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<html><head><meta charset="utf-8"><title>Relation.Binary.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">-- Bundles for homogeneous binary relations</a>
<a id="150" class="Comment">------------------------------------------------------------------------</a>
<a id="224" class="Comment">-- The contents of this module should be accessed via `Relation.Binary`.</a>
<a id="298" class="Symbol">{-#</a> <a id="302" class="Keyword">OPTIONS</a> <a id="310" class="Pragma">--cubical-compatible</a> <a id="331" class="Pragma">--safe</a> <a id="338" class="Symbol">#-}</a>
<a id="343" class="Keyword">module</a> <a id="350" href="Relation.Binary.Bundles.html" class="Module">Relation.Binary.Bundles</a> <a id="374" class="Keyword">where</a>
<a id="381" class="Keyword">open</a> <a id="386" class="Keyword">import</a> <a id="393" href="Function.Base.html" class="Module">Function.Base</a> <a id="407" class="Keyword">using</a> <a id="413" class="Symbol">(</a><a id="414" href="Function.Base.html#1638" class="Function">flip</a><a id="418" class="Symbol">)</a>
<a id="420" class="Keyword">open</a> <a id="425" class="Keyword">import</a> <a id="432" href="Level.html" class="Module">Level</a>
<a id="438" class="Keyword">open</a> <a id="443" class="Keyword">import</a> <a id="450" href="Relation.Nullary.Negation.html" class="Module">Relation.Nullary.Negation</a> <a id="476" class="Keyword">using</a> <a id="482" class="Symbol">(</a><a id="483" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬_</a><a id="485" class="Symbol">)</a>
<a id="487" class="Keyword">open</a> <a id="492" class="Keyword">import</a> <a id="499" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a>
<a id="520" class="Keyword">open</a> <a id="525" class="Keyword">import</a> <a id="532" href="Relation.Binary.Definitions.html" class="Module">Relation.Binary.Definitions</a>
<a id="560" class="Keyword">open</a> <a id="565" class="Keyword">import</a> <a id="572" href="Relation.Binary.Structures.html" class="Module">Relation.Binary.Structures</a>
<a id="600" class="Comment">------------------------------------------------------------------------</a>
<a id="673" class="Comment">-- Setoids</a>
<a id="684" class="Comment">------------------------------------------------------------------------</a>
<a id="758" class="Keyword">record</a> <a id="PartialSetoid"></a><a id="765" href="Relation.Binary.Bundles.html#765" class="Record">PartialSetoid</a> <a id="779" href="Relation.Binary.Bundles.html#779" class="Bound">a</a> <a id="781" href="Relation.Binary.Bundles.html#781" class="Bound">ℓ</a> <a id="783" class="Symbol">:</a> <a id="785" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="789" class="Symbol">(</a><a id="790" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="794" class="Symbol">(</a><a id="795" href="Relation.Binary.Bundles.html#779" class="Bound">a</a> <a id="797" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="799" href="Relation.Binary.Bundles.html#781" class="Bound">ℓ</a><a id="800" class="Symbol">))</a> <a id="803" class="Keyword">where</a>
<a id="811" class="Keyword">infix</a> <a id="817" class="Number">4</a> <a id="819" href="Relation.Binary.Bundles.html#868" class="Field Operator">_≈_</a>
<a id="825" class="Keyword">field</a>
<a id="PartialSetoid.Carrier"></a><a id="835" href="Relation.Binary.Bundles.html#835" class="Field">Carrier</a> <a id="856" class="Symbol">:</a> <a id="858" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="862" href="Relation.Binary.Bundles.html#779" class="Bound">a</a>
<a id="PartialSetoid._≈_"></a><a id="868" href="Relation.Binary.Bundles.html#868" class="Field Operator">_≈_</a> <a id="889" class="Symbol">:</a> <a id="891" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="895" href="Relation.Binary.Bundles.html#835" class="Field">Carrier</a> <a id="903" href="Relation.Binary.Bundles.html#781" class="Bound">ℓ</a>
