class="Symbol">(</a><a id="1425" href="Relation.Binary.Construct.On.html#1425" class="Bound"><</a> <a id="1427" class="Symbol">:</a> <a id="1429" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1433" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1435" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1436" class="Symbol">)</a> <a id="1438" class="Symbol">→</a> <a id="1440" href="Relation.Binary.Definitions.html#2362" class="Function">Asymmetric</a> <a id="1451" href="Relation.Binary.Construct.On.html#1425" class="Bound"><</a> <a id="1453" class="Symbol">→</a> <a id="1455" href="Relation.Binary.Definitions.html#2362" class="Function">Asymmetric</a> <a id="1466" class="Symbol">(</a><a id="1467" href="Relation.Binary.Construct.On.html#1425" class="Bound"><</a> <a id="1469" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1472" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1473" class="Symbol">)</a>
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<a id="1477" href="Relation.Binary.Construct.On.html#1411" class="Function">asymmetric</a> <a id="1488" class="Symbol">_</a> <a id="1490" href="Relation.Binary.Construct.On.html#1490" class="Bound">asym</a> <a id="1495" class="Symbol">=</a> <a id="1497" href="Relation.Binary.Construct.On.html#1490" class="Bound">asym</a>
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<a id="1505" href="Relation.Binary.Construct.On.html#1505" class="Function">respects</a> <a id="1514" class="Symbol">:</a> <a id="1516" class="Symbol">(</a><a id="1517" href="Relation.Binary.Construct.On.html#1517" class="Bound">∼</a> <a id="1519" class="Symbol">:</a> <a id="1521" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1525" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1527" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1528" class="Symbol">)</a> <a id="1530" class="Symbol">(</a><a id="1531" href="Relation.Binary.Construct.On.html#1531" class="Bound">P</a> <a id="1533" class="Symbol">:</a> <a id="1535" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1537" class="Symbol">→</a> <a id="1539" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1543" href="Relation.Binary.Construct.On.html#554" class="Generalizable">p</a><a id="1544" class="Symbol">)</a> <a id="1546" class="Symbol">→</a>
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<a id="1561" href="Relation.Binary.Construct.On.html#1531" class="Bound">P</a> <a id="1563" href="Relation.Binary.Definitions.html#3602" class="Function Operator">Respects</a> <a id="1572" href="Relation.Binary.Construct.On.html#1517" class="Bound">∼</a> <a id="1574" class="Symbol">→</a> <a id="1576" class="Symbol">(</a><a id="1577" href="Relation.Binary.Construct.On.html#1531" class="Bound">P</a> <a id="1579" href="Function.Base.html#1040" class="Function Operator">∘</a> <a id="1581" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1582" class="Symbol">)</a> <a id="1584" href="Relation.Binary.Definitions.html#3602" class="Function Operator">Respects</a> <a id="1593" class="Symbol">(</a><a id="1594" href="Relation.Binary.Construct.On.html#1517" class="Bound">∼</a> <a id="1596" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1599" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1600" class="Symbol">)</a>
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<a id="1604" href="Relation.Binary.Construct.On.html#1505" class="Function">respects</a> <a id="1613" class="Symbol">_</a> <a id="1615" class="Symbol">_</a> <a id="1617" href="Relation.Binary.Construct.On.html#1617" class="Bound">resp</a> <a id="1622" class="Symbol">=</a> <a id="1624" href="Relation.Binary.Construct.On.html#1617" class="Bound">resp</a>
|
|||
|
|
|
|||
|
|
<a id="1632" href="Relation.Binary.Construct.On.html#1632" class="Function">respects₂</a> <a id="1642" class="Symbol">:</a> <a id="1644" class="Symbol">(</a><a id="1645" href="Relation.Binary.Construct.On.html#1645" class="Bound">∼₁</a> <a id="1648" class="Symbol">:</a> <a id="1650" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1654" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1656" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="1658" class="Symbol">)</a> <a id="1660" class="Symbol">(</a><a id="1661" href="Relation.Binary.Construct.On.html#1661" class="Bound">∼₂</a> <a id="1664" class="Symbol">:</a> <a id="1666" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1670" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1672" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="1674" class="Symbol">)</a> <a id="1676" class="Symbol">→</a>
|
|||
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|
<a id="1692" href="Relation.Binary.Construct.On.html#1645" class="Bound">∼₁</a> <a id="1695" href="Relation.Binary.Definitions.html#4086" class="Function Operator">Respects₂</a> <a id="1705" href="Relation.Binary.Construct.On.html#1661" class="Bound">∼₂</a> <a id="1708" class="Symbol">→</a> <a id="1710" class="Symbol">(</a><a id="1711" href="Relation.Binary.Construct.On.html#1645" class="Bound">∼₁</a> <a id="1714" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1717" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1718" class="Symbol">)</a> <a id="1720" href="Relation.Binary.Definitions.html#4086" class="Function Operator">Respects₂</a> <a id="1730" class="Symbol">(</a><a id="1731" href="Relation.Binary.Construct.On.html#1661" class="Bound">∼₂</a> <a id="1734" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1737" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1738" class="Symbol">)</a>
|
|||
|
|
<a id="1742" href="Relation.Binary.Construct.On.html#1632" class="Function">respects₂</a> <a id="1752" class="Symbol">_</a> <a id="1754" class="Symbol">_</a> <a id="1756" class="Symbol">(</a><a id="1757" href="Relation.Binary.Construct.On.html#1757" class="Bound">resp₁</a> <a id="1763" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1765" href="Relation.Binary.Construct.On.html#1765" class="Bound">resp₂</a><a id="1770" class="Symbol">)</a> <a id="1772" class="Symbol">=</a> <a id="1774" class="Symbol">(</a><a id="1775" href="Relation.Binary.Construct.On.html#1757" class="Bound">resp₁</a> <a id="1781" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1783" href="Relation.Binary.Construct.On.html#1765" class="Bound">resp₂</a><a id="1788" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="1793" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="1803" class="Symbol">:</a> <a id="1805" class="Symbol">(</a><a id="1806" href="Relation.Binary.Construct.On.html#1806" class="Bound">∼</a> <a id="1808" class="Symbol">:</a> <a id="1810" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1814" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1816" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1817" class="Symbol">)</a> <a id="1819" class="Symbol">→</a> <a id="1821" href="Relation.Binary.Definitions.html#4584" class="Function">Decidable</a> <a id="1831" href="Relation.Binary.Construct.On.html#1806" class="Bound">∼</a> <a id="1833" class="Symbol">→</a> <a id="1835" href="Relation.Binary.Definitions.html#4584" class="Function">Decidable</a> <a id="1845" class="Symbol">(</a><a id="1846" href="Relation.Binary.Construct.On.html#1806" class="Bound">∼</a> <a id="1848" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1851" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1852" class="Symbol">)</a>
|
|||
|
|
<a id="1856" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="1866" class="Symbol">_</a> <a id="1868" href="Relation.Binary.Construct.On.html#1868" class="Bound">dec</a> <a id="1872" href="Relation.Binary.Construct.On.html#1872" class="Bound">x</a> <a id="1874" href="Relation.Binary.Construct.On.html#1874" class="Bound">y</a> <a id="1876" class="Symbol">=</a> <a id="1878" href="Relation.Binary.Construct.On.html#1868" class="Bound">dec</a> <a id="1882" class="Symbol">(</a><a id="1883" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="1885" href="Relation.Binary.Construct.On.html#1872" class="Bound">x</a><a id="1886" class="Symbol">)</a> <a id="1888" class="Symbol">(</a><a id="1889" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="1891" href="Relation.Binary.Construct.On.html#1874" class="Bound">y</a><a id="1892" class="Symbol">)</a>
