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45 lines
11 KiB
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<!DOCTYPE HTML>
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<html><head><meta charset="utf-8"><title>Relation.Binary.Indexed.Heterogeneous.Bundles</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">-- Indexed binary relations</a>
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<a id="134" class="Comment">------------------------------------------------------------------------</a>
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<a id="208" class="Comment">-- The contents of this module should be accessed via</a>
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<a id="262" class="Comment">-- `Relation.Binary.Indexed.Heterogeneous`.</a>
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<a id="307" class="Symbol">{-#</a> <a id="311" class="Keyword">OPTIONS</a> <a id="319" class="Pragma">--without-K</a> <a id="331" class="Pragma">--safe</a> <a id="338" class="Symbol">#-}</a>
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<a id="343" class="Keyword">module</a> <a id="350" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Bundles</a> <a id="396" class="Keyword">where</a>
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<a id="403" class="Keyword">open</a> <a id="408" class="Keyword">import</a> <a id="415" href="Function.Base.html" class="Module">Function.Base</a>
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<a id="429" class="Keyword">open</a> <a id="434" class="Keyword">import</a> <a id="441" href="Level.html" class="Module">Level</a> <a id="447" class="Keyword">using</a> <a id="453" class="Symbol">(</a><a id="454" href="Agda.Primitive.html#780" class="Primitive">suc</a><a id="457" class="Symbol">;</a> <a id="459" href="Agda.Primitive.html#810" class="Primitive Operator">_⊔_</a><a id="462" class="Symbol">)</a>
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<a id="464" class="Keyword">open</a> <a id="469" class="Keyword">import</a> <a id="476" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="492" class="Keyword">using</a> <a id="498" class="Symbol">(</a><a id="499" href="Relation.Binary.Core.html#1254" class="Function Operator">_⇒_</a><a id="502" class="Symbol">)</a>
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<a id="504" class="Keyword">open</a> <a id="509" class="Keyword">import</a> <a id="516" href="Relation.Binary.PropositionalEquality.Core.html" class="Module">Relation.Binary.PropositionalEquality.Core</a> <a id="559" class="Symbol">as</a> <a id="562" class="Module">P</a> <a id="564" class="Keyword">using</a> <a id="570" class="Symbol">(</a><a id="571" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">_≡_</a><a id="574" class="Symbol">)</a>
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<a id="576" class="Keyword">open</a> <a id="581" class="Keyword">import</a> <a id="588" href="Relation.Binary.Indexed.Heterogeneous.Core.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Core</a>
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<a id="631" class="Keyword">open</a> <a id="636" class="Keyword">import</a> <a id="643" href="Relation.Binary.Indexed.Heterogeneous.Structures.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Structures</a>
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<a id="693" class="Comment">------------------------------------------------------------------------</a>
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<a id="766" class="Comment">-- Definitions</a>
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<a id="782" class="Keyword">record</a> <a id="IndexedSetoid"></a><a id="789" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#789" class="Record">IndexedSetoid</a> <a id="803" class="Symbol">{</a><a id="804" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#804" class="Bound">i</a><a id="805" class="Symbol">}</a> <a id="807" class="Symbol">(</a><a id="808" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#808" class="Bound">I</a> <a id="810" class="Symbol">:</a> <a id="812" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="816" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#804" class="Bound">i</a><a id="817" class="Symbol">)</a> <a id="819" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#819" class="Bound">c</a> <a id="821" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#821" class="Bound">ℓ</a> <a id="823" class="Symbol">:</a> <a id="825" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="829" class="Symbol">(</a><a id="830" href="Agda.Primitive.html#780" class="Primitive">suc</a> <a id="834" class="Symbol">(</a><a id="835" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#804" class="Bound">i</a> <a id="837" href="Agda.Primitive.html#810" class="Primitive Operator">⊔</a> <a id="839" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#819" class="Bound">c</a> <a id="841" href="Agda.Primitive.html#810" class="Primitive Operator">⊔</a> <a id="843" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#821" class="Bound">ℓ</a><a id="844" class="Symbol">))</a> <a id="847" class="Keyword">where</a>
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<a id="855" class="Keyword">infix</a> <a id="861" class="Number">4</a> <a id="863" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#909" class="Field Operator">_≈_</a>
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<a id="869" class="Keyword">field</a>
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<a id="IndexedSetoid.Carrier"></a><a id="879" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#879" class="Field">Carrier</a> <a id="893" class="Symbol">:</a> <a id="895" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#808" class="Bound">I</a> <a id="897" class="Symbol">→</a> <a id="899" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="903" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#819" class="Bound">c</a>