<a id="PartialSetoid.isPartialEquivalence"></a><a id="909" href="Relation.Binary.Bundles.html#909" class="Field">isPartialEquivalence</a> <a id="930" class="Symbol">:</a> <a id="932" href="Relation.Binary.Structures.html#1147" class="Record">IsPartialEquivalence</a> <a id="953" href="Relation.Binary.Bundles.html#868" class="Field Operator">_≈_</a>
<a id="960" class="Keyword">open</a> <a id="965" href="Relation.Binary.Structures.html#1147" class="Module">IsPartialEquivalence</a> <a id="986" href="Relation.Binary.Bundles.html#909" class="Field">isPartialEquivalence</a> <a id="1007" class="Keyword">public</a>
<a id="1017" class="Keyword">infix</a> <a id="1023" class="Number">4</a> <a id="1025" href="Relation.Binary.Bundles.html#1031" class="Function Operator">_≉_</a>
<a id="PartialSetoid._≉_"></a><a id="1031" href="Relation.Binary.Bundles.html#1031" class="Function Operator">_≉_</a> <a id="1035" class="Symbol">:</a> <a id="1037" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1041" href="Relation.Binary.Bundles.html#835" class="Field">Carrier</a> <a id="1049" class="Symbol">_</a>
<a id="1053" href="Relation.Binary.Bundles.html#1053" class="Bound">x</a> <a id="1055" href="Relation.Binary.Bundles.html#1031" class="Function Operator">≉</a> <a id="1057" href="Relation.Binary.Bundles.html#1057" class="Bound">y</a> <a id="1059" class="Symbol">=</a> <a id="1061" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬</a> <a id="1063" class="Symbol">(</a><a id="1064" href="Relation.Binary.Bundles.html#1053" class="Bound">x</a> <a id="1066" href="Relation.Binary.Bundles.html#868" class="Field Operator">≈</a> <a id="1068" href="Relation.Binary.Bundles.html#1057" class="Bound">y</a><a id="1069" class="Symbol">)</a>
<a id="1073" class="Keyword">record</a> <a id="Setoid"></a><a id="1080" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="1087" href="Relation.Binary.Bundles.html#1087" class="Bound">c</a> <a id="1089" href="Relation.Binary.Bundles.html#1089" class="Bound">ℓ</a> <a id="1091" class="Symbol">:</a> <a id="1093" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1097" class="Symbol">(</a><a id="1098" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1102" class="Symbol">(</a><a id="1103" href="Relation.Binary.Bundles.html#1087" class="Bound">c</a> <a id="1105" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1107" href="Relation.Binary.Bundles.html#1089" class="Bound">ℓ</a><a id="1108" class="Symbol">))</a> <a id="1111" class="Keyword">where</a>
<a id="1119" class="Keyword">infix</a> <a id="1125" class="Number">4</a> <a id="1127" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="1133" class="Keyword">field</a>
<a id="Setoid.Carrier"></a><a id="1143" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="1157" class="Symbol">:</a> <a id="1159" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1163" href="Relation.Binary.Bundles.html#1087" class="Bound">c</a>
<a id="Setoid._≈_"></a><a id="1169" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="1183" class="Symbol">:</a> <a id="1185" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1189" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="1197" href="Relation.Binary.Bundles.html#1089" class="Bound">ℓ</a>
<a id="Setoid.isEquivalence"></a><a id="1203" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="1217" class="Symbol">:</a> <a id="1219" href="Relation.Binary.Structures.html#1550" class="Record">IsEquivalence</a> <a id="1233" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a>
<a id="1240" class="Keyword">open</a> <a id="1245" href="Relation.Binary.Structures.html#1550" class="Module">IsEquivalence</a> <a id="1259" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="1273" class="Keyword">public</a>