|
|||
|
|
|
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|
|
<a id="1897" href="Relation.Binary.Construct.On.html#1897" class="Function">total</a> <a id="1903" class="Symbol">:</a> <a id="1905" class="Symbol">(</a><a id="1906" href="Relation.Binary.Construct.On.html#1906" class="Bound">∼</a> <a id="1908" class="Symbol">:</a> <a id="1910" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1914" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="1916" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="1917" class="Symbol">)</a> <a id="1919" class="Symbol">→</a> <a id="1921" href="Relation.Binary.Definitions.html#2593" class="Function">Total</a> <a id="1927" href="Relation.Binary.Construct.On.html#1906" class="Bound">∼</a> <a id="1929" class="Symbol">→</a> <a id="1931" href="Relation.Binary.Definitions.html#2593" class="Function">Total</a> <a id="1937" class="Symbol">(</a><a id="1938" href="Relation.Binary.Construct.On.html#1906" class="Bound">∼</a> <a id="1940" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="1943" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="1944" class="Symbol">)</a>
|
|||
|
|
<a id="1948" href="Relation.Binary.Construct.On.html#1897" class="Function">total</a> <a id="1954" class="Symbol">_</a> <a id="1956" href="Relation.Binary.Construct.On.html#1956" class="Bound">tot</a> <a id="1960" href="Relation.Binary.Construct.On.html#1960" class="Bound">x</a> <a id="1962" href="Relation.Binary.Construct.On.html#1962" class="Bound">y</a> <a id="1964" class="Symbol">=</a> <a id="1966" href="Relation.Binary.Construct.On.html#1956" class="Bound">tot</a> <a id="1970" class="Symbol">(</a><a id="1971" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="1973" href="Relation.Binary.Construct.On.html#1960" class="Bound">x</a><a id="1974" class="Symbol">)</a> <a id="1976" class="Symbol">(</a><a id="1977" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="1979" href="Relation.Binary.Construct.On.html#1962" class="Bound">y</a><a id="1980" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="1985" href="Relation.Binary.Construct.On.html#1985" class="Function">trichotomous</a> <a id="1998" class="Symbol">:</a> <a id="2000" class="Symbol">(</a><a id="2001" href="Relation.Binary.Construct.On.html#2001" class="Bound">≈</a> <a id="2003" class="Symbol">:</a> <a id="2005" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2009" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="2011" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="2013" class="Symbol">)</a> <a id="2015" class="Symbol">(</a><a id="2016" href="Relation.Binary.Construct.On.html#2016" class="Bound"><</a> <a id="2018" class="Symbol">:</a> <a id="2020" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2024" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="2026" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="2028" class="Symbol">)</a> <a id="2030" class="Symbol">→</a>
|
|||
|
|
<a id="2049" href="Relation.Binary.Definitions.html#2964" class="Function">Trichotomous</a> <a id="2062" href="Relation.Binary.Construct.On.html#2001" class="Bound">≈</a> <a id="2064" href="Relation.Binary.Construct.On.html#2016" class="Bound"><</a> <a id="2066" class="Symbol">→</a> <a id="2068" href="Relation.Binary.Definitions.html#2964" class="Function">Trichotomous</a> <a id="2081" class="Symbol">(</a><a id="2082" href="Relation.Binary.Construct.On.html#2001" class="Bound">≈</a> <a id="2084" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2087" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="2088" class="Symbol">)</a> <a id="2090" class="Symbol">(</a><a id="2091" href="Relation.Binary.Construct.On.html#2016" class="Bound"><</a> <a id="2093" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2096" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="2097" class="Symbol">)</a>
|
|||
|
|
<a id="2101" href="Relation.Binary.Construct.On.html#1985" class="Function">trichotomous</a> <a id="2114" class="Symbol">_</a> <a id="2116" class="Symbol">_</a> <a id="2118" href="Relation.Binary.Construct.On.html#2118" class="Bound">compare</a> <a id="2126" href="Relation.Binary.Construct.On.html#2126" class="Bound">x</a> <a id="2128" href="Relation.Binary.Construct.On.html#2128" class="Bound">y</a> <a id="2130" class="Symbol">=</a> <a id="2132" href="Relation.Binary.Construct.On.html#2118" class="Bound">compare</a> <a id="2140" class="Symbol">(</a><a id="2141" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="2143" href="Relation.Binary.Construct.On.html#2126" class="Bound">x</a><a id="2144" class="Symbol">)</a> <a id="2146" class="Symbol">(</a><a id="2147" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="2149" href="Relation.Binary.Construct.On.html#2128" class="Bound">y</a><a id="2150" class="Symbol">)</a>
|
|||
|
|
|
|||
|
|
<a id="2155" href="Relation.Binary.Construct.On.html#2155" class="Function">accessible</a> <a id="2166" class="Symbol">:</a> <a id="2168" class="Symbol">∀</a> <a id="2170" class="Symbol">{</a><a id="2171" href="Relation.Binary.Construct.On.html#2171" class="Bound">∼</a> <a id="2173" class="Symbol">:</a> <a id="2175" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2179" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="2181" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="2182" class="Symbol">}</a> <a id="2184" class="Symbol">{</a><a id="2185" href="Relation.Binary.Construct.On.html#2185" class="Bound">x</a><a id="2186" class="Symbol">}</a> <a id="2188" class="Symbol">→</a> <a id="2190" href="Induction.WellFounded.html#1009" class="Datatype">Acc</a> <a id="2194" href="Relation.Binary.Construct.On.html#2171" class="Bound">∼</a> <a id="2196" class="Symbol">(</a><a id="2197" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="2199" href="Relation.Binary.Construct.On.html#2185" class="Bound">x</a><a id="2200" class="Symbol">)</a> <a id="2202" class="Symbol">→</a> <a id="2204" href="Induction.WellFounded.html#1009" class="Datatype">Acc</a> <a id="2208" class="Symbol">(</a><a id="2209" href="Relation.Binary.Construct.On.html#2171" class="Bound">∼</a> <a id="2211" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2214" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="2215" class="Symbol">)</a> <a id="2217" href="Relation.Binary.Construct.On.html#2185" class="Bound">x</a>
|
|||
|
|
<a id="2221" href="Relation.Binary.Construct.On.html#2155" class="Function">accessible</a> <a id="2232" class="Symbol">(</a><a id="2233" href="Induction.WellFounded.html#1071" class="InductiveConstructor">acc</a> <a id="2237" href="Relation.Binary.Construct.On.html#2237" class="Bound">rs</a><a id="2239" class="Symbol">)</a> <a id="2241" class="Symbol">=</a> <a id="2243" href="Induction.WellFounded.html#1071" class="InductiveConstructor">acc</a> <a id="2247" class="Symbol">(λ</a> <a id="2250" href="Relation.Binary.Construct.On.html#2250" class="Bound">y</a> <a id="2252" href="Relation.Binary.Construct.On.html#2252" class="Bound">fy<fx</a> <a id="2258" class="Symbol">→</a> <a id="2260" href="Relation.Binary.Construct.On.html#2155" class="Function">accessible</a> <a id="2271" class="Symbol">(</a><a id="2272" href="Relation.Binary.Construct.On.html#2237" class="Bound">rs</a> <a id="2275" class="Symbol">(</a><a id="2276" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="2278" href="Relation.Binary.Construct.On.html#2250" class="Bound">y</a><a id="2279" class="Symbol">)</a> <a id="2281" href="Relation.Binary.Construct.On.html#2252" class="Bound">fy<fx</a><a id="2286" class="Symbol">))</a>
|
|||
|
|
|
|||
|
|