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<a id="IndexedSetoid._≈_"></a><a id="909" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#909" class="Field Operator">_≈_</a> <a id="923" class="Symbol">:</a> <a id="925" href="Relation.Binary.Indexed.Heterogeneous.Core.html#856" class="Function">IRel</a> <a id="930" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#879" class="Field">Carrier</a> <a id="938" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#821" class="Bound">ℓ</a>
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<a id="IndexedSetoid.isEquivalence"></a><a id="944" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#944" class="Field">isEquivalence</a> <a id="958" class="Symbol">:</a> <a id="960" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#852" class="Record">IsIndexedEquivalence</a> <a id="981" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#879" class="Field">Carrier</a> <a id="989" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#909" class="Field Operator">_≈_</a>
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<a id="996" class="Keyword">open</a> <a id="1001" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#852" class="Module">IsIndexedEquivalence</a> <a id="1022" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#944" class="Field">isEquivalence</a> <a id="1036" class="Keyword">public</a>
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<a id="1045" class="Keyword">record</a> <a id="IndexedPreorder"></a><a id="1052" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1052" class="Record">IndexedPreorder</a> <a id="1068" class="Symbol">{</a><a id="1069" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1069" class="Bound">i</a><a id="1070" class="Symbol">}</a> <a id="1072" class="Symbol">(</a><a id="1073" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1073" class="Bound">I</a> <a id="1075" class="Symbol">:</a> <a id="1077" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="1081" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1069" class="Bound">i</a><a id="1082" class="Symbol">)</a> <a id="1084" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1084" class="Bound">c</a> <a id="1086" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1086" class="Bound">ℓ₁</a> <a id="1089" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1089" class="Bound">ℓ₂</a> <a id="1092" class="Symbol">:</a>
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<a id="1117" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="1121" class="Symbol">(</a><a id="1122" href="Agda.Primitive.html#780" class="Primitive">suc</a> <a id="1126" class="Symbol">(</a><a id="1127" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1069" class="Bound">i</a> <a id="1129" href="Agda.Primitive.html#810" class="Primitive Operator">⊔</a> <a id="1131" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1084" class="Bound">c</a> <a id="1133" href="Agda.Primitive.html#810" class="Primitive Operator">⊔</a> <a id="1135" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1086" class="Bound">ℓ₁</a> <a id="1138" href="Agda.Primitive.html#810" class="Primitive Operator">⊔</a> <a id="1140" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1089" class="Bound">ℓ₂</a><a id="1142" class="Symbol">))</a> <a id="1145" class="Keyword">where</a>
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<a id="1153" class="Keyword">infix</a> <a id="1159" class="Number">4</a> <a id="1161" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1208" class="Field Operator">_≈_</a> <a id="1165" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1270" class="Field Operator">_∼_</a>
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<a id="1171" class="Keyword">field</a>
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<a id="IndexedPreorder.Carrier"></a><a id="1181" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1181" class="Field">Carrier</a> <a id="1192" class="Symbol">:</a> <a id="1194" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1073" class="Bound">I</a> <a id="1196" class="Symbol">→</a> <a id="1198" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="1202" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1084" class="Bound">c</a>
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<a id="IndexedPreorder._≈_"></a><a id="1208" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1208" class="Field Operator">_≈_</a> <a id="1219" class="Symbol">:</a> <a id="1221" href="Relation.Binary.Indexed.Heterogeneous.Core.html#856" class="Function">IRel</a> <a id="1226" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1181" class="Field">Carrier</a> <a id="1234" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1086" class="Bound">ℓ₁</a> <a id="1238" class="Comment">-- The underlying equality.</a>
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<a id="IndexedPreorder._∼_"></a><a id="1270" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1270" class="Field Operator">_∼_</a> <a id="1281" class="Symbol">:</a> <a id="1283" href="Relation.Binary.Indexed.Heterogeneous.Core.html#856" class="Function">IRel</a> <a id="1288" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1181" class="Field">Carrier</a> <a id="1296" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1089" class="Bound">ℓ₂</a> <a id="1300" class="Comment">-- The relation.</a>
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<a id="IndexedPreorder.isPreorder"></a><a id="1321" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1321" class="Field">isPreorder</a> <a id="1332" class="Symbol">:</a> <a id="1334" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1070" class="Record">IsIndexedPreorder</a> <a id="1352" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1181" class="Field">Carrier</a> <a id="1360" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1208" class="Field Operator">_≈_</a> <a id="1364" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1270" class="Field Operator">_∼_</a>
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<a id="1371" class="Keyword">open</a> <a id="1376" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1070" class="Module">IsIndexedPreorder</a> <a id="1394" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1321" class="Field">isPreorder</a> <a id="1405" class="Keyword">public</a>
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