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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">--cubical-compatible</a> <a id="340" class="Pragma">--safe</a> <a id="347" class="Symbol">#-}</a>
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<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>
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<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>
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<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#931" class="Primitive">suc</a><a id="466" class="Symbol">;</a> <a id="468" href="Agda.Primitive.html#961" class="Primitive Operator">_⊔_</a><a id="471" class="Symbol">)</a>
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<a id="473" class="Keyword">open</a> <a id="478" class="Keyword">import</a> <a id="485" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a> <a id="506" class="Keyword">using</a> <a id="512" class="Symbol">(</a><a id="513" href="Relation.Binary.Core.html#1268" class="Function Operator">_⇒_</a><a id="516" class="Symbol">)</a>
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<a id="518" class="Keyword">open</a> <a id="523" class="Keyword">import</a> <a id="530" href="Relation.Binary.PropositionalEquality.Core.html" class="Module">Relation.Binary.PropositionalEquality.Core</a> <a id="573" class="Symbol">as</a> <a id="576" class="Module">P</a> <a id="578" class="Keyword">using</a> <a id="584" class="Symbol">(</a><a id="585" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a><a id="588" class="Symbol">)</a>
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<a id="590" class="Keyword">open</a> <a id="595" class="Keyword">import</a> <a id="602" href="Relation.Binary.Indexed.Heterogeneous.Core.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Core</a>
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<a id="645" class="Keyword">open</a> <a id="650" class="Keyword">import</a> <a id="657" href="Relation.Binary.Indexed.Heterogeneous.Structures.html" class="Module">Relation.Binary.Indexed.Heterogeneous.Structures</a>
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<a id="707" class="Comment">------------------------------------------------------------------------</a>
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<a id="780" class="Comment">-- Definitions</a>
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<a id="796" class="Keyword">record</a> <a id="IndexedSetoid"></a><a id="803" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#803" class="Record">IndexedSetoid</a> <a id="817" class="Symbol">{</a><a id="818" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#818" class="Bound">i</a><a id="819" class="Symbol">}</a> <a id="821" class="Symbol">(</a><a id="822" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#822" class="Bound">I</a> <a id="824" class="Symbol">:</a> <a id="826" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="830" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#818" class="Bound">i</a><a id="831" class="Symbol">)</a> <a id="833" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#833" class="Bound">c</a> <a id="835" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#835" class="Bound">ℓ</a> <a id="837" class="Symbol">:</a> <a id="839" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="843" class="Symbol">(</a><a id="844" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="848" class="Symbol">(</a><a id="849" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#818" class="Bound">i</a> <a id="851" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="853" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#833" class="Bound">c</a> <a id="855" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="857" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#835" class="Bound">ℓ</a><a id="858" class="Symbol">))</a> <a id="861" class="Keyword">where</a>
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<a id="869" class="Keyword">infix</a> <a id="875" class="Number">4</a> <a id="877" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#923" class="Field Operator">_≈_</a>
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<a id="883" class="Keyword">field</a>
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<a id="IndexedSetoid.Carrier"></a><a id="893" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#893" class="Field">Carrier</a> <a id="907" class="Symbol">:</a> <a id="909" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#822" class="Bound">I</a> <a id="911" class="Symbol">→</a> <a id="913" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="917" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#833" class="Bound">c</a>
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<a id="IndexedSetoid._≈_"></a><a id="923" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#923" class="Field Operator">_≈_</a> <a id="937" class="Symbol">:</a> <a id="939" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="944" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#893" class="Field">Carrier</a> <a id="952" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#835" class="Bound">ℓ</a>
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<a id="IndexedSetoid.isEquivalence"></a><a id="958" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#958" class="Field">isEquivalence</a> <a id="972" class="Symbol">:</a> <a id="974" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#866" class="Record">IsIndexedEquivalence</a> <a id="995" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#893" class="Field">Carrier</a> <a id="1003" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#923" class="Field Operator">_≈_</a>
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<a id="1010" class="Keyword">open</a> <a id="1015" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#866" class="Module">IsIndexedEquivalence</a> <a id="1036" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#958" class="Field">isEquivalence</a> <a id="1050" class="Keyword">public</a>