<a id="2292" href="Relation.Binary.Construct.On.html#2292" class="Function">wellFounded</a> <a id="2304" class="Symbol">:</a> <a id="2306" class="Symbol">{</a><a id="2307" href="Relation.Binary.Construct.On.html#2307" class="Bound">∼</a> <a id="2309" class="Symbol">:</a> <a id="2311" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2315" href="Relation.Binary.Construct.On.html#708" class="Bound">A</a> <a id="2317" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="2318" class="Symbol">}</a> <a id="2320" class="Symbol">→</a> <a id="2322" href="Induction.WellFounded.html#1257" class="Function">WellFounded</a> <a id="2334" href="Relation.Binary.Construct.On.html#2307" class="Bound">∼</a> <a id="2336" class="Symbol">→</a> <a id="2338" href="Induction.WellFounded.html#1257" class="Function">WellFounded</a> <a id="2350" class="Symbol">(</a><a id="2351" href="Relation.Binary.Construct.On.html#2307" class="Bound">∼</a> <a id="2353" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2356" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a><a id="2357" class="Symbol">)</a>
|
|||
|
|
<a id="2361" href="Relation.Binary.Construct.On.html#2292" class="Function">wellFounded</a> <a id="2373" href="Relation.Binary.Construct.On.html#2373" class="Bound">wf</a> <a id="2376" href="Relation.Binary.Construct.On.html#2376" class="Bound">x</a> <a id="2378" class="Symbol">=</a> <a id="2380" href="Relation.Binary.Construct.On.html#2155" class="Function">accessible</a> <a id="2391" class="Symbol">(</a><a id="2392" href="Relation.Binary.Construct.On.html#2373" class="Bound">wf</a> <a id="2395" class="Symbol">(</a><a id="2396" href="Relation.Binary.Construct.On.html#700" class="Bound">f</a> <a id="2398" href="Relation.Binary.Construct.On.html#2376" class="Bound">x</a><a id="2399" class="Symbol">))</a>
|
|||
|
|
|
|||
|
|
<a id="2403" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="2476" class="Comment">-- Structures</a>
|
|||
|
|
|
|||
|
|
<a id="2491" class="Keyword">module</a> <a id="2498" href="Relation.Binary.Construct.On.html#2498" class="Module">_</a> <a id="2500" class="Symbol">(</a><a id="2501" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a> <a id="2503" class="Symbol">:</a> <a id="2505" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="2507" class="Symbol">→</a> <a id="2509" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a><a id="2510" class="Symbol">)</a> <a id="2512" class="Symbol">{</a><a id="2513" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2515" class="Symbol">:</a> <a id="2517" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2521" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a> <a id="2523" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="2525" class="Symbol">}</a> <a id="2527" class="Keyword">where</a>
|
|||
|
|
|
|||
|
|
<a id="2536" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="2550" class="Symbol">:</a> <a id="2552" href="Relation.Binary.Structures.html#1531" class="Record">IsEquivalence</a> <a id="2566" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2568" class="Symbol">→</a>
|
|||
|
|
<a id="2588" href="Relation.Binary.Structures.html#1531" class="Record">IsEquivalence</a> <a id="2602" class="Symbol">(</a><a id="2603" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2605" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2608" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a><a id="2609" class="Symbol">)</a>
|
|||
|
|
<a id="2613" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="2627" href="Relation.Binary.Construct.On.html#2627" class="Bound">eq</a> <a id="2630" class="Symbol">=</a> <a id="2632" class="Keyword">record</a>
|
|||
|
|
<a id="2643" class="Symbol">{</a> <a id="2645" href="Relation.Binary.Structures.html#1577" class="Field">refl</a> <a id="2651" class="Symbol">=</a> <a id="2653" href="Relation.Binary.Construct.On.html#831" class="Function">reflexive</a> <a id="2664" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a> <a id="2666" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2668" href="Relation.Binary.Structures.html#1577" class="Field">Eq.refl</a>
|
|||
|
|
<a id="2680" class="Symbol">;</a> <a id="2682" href="Relation.Binary.Structures.html#1603" class="Field">sym</a> <a id="2688" class="Symbol">=</a> <a id="2690" href="Relation.Binary.Construct.On.html#1068" class="Function">symmetric</a> <a id="2701" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a> <a id="2703" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2705" href="Relation.Binary.Structures.html#1603" class="Field">Eq.sym</a>
|
|||
|
|
<a id="2716" class="Symbol">;</a> <a id="2718" href="Relation.Binary.Structures.html#1629" class="Field">trans</a> <a id="2724" class="Symbol">=</a> <a id="2726" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="2737" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a> <a id="2739" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2741" href="Relation.Binary.Structures.html#1629" class="Field">Eq.trans</a>
|
|||
|
|
<a id="2754" class="Symbol">}</a> <a id="2756" class="Keyword">where</a> <a id="2762" class="Keyword">module</a> <a id="2769" href="Relation.Binary.Construct.On.html#2769" class="Module">Eq</a> <a id="2772" class="Symbol">=</a> <a id="2774" href="Relation.Binary.Structures.html#1531" class="Module">IsEquivalence</a> <a id="2788" href="Relation.Binary.Construct.On.html#2627" class="Bound">eq</a>
|
|||
|
|
|
|||
|
|
<a id="2794" href="Relation.Binary.Construct.On.html#2794" class="Function">isDecEquivalence</a> <a id="2811" class="Symbol">:</a> <a id="2813" href="Relation.Binary.Structures.html#1833" class="Record">IsDecEquivalence</a> <a id="2830" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2832" class="Symbol">→</a>
|
|||
|
|
<a id="2855" href="Relation.Binary.Structures.html#1833" class="Record">IsDecEquivalence</a> <a id="2872" class="Symbol">(</a><a id="2873" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="2875" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="2878" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a><a id="2879" class="Symbol">)</a>
|
|||
|
|
<a id="2883" href="Relation.Binary.Construct.On.html#2794" class="Function">isDecEquivalence</a> <a id="2900" href="Relation.Binary.Construct.On.html#2900" class="Bound">dec</a> <a id="2904" class="Symbol">=</a> <a id="2906" class="Keyword">record</a>
|
|||
|
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<a id="2917" class="Symbol">{</a> <a id="2919" href="Relation.Binary.Structures.html#1896" class="Field">isEquivalence</a> <a id="2933" class="Symbol">=</a> <a id="2935" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="2949" href="Relation.Binary.Structures.html#1896" class="Field">Dec.isEquivalence</a>
|
|||
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|
<a id="2971" class="Symbol">;</a> <a id="2973" href="Relation.Binary.Structures.html#1930" class="Field Operator">_≟_</a> <a id="2987" class="Symbol">=</a> <a id="2989" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="2999" href="Relation.Binary.Construct.On.html#2501" class="Bound">f</a> <a id="3001" href="Relation.Binary.Construct.On.html#2513" class="Bound">≈</a> <a id="3003" href="Relation.Binary.Structures.html#1930" class="Field Operator">Dec._≟_</a>
|
|||
|
|
<a id="3015" class="Symbol">}</a> <a id="3017" class="Keyword">where</a> <a id="3023" class="Keyword">module</a> <a id="3030" href="Relation.Binary.Construct.On.html#3030" class="Module">Dec</a> <a id="3034" class="Symbol">=</a> <a id="3036" href="Relation.Binary.Structures.html#1833" class="Module">IsDecEquivalence</a> <a id="3053" href="Relation.Binary.Construct.On.html#2900" class="Bound">dec</a>
|
|||
|
|
|
|||
|
|
<a id="3058" class="Keyword">module</a> <a id="3065" href="Relation.Binary.Construct.On.html#3065" class="Module">_</a> <a id="3067" class="Symbol">(</a><a id="3068" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3070" class="Symbol">:</a> <a id="3072" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="3074" class="Symbol">→</a> <a id="3076" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a><a id="3077" class="Symbol">)</a> <a id="3079" class="Symbol">{</a><a id="3080" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3082" class="Symbol">:</a> <a id="3084" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3088" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a> <a id="3090" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a><a id="3092" class="Symbol">}</a> <a id="3094" class="Symbol">{</a><a id="3095" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3097" class="Symbol">:</a> <a id="3099" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3103" href="Relation.Binary.Construct.On.html#576" class="Generalizable">A</a> <a id="3105" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="3107" class="Symbol">}</a> <a id="3109" class="Keyword">where</a>
