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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>
<a id="74" class="Comment">-- The Agda standard library</a>
<a id="103" class="Comment">--</a>
<a id="106" class="Comment">-- Indexed binary relations</a>
<a id="134" class="Comment">------------------------------------------------------------------------</a>
<a id="208" class="Comment">-- The contents of this module should be accessed via</a>
<a id="262" class="Comment">-- `Relation.Binary.Indexed.Heterogeneous`.</a>
<a id="307" class="Symbol">{-#</a> <a id="311" class="Keyword">OPTIONS</a> <a id="319" class="Pragma">--cubical-compatible</a> <a id="340" class="Pragma">--safe</a> <a id="347" class="Symbol">#-}</a>
<a id="352" class="Keyword">module</a> <a id="359" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Bundles</a> <a id="405" class="Keyword">where</a>
<a id="412" class="Keyword">open</a> <a id="417" class="Keyword">import</a> <a id="424" href="Function.Base.html" class="Module">Function.Base</a>
<a id="438" class="Keyword">open</a> <a id="443" class="Keyword">import</a> <a id="450" href="Level.html" class="Module">Level</a> <a id="456" class="Keyword">using</a> <a id="462" class="Symbol">(</a><a id="463" href="Agda.Primitive.html#774" class="Primitive">suc</a><a id="466" class="Symbol">;</a> <a id="468" href="Agda.Primitive.html#804" class="Primitive Operator">_⊔_</a><a id="471" class="Symbol">)</a>
<a id="473" class="Keyword">open</a> <a id="478" class="Keyword">import</a> <a id="485" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="501" class="Keyword">using</a> <a id="507" class="Symbol">(</a><a id="508" href="Relation.Binary.Core.html#1263" class="Function Operator">_⇒_</a><a id="511" class="Symbol">)</a>
<a id="513" class="Keyword">open</a> <a id="518" class="Keyword">import</a> <a id="525" href="Relation.Binary.PropositionalEquality.Core.html" class="Module">Relation.Binary.PropositionalEquality.Core</a> <a id="568" class="Symbol">as</a> <a id="571" class="Module">P</a> <a id="573" class="Keyword">using</a> <a id="579" class="Symbol">(</a><a id="580" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a><a id="583" class="Symbol">)</a>
<a id="585" class="Keyword">open</a> <a id="590" class="Keyword">import</a> <a id="597" href="Relation.Binary.Indexed.Heterogeneous.Core.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Core</a>
<a id="640" class="Keyword">open</a> <a id="645" class="Keyword">import</a> <a id="652" href="Relation.Binary.Indexed.Heterogeneous.Structures.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Structures</a>
<a id="702" class="Comment">------------------------------------------------------------------------</a>
<a id="775" class="Comment">-- Definitions</a>
<a id="791" class="Keyword">record</a> <a id="IndexedSetoid"></a><a id="798" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#798" class="Record">IndexedSetoid</a> <a id="812" class="Symbol">{</a><a id="813" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#813" class="Bound">i</a><a id="814" class="Symbol">}</a> <a id="816" class="Symbol">(</a><a id="817" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#817" class="Bound">I</a> <a id="819" class="Symbol">:</a> <a id="821" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="825" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#813" class="Bound">i</a><a id="826" class="Symbol">)</a> <a id="828" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#828" class="Bound">c</a> <a id="830" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#830" class="Bound">ℓ</a> <a id="832" class="Symbol">:</a> <a id="834" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="838" class="Symbol">(</a><a id="839" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="843" class="Symbol">(</a><a id="844" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#813" class="Bound">i</a> <a id="846" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="848" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#828" class="Bound">c</a> <a id="850" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="852" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#830" class="Bound">ℓ</a><a id="853" class="Symbol">))</a> <a id="856" class="Keyword">where</a>
<a id="864" class="Keyword">infix</a> <a id="870" class="Number">4</a> <a id="872" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#918" class="Field Operator">_≈_</a>
<a id="878" class="Keyword">field</a>
<a id="IndexedSetoid.Carrier"></a><a id="888" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#888" class="Field">Carrier</a> <a id="902" class="Symbol">:</a> <a id="904" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#817" class="Bound">I</a> <a id="906" class="Symbol">→</a> <a id="908" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="912" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#828" class="Bound">c</a>
<a id="IndexedSetoid._≈_"></a><a id="918" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#918" class="Field Operator">_≈_</a> <a id="932" class="Symbol">:</a> <a id="934" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="939" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#888" class="Field">Carrier</a> <a id="947" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#830" class="Bound">ℓ</a>