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<a id="1059" class="Keyword">record</a> <a id="IndexedPreorder"></a><a id="1066" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1066" class="Record">IndexedPreorder</a> <a id="1082" class="Symbol">{</a><a id="1083" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1083" class="Bound">i</a><a id="1084" class="Symbol">}</a> <a id="1086" class="Symbol">(</a><a id="1087" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1087" class="Bound">I</a> <a id="1089" class="Symbol">:</a> <a id="1091" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1095" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1083" class="Bound">i</a><a id="1096" class="Symbol">)</a> <a id="1098" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">c</a> <a id="1100" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1100" class="Bound">ℓ₁</a> <a id="1103" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1103" class="Bound">ℓ₂</a> <a id="1106" class="Symbol">:</a>
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<a id="1131" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1135" class="Symbol">(</a><a id="1136" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1140" class="Symbol">(</a><a id="1141" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1083" class="Bound">i</a> <a id="1143" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1145" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">c</a> <a id="1147" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1149" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1100" class="Bound">ℓ₁</a> <a id="1152" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1154" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1103" class="Bound">ℓ₂</a><a id="1156" class="Symbol">))</a> <a id="1159" class="Keyword">where</a>
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<a id="1167" class="Keyword">infix</a> <a id="1173" class="Number">4</a> <a id="1175" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1222" class="Field Operator">_≈_</a> <a id="1179" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1284" class="Field Operator">_≲_</a>
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<a id="1185" class="Keyword">field</a>
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<a id="IndexedPreorder.Carrier"></a><a id="1195" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1195" class="Field">Carrier</a> <a id="1206" class="Symbol">:</a> <a id="1208" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1087" class="Bound">I</a> <a id="1210" class="Symbol">→</a> <a id="1212" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1216" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1098" class="Bound">c</a>
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<a id="IndexedPreorder._≈_"></a><a id="1222" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1222" class="Field Operator">_≈_</a> <a id="1233" class="Symbol">:</a> <a id="1235" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="1240" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1195" class="Field">Carrier</a> <a id="1248" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1100" class="Bound">ℓ₁</a> <a id="1252" class="Comment">-- The underlying equality.</a>
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<a id="IndexedPreorder._≲_"></a><a id="1284" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1284" class="Field Operator">_≲_</a> <a id="1295" class="Symbol">:</a> <a id="1297" href="Relation.Binary.Indexed.Heterogeneous.Core.html#865" class="Function">IRel</a> <a id="1302" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1195" class="Field">Carrier</a> <a id="1310" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1103" class="Bound">ℓ₂</a> <a id="1314" class="Comment">-- The relation.</a>
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<a id="IndexedPreorder.isPreorder"></a><a id="1335" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1335" class="Field">isPreorder</a> <a id="1346" class="Symbol">:</a> <a id="1348" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1084" class="Record">IsIndexedPreorder</a> <a id="1366" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1195" class="Field">Carrier</a> <a id="1374" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1222" class="Field Operator">_≈_</a> <a id="1378" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1284" class="Field Operator">_≲_</a>
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<a id="1385" class="Keyword">open</a> <a id="1390" href="Relation.Binary.Indexed.Heterogeneous.Structures.html#1084" class="Module">IsIndexedPreorder</a> <a id="1408" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1335" class="Field">isPreorder</a> <a id="1419" class="Keyword">public</a>
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<a id="1429" class="Keyword">infix</a> <a id="1435" class="Number">4</a> <a id="1437" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1443" class="Function Operator">_∼_</a>
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<a id="IndexedPreorder._∼_"></a><a id="1443" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1443" class="Function Operator">_∼_</a> <a id="1447" class="Symbol">=</a> <a id="1449" href="Relation.Binary.Indexed.Heterogeneous.Bundles.html#1284" class="Field Operator">_≲_</a>
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<a id="1456" class="Comment">------------------------------------------------------------------------</a>
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<a id="1529" class="Comment">-- DEPRECATED</a>
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<a id="1543" class="Comment">------------------------------------------------------------------------</a>
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<a id="1616" class="Comment">-- Please use the new names as continuing support for the old names is</a>
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<a id="1687" class="Comment">-- not guaranteed.</a>
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<a id="1707" class="Comment">-- Version 2.0</a>
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<a id="1723" class="Symbol">{-#</a> <a id="1727" class="Keyword">WARNING_ON_USAGE</a> <a id="1744" class="Pragma">IndexedPreorder._∼_</a>
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<a id="1764" class="String">"Warning: IndexedPreorder._∼_ was deprecated in v2.0. Please use IndexedPreorder._≲_ instead. "</a>
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<a id="1860" class="Symbol">#-}</a>
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</pre></body></html> |