|
|||
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<a id="3118" href="Relation.Binary.Construct.On.html#3118" class="Function">isPreorder</a> <a id="3129" class="Symbol">:</a> <a id="3131" href="Relation.Binary.Structures.html#2172" class="Record">IsPreorder</a> <a id="3142" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3144" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3146" class="Symbol">→</a> <a id="3148" href="Relation.Binary.Structures.html#2172" class="Record">IsPreorder</a> <a id="3159" class="Symbol">(</a><a id="3160" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3162" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3165" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3166" class="Symbol">)</a> <a id="3168" class="Symbol">(</a><a id="3169" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3171" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3174" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3175" class="Symbol">)</a>
|
|||
|
|
<a id="3179" href="Relation.Binary.Construct.On.html#3118" class="Function">isPreorder</a> <a id="3190" href="Relation.Binary.Construct.On.html#3190" class="Bound">pre</a> <a id="3194" class="Symbol">=</a> <a id="3196" class="Keyword">record</a>
|
|||
|
|
<a id="3207" class="Symbol">{</a> <a id="3209" href="Relation.Binary.Structures.html#2237" class="Field">isEquivalence</a> <a id="3223" class="Symbol">=</a> <a id="3225" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="3239" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3241" href="Relation.Binary.Structures.html#2237" class="Field">Pre.isEquivalence</a>
|
|||
|
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<a id="3263" class="Symbol">;</a> <a id="3265" href="Relation.Binary.Structures.html#2340" class="Field">reflexive</a> <a id="3279" class="Symbol">=</a> <a id="3281" href="Relation.Binary.Construct.On.html#720" class="Function">implies</a> <a id="3289" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3291" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3293" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3295" href="Relation.Binary.Structures.html#2340" class="Field">Pre.reflexive</a>
|
|||
|
|
<a id="3313" class="Symbol">;</a> <a id="3315" href="Relation.Binary.Structures.html#2370" class="Field">trans</a> <a id="3329" class="Symbol">=</a> <a id="3331" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="3342" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3344" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3346" href="Relation.Binary.Structures.html#2370" class="Field">Pre.trans</a>
|
|||
|
|
<a id="3360" class="Symbol">}</a> <a id="3362" class="Keyword">where</a> <a id="3368" class="Keyword">module</a> <a id="3375" href="Relation.Binary.Construct.On.html#3375" class="Module">Pre</a> <a id="3379" class="Symbol">=</a> <a id="3381" href="Relation.Binary.Structures.html#2172" class="Module">IsPreorder</a> <a id="3392" href="Relation.Binary.Construct.On.html#3190" class="Bound">pre</a>
|
|||
|
|
|
|||
|
|
<a id="3399" href="Relation.Binary.Construct.On.html#3399" class="Function">isPartialOrder</a> <a id="3414" class="Symbol">:</a> <a id="3416" href="Relation.Binary.Structures.html#3183" class="Record">IsPartialOrder</a> <a id="3431" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3433" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3435" class="Symbol">→</a>
|
|||
|
|
<a id="3456" href="Relation.Binary.Structures.html#3183" class="Record">IsPartialOrder</a> <a id="3471" class="Symbol">(</a><a id="3472" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3474" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3477" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3478" class="Symbol">)</a> <a id="3480" class="Symbol">(</a><a id="3481" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3483" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3486" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3487" class="Symbol">)</a>
|
|||
|
|
<a id="3491" href="Relation.Binary.Construct.On.html#3399" class="Function">isPartialOrder</a> <a id="3506" href="Relation.Binary.Construct.On.html#3506" class="Bound">po</a> <a id="3509" class="Symbol">=</a> <a id="3511" class="Keyword">record</a>
|
|||
|
|
<a id="3522" class="Symbol">{</a> <a id="3524" href="Relation.Binary.Structures.html#3252" class="Field">isPreorder</a> <a id="3535" class="Symbol">=</a> <a id="3537" href="Relation.Binary.Construct.On.html#3118" class="Function">isPreorder</a> <a id="3548" href="Relation.Binary.Structures.html#3252" class="Field">Po.isPreorder</a>
|
|||
|
|
<a id="3566" class="Symbol">;</a> <a id="3568" href="Relation.Binary.Structures.html#3284" class="Field">antisym</a> <a id="3579" class="Symbol">=</a> <a id="3581" href="Relation.Binary.Construct.On.html#1252" class="Function">antisymmetric</a> <a id="3595" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3597" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3599" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3601" href="Relation.Binary.Structures.html#3284" class="Field">Po.antisym</a>
|
|||
|
|
<a id="3616" class="Symbol">}</a> <a id="3618" class="Keyword">where</a> <a id="3624" class="Keyword">module</a> <a id="3631" href="Relation.Binary.Construct.On.html#3631" class="Module">Po</a> <a id="3634" class="Symbol">=</a> <a id="3636" href="Relation.Binary.Structures.html#3183" class="Module">IsPartialOrder</a> <a id="3651" href="Relation.Binary.Construct.On.html#3506" class="Bound">po</a>
|
|||
|
|
|
|||
|
|
<a id="3657" href="Relation.Binary.Construct.On.html#3657" class="Function">isDecPartialOrder</a> <a id="3675" class="Symbol">:</a> <a id="3677" href="Relation.Binary.Structures.html#3470" class="Record">IsDecPartialOrder</a> <a id="3695" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3697" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3699" class="Symbol">→</a>
|
|||
|
|
<a id="3723" href="Relation.Binary.Structures.html#3470" class="Record">IsDecPartialOrder</a> <a id="3741" class="Symbol">(</a><a id="3742" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="3744" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3747" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3748" class="Symbol">)</a> <a id="3750" class="Symbol">(</a><a id="3751" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="3753" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="3756" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="3757" class="Symbol">)</a>
|
|||
|
|
<a id="3761" href="Relation.Binary.Construct.On.html#3657" class="Function">isDecPartialOrder</a> <a id="3779" href="Relation.Binary.Construct.On.html#3779" class="Bound">dpo</a> <a id="3783" class="Symbol">=</a> <a id="3785" class="Keyword">record</a>
|
|||
|
|
<a id="3796" class="Symbol">{</a> <a id="3798" href="Relation.Binary.Structures.html#3561" class="Field">isPartialOrder</a> <a id="3813" class="Symbol">=</a> <a id="3815" href="Relation.Binary.Construct.On.html#3399" class="Function">isPartialOrder</a> <a id="3830" href="Relation.Binary.Structures.html#3561" class="Field">DPO.isPartialOrder</a>
|
|||
|
|
<a id="3853" class="Symbol">;</a> <a id="3855" href="Relation.Binary.Structures.html#3601" class="Field Operator">_≟_</a> <a id="3870" class="Symbol">=</a> <a id="3872" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="3882" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3884" class="Symbol">_</a> <a id="3886" href="Relation.Binary.Structures.html#3601" class="Field Operator">DPO._≟_</a>
|
|||
|
|
<a id="3898" class="Symbol">;</a> <a id="3900" href="Relation.Binary.Structures.html#3636" class="Field Operator">_≤?_</a> <a id="3915" class="Symbol">=</a> <a id="3917" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="3927" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="3929" class="Symbol">_</a> <a id="3931" href="Relation.Binary.Structures.html#3636" class="Field Operator">DPO._≤?_</a>