<a id="IndexedSetoid.isEquivalence"></a><a id="953" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#953" class="Field">isEquivalence</a> <a id="967" class="Symbol">:</a> <a id="969" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#861" class="Record">IsIndexedEquivalence</a> <a id="990" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#888" class="Field">Carrier</a> <a id="998" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#918" class="Field Operator">_≈_</a>
<a id="1005" class="Keyword">open</a> <a id="1010" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#861" class="Module">IsIndexedEquivalence</a> <a id="1031" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#953" class="Field">isEquivalence</a> <a id="1045" class="Keyword">public</a>
<a id="1054" class="Keyword">record</a> <a id="IndexedPreorder"></a><a id="1061" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1061" class="Record">IndexedPreorder</a> <a id="1077" class="Symbol">{</a><a id="1078" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1078" class="Bound">i</a><a id="1079" class="Symbol">}</a> <a id="1081" class="Symbol">(</a><a id="1082" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1082" class="Bound">I</a> <a id="1084" class="Symbol">:</a> <a id="1086" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1090" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1078" class="Bound">i</a><a id="1091" class="Symbol">)</a> <a id="1093" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1093" class="Bound">c</a> <a id="1095" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1095" class="Bound">ℓ₁</a> <a id="1098" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">ℓ₂</a> <a id="1101" class="Symbol">:</a>
<a id="1126" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1130" class="Symbol">(</a><a id="1131" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="1135" class="Symbol">(</a><a id="1136" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1078" class="Bound">i</a> <a id="1138" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1140" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1093" class="Bound">c</a> <a id="1142" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1144" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1095" class="Bound">ℓ₁</a> <a id="1147" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1149" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">ℓ₂</a><a id="1151" class="Symbol">))</a> <a id="1154" class="Keyword">where</a>
<a id="1162" class="Keyword">infix</a> <a id="1168" class="Number">4</a> <a id="1170" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1217" class="Field Operator">_≈_</a> <a id="1174" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1279" class="Field Operator">_∼_</a>
<a id="1180" class="Keyword">field</a>
<a id="IndexedPreorder.Carrier"></a><a id="1190" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1190" class="Field">Carrier</a> <a id="1201" class="Symbol">:</a> <a id="1203" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1082" class="Bound">I</a> <a id="1205" class="Symbol">→</a> <a id="1207" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1211" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1093" class="Bound">c</a>
<a id="IndexedPreorder._≈_"></a><a id="1217" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1217" class="Field Operator">_≈_</a> <a id="1228" class="Symbol">:</a> <a id="1230" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="1235" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1190" class="Field">Carrier</a> <a id="1243" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1095" class="Bound">ℓ₁</a> <a id="1247" class="Comment">-- The underlying equality.</a>
<a id="IndexedPreorder._∼_"></a><a id="1279" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1279" class="Field Operator">_∼_</a> <a id="1290" class="Symbol">:</a> <a id="1292" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="1297" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1190" class="Field">Carrier</a> <a id="1305" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">ℓ₂</a> <a id="1309" class="Comment">-- The relation.</a>
<a id="IndexedPreorder.isPreorder"></a><a id="1330" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1330" class="Field">isPreorder</a> <a id="1341" class="Symbol">:</a> <a id="1343" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1079" class="Record">IsIndexedPreorder</a> <a id="1361" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1190" class="Field">Carrier</a> <a id="1369" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1217" class="Field Operator">_≈_</a> <a id="1373" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1279" class="Field Operator">_∼_</a>
<a id="1380" class="Keyword">open</a> <a id="1385" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1079" class="Module">IsIndexedPreorder</a> <a id="1403" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1330" class="Field">isPreorder</a> <a id="1414" class="Keyword">public</a>
</pre></body></html>
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