|
|||
|
|
<a id="3944" class="Symbol">}</a> <a id="3946" class="Keyword">where</a> <a id="3952" class="Keyword">module</a> <a id="3959" href="Relation.Binary.Construct.On.html#3959" class="Module">DPO</a> <a id="3963" class="Symbol">=</a> <a id="3965" href="Relation.Binary.Structures.html#3470" class="Module">IsDecPartialOrder</a> <a id="3983" href="Relation.Binary.Construct.On.html#3779" class="Bound">dpo</a>
|
|||
|
|
|
|||
|
|
<a id="3990" href="Relation.Binary.Construct.On.html#3990" class="Function">isStrictPartialOrder</a> <a id="4011" class="Symbol">:</a> <a id="4013" href="Relation.Binary.Structures.html#3959" class="Record">IsStrictPartialOrder</a> <a id="4034" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4036" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4038" class="Symbol">→</a>
|
|||
|
|
<a id="4065" href="Relation.Binary.Structures.html#3959" class="Record">IsStrictPartialOrder</a> <a id="4086" class="Symbol">(</a><a id="4087" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4089" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4092" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4093" class="Symbol">)</a> <a id="4095" class="Symbol">(</a><a id="4096" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4098" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4101" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4102" class="Symbol">)</a>
|
|||
|
|
<a id="4106" href="Relation.Binary.Construct.On.html#3990" class="Function">isStrictPartialOrder</a> <a id="4127" href="Relation.Binary.Construct.On.html#4127" class="Bound">spo</a> <a id="4131" class="Symbol">=</a> <a id="4133" class="Keyword">record</a>
|
|||
|
|
<a id="4144" class="Symbol">{</a> <a id="4146" href="Relation.Binary.Structures.html#4034" class="Field">isEquivalence</a> <a id="4160" class="Symbol">=</a> <a id="4162" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="4176" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4178" href="Relation.Binary.Structures.html#4034" class="Field">Spo.isEquivalence</a>
|
|||
|
|
<a id="4200" class="Symbol">;</a> <a id="4202" href="Relation.Binary.Structures.html#4068" class="Field">irrefl</a> <a id="4216" class="Symbol">=</a> <a id="4218" href="Relation.Binary.Construct.On.html#921" class="Function">irreflexive</a> <a id="4230" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4232" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4234" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4236" href="Relation.Binary.Structures.html#4068" class="Field">Spo.irrefl</a>
|
|||
|
|
<a id="4251" class="Symbol">;</a> <a id="4253" href="Relation.Binary.Structures.html#4108" class="Field">trans</a> <a id="4267" class="Symbol">=</a> <a id="4269" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="4280" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4282" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4284" href="Relation.Binary.Structures.html#4108" class="Field">Spo.trans</a>
|
|||
|
|
<a id="4298" class="Symbol">;</a> <a id="4300" href="Relation.Binary.Structures.html#4143" class="Field"><-resp-≈</a> <a id="4314" class="Symbol">=</a> <a id="4316" href="Relation.Binary.Construct.On.html#1632" class="Function">respects₂</a> <a id="4326" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4328" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4330" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4332" href="Relation.Binary.Structures.html#4143" class="Field">Spo.<-resp-≈</a>
|
|||
|
|
<a id="4349" class="Symbol">}</a> <a id="4351" class="Keyword">where</a> <a id="4357" class="Keyword">module</a> <a id="4364" href="Relation.Binary.Construct.On.html#4364" class="Module">Spo</a> <a id="4368" class="Symbol">=</a> <a id="4370" href="Relation.Binary.Structures.html#3959" class="Module">IsStrictPartialOrder</a> <a id="4391" href="Relation.Binary.Construct.On.html#4127" class="Bound">spo</a>
|
|||
|
|
|
|||
|
|
<a id="4398" href="Relation.Binary.Construct.On.html#4398" class="Function">isTotalOrder</a> <a id="4411" class="Symbol">:</a> <a id="4413" href="Relation.Binary.Structures.html#5306" class="Record">IsTotalOrder</a> <a id="4426" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4428" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4430" class="Symbol">→</a>
|
|||
|
|
<a id="4449" href="Relation.Binary.Structures.html#5306" class="Record">IsTotalOrder</a> <a id="4462" class="Symbol">(</a><a id="4463" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4465" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4468" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4469" class="Symbol">)</a> <a id="4471" class="Symbol">(</a><a id="4472" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4474" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4477" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4478" class="Symbol">)</a>
|
|||
|
|
<a id="4482" href="Relation.Binary.Construct.On.html#4398" class="Function">isTotalOrder</a> <a id="4495" href="Relation.Binary.Construct.On.html#4495" class="Bound">to</a> <a id="4498" class="Symbol">=</a> <a id="4500" class="Keyword">record</a>
|
|||
|
|
<a id="4511" class="Symbol">{</a> <a id="4513" href="Relation.Binary.Structures.html#5373" class="Field">isPartialOrder</a> <a id="4528" class="Symbol">=</a> <a id="4530" href="Relation.Binary.Construct.On.html#3399" class="Function">isPartialOrder</a> <a id="4545" href="Relation.Binary.Structures.html#5373" class="Field">To.isPartialOrder</a>
|
|||
|
|
<a id="4567" class="Symbol">;</a> <a id="4569" href="Relation.Binary.Structures.html#5413" class="Field">total</a> <a id="4584" class="Symbol">=</a> <a id="4586" href="Relation.Binary.Construct.On.html#1897" class="Function">total</a> <a id="4592" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4594" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4596" href="Relation.Binary.Structures.html#5413" class="Field">To.total</a>
|
|||
|
|
<a id="4609" class="Symbol">}</a> <a id="4611" class="Keyword">where</a> <a id="4617" class="Keyword">module</a> <a id="4624" href="Relation.Binary.Construct.On.html#4624" class="Module">To</a> <a id="4627" class="Symbol">=</a> <a id="4629" href="Relation.Binary.Structures.html#5306" class="Module">IsTotalOrder</a> <a id="4642" href="Relation.Binary.Construct.On.html#4495" class="Bound">to</a>
|
|||
|
|
|
|||
|
|
<a id="4648" href="Relation.Binary.Construct.On.html#4648" class="Function">isDecTotalOrder</a> <a id="4664" class="Symbol">:</a> <a id="4666" href="Relation.Binary.Structures.html#5623" class="Record">IsDecTotalOrder</a> <a id="4682" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4684" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4686" class="Symbol">→</a>
|
|||
|
|
<a id="4708" href="Relation.Binary.Structures.html#5623" class="Record">IsDecTotalOrder</a> <a id="4724" class="Symbol">(</a><a id="4725" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4727" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4730" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4731" class="Symbol">)</a> <a id="4733" class="Symbol">(</a><a id="4734" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4736" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="4739" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="4740" class="Symbol">)</a>
|
|||
|
|
<a id="4744" href="Relation.Binary.Construct.On.html#4648" class="Function">isDecTotalOrder</a> <a id="4760" href="Relation.Binary.Construct.On.html#4760" class="Bound">dec</a> <a id="4764" class="Symbol">=</a> <a id="4766" class="Keyword">record</a>
|
|||
|
|
<a id="4777" class="Symbol">{</a> <a id="4779" href="Relation.Binary.Structures.html#5712" class="Field">isTotalOrder</a> <a id="4792" class="Symbol">=</a> <a id="4794" href="Relation.Binary.Construct.On.html#4398" class="Function">isTotalOrder</a> <a id="4807" href="Relation.Binary.Structures.html#5712" class="Field">Dec.isTotalOrder</a>
|
|||
|
|
<a id="4828" class="Symbol">;</a> <a id="4830" href="Relation.Binary.Structures.html#5748" class="Field Operator">_≟_</a> <a id="4843" class="Symbol">=</a> <a id="4845" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="4855" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4857" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="4859" href="Relation.Binary.Structures.html#5748" class="Field Operator">Dec._≟_</a>
|
|||
|
|
<a id="4871" class="Symbol">;</a> <a id="4873" href="Relation.Binary.Structures.html#5781" class="Field Operator">_≤?_</a> <a id="4886" class="Symbol">=</a> <a id="4888" href="Relation.Binary.Construct.On.html#1793" class="Function">decidable</a> <a id="4898" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="4900" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="4902" href="Relation.Binary.Structures.html#5781" class="Field Operator">Dec._≤?_</a>
|
|||
|
|
<a id="4915" class="Symbol">}</a> <a id="4917" class="Keyword">where</a> <a id="4923" class="Keyword">module</a> <a id="4930" href="Relation.Binary.Construct.On.html#4930" class="Module">Dec</a> <a id="4934" class="Symbol">=</a> <a id="4936" href="Relation.Binary.Structures.html#5623" class="Module">IsDecTotalOrder</a> <a id="4952" href="Relation.Binary.Construct.On.html#4760" class="Bound">dec</a>
|
|||
|
|
|
|||
|
|
<a id="4959" href="Relation.Binary.Construct.On.html#4959" class="Function">isStrictTotalOrder</a> <a id="4978" class="Symbol">:</a> <a id="4980" href="Relation.Binary.Structures.html#6548" class="Record">IsStrictTotalOrder</a> <a id="4999" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="5001" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="5003" class="Symbol">→</a>
|
|||
|
|
<a id="5028" href="Relation.Binary.Structures.html#6548" class="Record">IsStrictTotalOrder</a> <a id="5047" class="Symbol">(</a><a id="5048" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="5050" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="5053" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="5054" class="Symbol">)</a> <a id="5056" class="Symbol">(</a><a id="5057" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="5059" href="Function.Base.html#6294" class="Function Operator">on</a> <a id="5062" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a><a id="5063" class="Symbol">)</a>
|
|||
|
|
<a id="5067" href="Relation.Binary.Construct.On.html#4959" class="Function">isStrictTotalOrder</a> <a id="5086" href="Relation.Binary.Construct.On.html#5086" class="Bound">sto</a> <a id="5090" class="Symbol">=</a> <a id="5092" class="Keyword">record</a>
|
|||
|
|
<a id="5103" class="Symbol">{</a> <a id="5105" href="Relation.Binary.Structures.html#6621" class="Field">isEquivalence</a> <a id="5119" class="Symbol">=</a> <a id="5121" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="5135" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="5137" href="Relation.Binary.Structures.html#6621" class="Field">Sto.isEquivalence</a>
|
|||
|
|
<a id="5159" class="Symbol">;</a> <a id="5161" href="Relation.Binary.Structures.html#6655" class="Field">trans</a> <a id="5175" class="Symbol">=</a> <a id="5177" href="Relation.Binary.Construct.On.html#1156" class="Function">transitive</a> <a id="5188" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="5190" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="5192" href="Relation.Binary.Structures.html#6655" class="Field">Sto.trans</a>
|
|||
|
|
<a id="5206" class="Symbol">;</a> <a id="5208" href="Relation.Binary.Structures.html#6690" class="Field">compare</a> <a id="5222" class="Symbol">=</a> <a id="5224" href="Relation.Binary.Construct.On.html#1985" class="Function">trichotomous</a> <a id="5237" href="Relation.Binary.Construct.On.html#3068" class="Bound">f</a> <a id="5239" href="Relation.Binary.Construct.On.html#3080" class="Bound">≈</a> <a id="5241" href="Relation.Binary.Construct.On.html#3095" class="Bound">∼</a> <a id="5243" href="Relation.Binary.Structures.html#6690" class="Field">Sto.compare</a>
|
|||
|
|
<a id="5259" class="Symbol">}</a> <a id="5261" class="Keyword">where</a> <a id="5267" class="Keyword">module</a> <a id="5274" href="Relation.Binary.Construct.On.html#5274" class="Module">Sto</a> <a id="5278" class="Symbol">=</a> <a id="5280" href="Relation.Binary.Structures.html#6548" class="Module">IsStrictTotalOrder</a> <a id="5299" href="Relation.Binary.Construct.On.html#5086" class="Bound">sto</a>
|
|||
|
|
|
|||
|
|
<a id="5304" class="Comment">------------------------------------------------------------------------</a>
|
|||
|
|
<a id="5377" class="Comment">-- Bundles</a>
|
|||
|
|
|
|||
|
|
<a id="preorder"></a><a id="5389" href="Relation.Binary.Construct.On.html#5389" class="Function">preorder</a> <a id="5398" class="Symbol">:</a> <a id="5400" class="Symbol">(</a><a id="5401" href="Relation.Binary.Construct.On.html#5401" class="Bound">P</a> <a id="5403" class="Symbol">:</a> <a id="5405" href="Relation.Binary.Bundles.html#1929" class="Record">Preorder</a> <a id="5414" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="5416" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="5419" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="5421" class="Symbol">)</a> <a id="5423" class="Symbol">→</a>
|
|||
|
|
<a id="5436" class="Symbol">(</a><a id="5437" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="5439" class="Symbol">→</a> <a id="5441" href="Relation.Binary.Bundles.html#2008" class="Field">Preorder.Carrier</a> <a id="5458" href="Relation.Binary.Construct.On.html#5401" class="Bound">P</a><a id="5459" class="Symbol">)</a> <a id="5461" class="Symbol">→</a>
|
|||
|
|
<a id="5474" href="Relation.Binary.Bundles.html#1929" class="Record">Preorder</a> <a id="5483" class="Symbol">_</a> <a id="5485" class="Symbol">_</a> <a id="5487" class="Symbol">_</a>
|
|||
|
|
<a id="5489" href="Relation.Binary.Construct.On.html#5389" class="Function">preorder</a> <a id="5498" href="Relation.Binary.Construct.On.html#5498" class="Bound">P</a> <a id="5500" href="Relation.Binary.Construct.On.html#5500" class="Bound">f</a> <a id="5502" class="Symbol">=</a> <a id="5504" class="Keyword">record</a>
|
|||
|
|
<a id="5513" class="Symbol">{</a> <a id="5515" href="Relation.Binary.Bundles.html#2142" class="Field">isPreorder</a> <a id="5526" class="Symbol">=</a> <a id="5528" href="Relation.Binary.Construct.On.html#3118" class="Function">isPreorder</a> <a id="5539" href="Relation.Binary.Construct.On.html#5500" class="Bound">f</a> <a id="5541" class="Symbol">(</a><a id="5542" href="Relation.Binary.Bundles.html#2142" class="Field">Preorder.isPreorder</a> <a id="5562" href="Relation.Binary.Construct.On.html#5498" class="Bound">P</a><a id="5563" class="Symbol">)</a>
|
|||
|
|
<a id="5567" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="setoid"></a><a id="5570" href="Relation.Binary.Construct.On.html#5570" class="Function">setoid</a> <a id="5577" class="Symbol">:</a> <a id="5579" class="Symbol">(</a><a id="5580" href="Relation.Binary.Construct.On.html#5580" class="Bound">S</a> <a id="5582" class="Symbol">:</a> <a id="5584" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="5591" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="5593" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="5594" class="Symbol">)</a> <a id="5596" class="Symbol">→</a>
|
|||
|
|
<a id="5607" class="Symbol">(</a><a id="5608" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="5610" class="Symbol">→</a> <a id="5612" href="Relation.Binary.Bundles.html#1081" class="Field">Setoid.Carrier</a> <a id="5627" href="Relation.Binary.Construct.On.html#5580" class="Bound">S</a><a id="5628" class="Symbol">)</a> <a id="5630" class="Symbol">→</a>
|
|||
|
|
<a id="5641" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="5648" class="Symbol">_</a> <a id="5650" class="Symbol">_</a>
|
|||
|
|
<a id="5652" href="Relation.Binary.Construct.On.html#5570" class="Function">setoid</a> <a id="5659" href="Relation.Binary.Construct.On.html#5659" class="Bound">S</a> <a id="5661" href="Relation.Binary.Construct.On.html#5661" class="Bound">f</a> <a id="5663" class="Symbol">=</a> <a id="5665" class="Keyword">record</a>
|
|||
|
|
<a id="5674" class="Symbol">{</a> <a id="5676" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="5690" class="Symbol">=</a> <a id="5692" href="Relation.Binary.Construct.On.html#2536" class="Function">isEquivalence</a> <a id="5706" href="Relation.Binary.Construct.On.html#5661" class="Bound">f</a> <a id="5708" class="Symbol">(</a><a id="5709" href="Relation.Binary.Bundles.html#1141" class="Field">Setoid.isEquivalence</a> <a id="5730" href="Relation.Binary.Construct.On.html#5659" class="Bound">S</a><a id="5731" class="Symbol">)</a>
|
|||
|
|
<a id="5735" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="decSetoid"></a><a id="5738" href="Relation.Binary.Construct.On.html#5738" class="Function">decSetoid</a> <a id="5748" class="Symbol">:</a> <a id="5750" class="Symbol">(</a><a id="5751" href="Relation.Binary.Construct.On.html#5751" class="Bound">D</a> <a id="5753" class="Symbol">:</a> <a id="5755" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="5765" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="5767" href="Relation.Binary.Construct.On.html#556" class="Generalizable">ℓ</a><a id="5768" class="Symbol">)</a> <a id="5770" class="Symbol">→</a>
|
|||
|
|
<a id="5784" class="Symbol">(</a><a id="5785" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="5787" class="Symbol">→</a> <a id="5789" href="Relation.Binary.Bundles.html#1466" class="Field">DecSetoid.Carrier</a> <a id="5807" href="Relation.Binary.Construct.On.html#5751" class="Bound">D</a><a id="5808" class="Symbol">)</a> <a id="5810" class="Symbol">→</a>
|
|||
|
|
<a id="5824" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="5834" class="Symbol">_</a> <a id="5836" class="Symbol">_</a>
|
|||
|
|
<a id="5838" href="Relation.Binary.Construct.On.html#5738" class="Function">decSetoid</a> <a id="5848" href="Relation.Binary.Construct.On.html#5848" class="Bound">D</a> <a id="5850" href="Relation.Binary.Construct.On.html#5850" class="Bound">f</a> <a id="5852" class="Symbol">=</a> <a id="5854" class="Keyword">record</a>
|
|||
|
|
<a id="5863" class="Symbol">{</a> <a id="5865" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="5882" class="Symbol">=</a> <a id="5884" href="Relation.Binary.Construct.On.html#2794" class="Function">isDecEquivalence</a> <a id="5901" href="Relation.Binary.Construct.On.html#5850" class="Bound">f</a> <a id="5903" class="Symbol">(</a><a id="5904" href="Relation.Binary.Bundles.html#1532" class="Field">DecSetoid.isDecEquivalence</a> <a id="5931" href="Relation.Binary.Construct.On.html#5848" class="Bound">D</a><a id="5932" class="Symbol">)</a>
|
|||
|
|
<a id="5936" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="poset"></a><a id="5939" href="Relation.Binary.Construct.On.html#5939" class="Function">poset</a> <a id="5945" class="Symbol">:</a> <a id="5947" class="Symbol">∀</a> <a id="5949" class="Symbol">(</a><a id="5950" href="Relation.Binary.Construct.On.html#5950" class="Bound">P</a> <a id="5952" class="Symbol">:</a> <a id="5954" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="5960" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="5962" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="5965" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="5967" class="Symbol">)</a> <a id="5969" class="Symbol">→</a>
|
|||
|
|
<a id="5979" class="Symbol">(</a><a id="5980" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="5982" class="Symbol">→</a> <a id="5984" href="Relation.Binary.Bundles.html#3113" class="Field">Poset.Carrier</a> <a id="5998" href="Relation.Binary.Construct.On.html#5950" class="Bound">P</a><a id="5999" class="Symbol">)</a> <a id="6001" class="Symbol">→</a>
|
|||
|
|
<a id="6011" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="6017" class="Symbol">_</a> <a id="6019" class="Symbol">_</a> <a id="6021" class="Symbol">_</a>
|
|||
|
|
<a id="6023" href="Relation.Binary.Construct.On.html#5939" class="Function">poset</a> <a id="6029" href="Relation.Binary.Construct.On.html#6029" class="Bound">P</a> <a id="6031" href="Relation.Binary.Construct.On.html#6031" class="Bound">f</a> <a id="6033" class="Symbol">=</a> <a id="6035" class="Keyword">record</a>
|
|||
|
|
<a id="6044" class="Symbol">{</a> <a id="6046" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="6061" class="Symbol">=</a> <a id="6063" href="Relation.Binary.Construct.On.html#3399" class="Function">isPartialOrder</a> <a id="6078" href="Relation.Binary.Construct.On.html#6031" class="Bound">f</a> <a id="6080" class="Symbol">(</a><a id="6081" href="Relation.Binary.Bundles.html#3212" class="Field">Poset.isPartialOrder</a> <a id="6102" href="Relation.Binary.Construct.On.html#6029" class="Bound">P</a><a id="6103" class="Symbol">)</a>
|
|||
|
|
<a id="6107" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="decPoset"></a><a id="6110" href="Relation.Binary.Construct.On.html#6110" class="Function">decPoset</a> <a id="6119" class="Symbol">:</a> <a id="6121" class="Symbol">(</a><a id="6122" href="Relation.Binary.Construct.On.html#6122" class="Bound">D</a> <a id="6124" class="Symbol">:</a> <a id="6126" href="Relation.Binary.Bundles.html#3471" class="Record">DecPoset</a> <a id="6135" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="6137" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="6140" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="6142" class="Symbol">)</a> <a id="6144" class="Symbol">→</a>
|
|||
|
|
<a id="6157" class="Symbol">(</a><a id="6158" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="6160" class="Symbol">→</a> <a id="6162" href="Relation.Binary.Bundles.html#3550" class="Field">DecPoset.Carrier</a> <a id="6179" href="Relation.Binary.Construct.On.html#6122" class="Bound">D</a><a id="6180" class="Symbol">)</a> <a id="6182" class="Symbol">→</a>
|
|||
|
|
<a id="6195" href="Relation.Binary.Bundles.html#3471" class="Record">DecPoset</a> <a id="6204" class="Symbol">_</a> <a id="6206" class="Symbol">_</a> <a id="6208" class="Symbol">_</a>
|
|||
|
|
<a id="6210" href="Relation.Binary.Construct.On.html#6110" class="Function">decPoset</a> <a id="6219" href="Relation.Binary.Construct.On.html#6219" class="Bound">D</a> <a id="6221" href="Relation.Binary.Construct.On.html#6221" class="Bound">f</a> <a id="6223" class="Symbol">=</a> <a id="6225" class="Keyword">record</a>
|
|||
|
|
<a id="6234" class="Symbol">{</a> <a id="6236" href="Relation.Binary.Bundles.html#3658" class="Field">isDecPartialOrder</a> <a id="6254" class="Symbol">=</a>
|
|||
|
|
<a id="6262" href="Relation.Binary.Construct.On.html#3657" class="Function">isDecPartialOrder</a> <a id="6280" href="Relation.Binary.Construct.On.html#6221" class="Bound">f</a> <a id="6282" class="Symbol">(</a><a id="6283" href="Relation.Binary.Bundles.html#3658" class="Field">DecPoset.isDecPartialOrder</a> <a id="6310" href="Relation.Binary.Construct.On.html#6219" class="Bound">D</a><a id="6311" class="Symbol">)</a>
|
|||
|
|
<a id="6315" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="strictPartialOrder"></a><a id="6318" href="Relation.Binary.Construct.On.html#6318" class="Function">strictPartialOrder</a> <a id="6337" class="Symbol">:</a> <a id="6339" class="Symbol">(</a><a id="6340" href="Relation.Binary.Construct.On.html#6340" class="Bound">S</a> <a id="6342" class="Symbol">:</a> <a id="6344" href="Relation.Binary.Bundles.html#4117" class="Record">StrictPartialOrder</a> <a id="6363" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="6365" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="6368" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="6370" class="Symbol">)</a> <a id="6372" class="Symbol">→</a>
|
|||
|
|
<a id="6395" class="Symbol">(</a><a id="6396" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="6398" class="Symbol">→</a> <a id="6400" href="Relation.Binary.Bundles.html#4206" class="Field">StrictPartialOrder.Carrier</a> <a id="6427" href="Relation.Binary.Construct.On.html#6340" class="Bound">S</a><a id="6428" class="Symbol">)</a> <a id="6430" class="Symbol">→</a>
|
|||
|
|
<a id="6453" href="Relation.Binary.Bundles.html#4117" class="Record">StrictPartialOrder</a> <a id="6472" class="Symbol">_</a> <a id="6474" class="Symbol">_</a> <a id="6476" class="Symbol">_</a>
|
|||
|
|
<a id="6478" href="Relation.Binary.Construct.On.html#6318" class="Function">strictPartialOrder</a> <a id="6497" href="Relation.Binary.Construct.On.html#6497" class="Bound">S</a> <a id="6499" href="Relation.Binary.Construct.On.html#6499" class="Bound">f</a> <a id="6501" class="Symbol">=</a> <a id="6503" class="Keyword">record</a>
|
|||
|
|
<a id="6512" class="Symbol">{</a> <a id="6514" href="Relation.Binary.Bundles.html#4323" class="Field">isStrictPartialOrder</a> <a id="6535" class="Symbol">=</a>
|
|||
|
|
<a id="6543" href="Relation.Binary.Construct.On.html#3990" class="Function">isStrictPartialOrder</a> <a id="6564" href="Relation.Binary.Construct.On.html#6499" class="Bound">f</a> <a id="6566" class="Symbol">(</a><a id="6567" href="Relation.Binary.Bundles.html#4323" class="Field">StrictPartialOrder.isStrictPartialOrder</a> <a id="6607" href="Relation.Binary.Construct.On.html#6497" class="Bound">S</a><a id="6608" class="Symbol">)</a>
|
|||
|
|
<a id="6612" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="totalOrder"></a><a id="6615" href="Relation.Binary.Construct.On.html#6615" class="Function">totalOrder</a> <a id="6626" class="Symbol">:</a> <a id="6628" class="Symbol">(</a><a id="6629" href="Relation.Binary.Construct.On.html#6629" class="Bound">T</a> <a id="6631" class="Symbol">:</a> <a id="6633" href="Relation.Binary.Bundles.html#5476" class="Record">TotalOrder</a> <a id="6644" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="6646" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="6649" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="6651" class="Symbol">)</a> <a id="6653" class="Symbol">→</a>
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|||
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<a id="6668" class="Symbol">(</a><a id="6669" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="6671" class="Symbol">→</a> <a id="6673" href="Relation.Binary.Bundles.html#5557" class="Field">TotalOrder.Carrier</a> <a id="6692" href="Relation.Binary.Construct.On.html#6629" class="Bound">T</a><a id="6693" class="Symbol">)</a> <a id="6695" class="Symbol">→</a>
|
|||
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|
<a id="6710" href="Relation.Binary.Bundles.html#5476" class="Record">TotalOrder</a> <a id="6721" class="Symbol">_</a> <a id="6723" class="Symbol">_</a> <a id="6725" class="Symbol">_</a>
|
|||
|
|
<a id="6727" href="Relation.Binary.Construct.On.html#6615" class="Function">totalOrder</a> <a id="6738" href="Relation.Binary.Construct.On.html#6738" class="Bound">T</a> <a id="6740" href="Relation.Binary.Construct.On.html#6740" class="Bound">f</a> <a id="6742" class="Symbol">=</a> <a id="6744" class="Keyword">record</a>
|
|||
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|
<a id="6753" class="Symbol">{</a> <a id="6755" href="Relation.Binary.Bundles.html#5650" class="Field">isTotalOrder</a> <a id="6768" class="Symbol">=</a> <a id="6770" href="Relation.Binary.Construct.On.html#4398" class="Function">isTotalOrder</a> <a id="6783" href="Relation.Binary.Construct.On.html#6740" class="Bound">f</a> <a id="6785" class="Symbol">(</a><a id="6786" href="Relation.Binary.Bundles.html#5650" class="Field">TotalOrder.isTotalOrder</a> <a id="6810" href="Relation.Binary.Construct.On.html#6738" class="Bound">T</a><a id="6811" class="Symbol">)</a>
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|||
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|
<a id="6815" class="Symbol">}</a>
|
|||
|
|
|
|||
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|
<a id="decTotalOrder"></a><a id="6818" href="Relation.Binary.Construct.On.html#6818" class="Function">decTotalOrder</a> <a id="6832" class="Symbol">:</a> <a id="6834" class="Symbol">(</a><a id="6835" href="Relation.Binary.Construct.On.html#6835" class="Bound">D</a> <a id="6837" class="Symbol">:</a> <a id="6839" href="Relation.Binary.Bundles.html#6016" class="Record">DecTotalOrder</a> <a id="6853" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="6855" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="6858" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="6860" class="Symbol">)</a> <a id="6862" class="Symbol">→</a>
|
|||
|
|
<a id="6880" class="Symbol">(</a><a id="6881" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="6883" class="Symbol">→</a> <a id="6885" href="Relation.Binary.Bundles.html#6100" class="Field">DecTotalOrder.Carrier</a> <a id="6907" href="Relation.Binary.Construct.On.html#6835" class="Bound">D</a><a id="6908" class="Symbol">)</a> <a id="6910" class="Symbol">→</a>
|
|||
|
|
<a id="6928" href="Relation.Binary.Bundles.html#6016" class="Record">DecTotalOrder</a> <a id="6942" class="Symbol">_</a> <a id="6944" class="Symbol">_</a> <a id="6946" class="Symbol">_</a>
|
|||
|
|
<a id="6948" href="Relation.Binary.Construct.On.html#6818" class="Function">decTotalOrder</a> <a id="6962" href="Relation.Binary.Construct.On.html#6962" class="Bound">D</a> <a id="6964" href="Relation.Binary.Construct.On.html#6964" class="Bound">f</a> <a id="6966" class="Symbol">=</a> <a id="6968" class="Keyword">record</a>
|
|||
|
|
<a id="6977" class="Symbol">{</a> <a id="6979" href="Relation.Binary.Bundles.html#6202" class="Field">isDecTotalOrder</a> <a id="6995" class="Symbol">=</a> <a id="6997" href="Relation.Binary.Construct.On.html#4648" class="Function">isDecTotalOrder</a> <a id="7013" href="Relation.Binary.Construct.On.html#6964" class="Bound">f</a> <a id="7015" class="Symbol">(</a><a id="7016" href="Relation.Binary.Bundles.html#6202" class="Field">DecTotalOrder.isDecTotalOrder</a> <a id="7046" href="Relation.Binary.Construct.On.html#6962" class="Bound">D</a><a id="7047" class="Symbol">)</a>
|
|||
|
|
<a id="7051" class="Symbol">}</a>
|
|||
|
|
|
|||
|
|
<a id="strictTotalOrder"></a><a id="7054" href="Relation.Binary.Construct.On.html#7054" class="Function">strictTotalOrder</a> <a id="7071" class="Symbol">:</a> <a id="7073" class="Symbol">(</a><a id="7074" href="Relation.Binary.Construct.On.html#7074" class="Bound">S</a> <a id="7076" class="Symbol">:</a> <a id="7078" href="Relation.Binary.Bundles.html#6937" class="Record">StrictTotalOrder</a> <a id="7095" href="Relation.Binary.Construct.On.html#550" class="Generalizable">a</a> <a id="7097" href="Relation.Binary.Construct.On.html#558" class="Generalizable">ℓ₁</a> <a id="7100" href="Relation.Binary.Construct.On.html#561" class="Generalizable">ℓ₂</a><a id="7102" class="Symbol">)</a> <a id="7104" class="Symbol">→</a>
|
|||
|
|
<a id="7125" class="Symbol">(</a><a id="7126" href="Relation.Binary.Construct.On.html#590" class="Generalizable">B</a> <a id="7128" class="Symbol">→</a> <a id="7130" href="Relation.Binary.Bundles.html#7024" class="Field">StrictTotalOrder.Carrier</a> <a id="7155" href="Relation.Binary.Construct.On.html#7074" class="Bound">S</a><a id="7156" class="Symbol">)</a> <a id="7158" class="Symbol">→</a>
|
|||
|
|
<a id="7179" href="Relation.Binary.Bundles.html#6937" class="Record">StrictTotalOrder</a> <a id="7196" class="Symbol">_</a> <a id="7198" class="Symbol">_</a> <a id="7200" class="Symbol">_</a>
|
|||
|
|
<a id="7202" href="Relation.Binary.Construct.On.html#7054" class="Function">strictTotalOrder</a> <a id="7219" href="Relation.Binary.Construct.On.html#7219" class="Bound">S</a> <a id="7221" href="Relation.Binary.Construct.On.html#7221" class="Bound">f</a> <a id="7223" class="Symbol">=</a> <a id="7225" class="Keyword">record</a>
|
|||
|
|
<a id="7234" class="Symbol">{</a> <a id="7236" href="Relation.Binary.Bundles.html#7135" class="Field">isStrictTotalOrder</a> <a id="7255" class="Symbol">=</a>
|
|||
|
|
<a id="7263" href="Relation.Binary.Construct.On.html#4959" class="Function">isStrictTotalOrder</a> <a id="7282" href="Relation.Binary.Construct.On.html#7221" class="Bound">f</a> <a id="7284" class="Symbol">(</a><a id="7285" href="Relation.Binary.Bundles.html#7135" class="Field">StrictTotalOrder.isStrictTotalOrder</a> <a id="7321" href="Relation.Binary.Construct.On.html#7219" class="Bound">S</a><a id="7322" class="Symbol">)</a>
|
|||
|
|
<a id="7326" class="Symbol">}</a>
|
|||
|
|
</pre></body></html>
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