<a id="1284" class="Keyword">using</a> <a id="1290" class="Symbol">(</a><a id="1291" href="Relation.Binary.Structures.html#1596" class="Field">refl</a><a id="1295" class="Symbol">;</a> <a id="1297" href="Relation.Binary.Structures.html#1674" class="Function">reflexive</a><a id="1306" class="Symbol">;</a> <a id="1308" href="Relation.Binary.Structures.html#1725" class="Function">isPartialEquivalence</a><a id="1328" class="Symbol">)</a>
<a id="Setoid.partialSetoid"></a><a id="1333" href="Relation.Binary.Bundles.html#1333" class="Function">partialSetoid</a> <a id="1347" class="Symbol">:</a> <a id="1349" href="Relation.Binary.Bundles.html#765" class="Record">PartialSetoid</a> <a id="1363" href="Relation.Binary.Bundles.html#1087" class="Bound">c</a> <a id="1365" href="Relation.Binary.Bundles.html#1089" class="Bound">ℓ</a>
<a id="1369" href="Relation.Binary.Bundles.html#1333" class="Function">partialSetoid</a> <a id="1383" class="Symbol">=</a> <a id="1385" class="Keyword">record</a>
<a id="1396" class="Symbol">{</a> <a id="1398" href="Relation.Binary.Bundles.html#909" class="Field">isPartialEquivalence</a> <a id="1419" class="Symbol">=</a> <a id="1421" href="Relation.Binary.Structures.html#1725" class="Function">isPartialEquivalence</a>
<a id="1446" class="Symbol">}</a>
<a id="1451" class="Keyword">open</a> <a id="1456" href="Relation.Binary.Bundles.html#765" class="Module">PartialSetoid</a> <a id="1470" href="Relation.Binary.Bundles.html#1333" class="Function">partialSetoid</a> <a id="1484" class="Keyword">public</a>
<a id="1495" class="Keyword">hiding</a> <a id="1502" class="Symbol">(</a><a id="1503" href="Relation.Binary.Bundles.html#835" class="Field">Carrier</a><a id="1510" class="Symbol">;</a> <a id="1512" href="Relation.Binary.Bundles.html#868" class="Field Operator">_≈_</a><a id="1515" class="Symbol">;</a> <a id="1517" href="Relation.Binary.Bundles.html#909" class="Field">isPartialEquivalence</a><a id="1537" class="Symbol">)</a>
<a id="1541" class="Keyword">record</a> <a id="DecSetoid"></a><a id="1548" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a> <a id="1558" href="Relation.Binary.Bundles.html#1558" class="Bound">c</a> <a id="1560" href="Relation.Binary.Bundles.html#1560" class="Bound">ℓ</a> <a id="1562" class="Symbol">:</a> <a id="1564" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1568" class="Symbol">(</a><a id="1569" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1573" class="Symbol">(</a><a id="1574" href="Relation.Binary.Bundles.html#1558" class="Bound">c</a> <a id="1576" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1578" href="Relation.Binary.Bundles.html#1560" class="Bound">ℓ</a><a id="1579" class="Symbol">))</a> <a id="1582" class="Keyword">where</a>
<a id="1590" class="Keyword">infix</a> <a id="1596" class="Number">4</a> <a id="1598" href="Relation.Binary.Bundles.html#1643" class="Field Operator">_≈_</a>
<a id="1604" class="Keyword">field</a>
<a id="DecSetoid.Carrier"></a><a id="1614" href="Relation.Binary.Bundles.html#1614" class="Field">Carrier</a> <a id="1631" class="Symbol">:</a> <a id="1633" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1637" href="Relation.Binary.Bundles.html#1558" class="Bound">c</a>
<a id="DecSetoid._≈_"></a><a id="1643" href="Relation.Binary.Bundles.html#1643" class="Field Operator">_≈_</a> <a id="1660" class="Symbol">:</a> <a id="1662" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="1666" href="Relation.Binary.Bundles.html#1614" class="Field">Carrier</a> <a id="1674" href="Relation.Binary.Bundles.html#1560" class="Bound">ℓ</a>
<a id="DecSetoid.isDecEquivalence"></a><a id="1680" href="Relation.Binary.Bundles.html#1680" class="Field">isDecEquivalence</a> <a id="1697" class="Symbol">:</a> <a id="1699" href="Relation.Binary.Structures.html#1852" class="Record">IsDecEquivalence</a> <a id="1716" href="Relation.Binary.Bundles.html#1643" class="Field Operator">_≈_</a>
<a id="1723" class="Keyword">open</a> <a id="1728" href="Relation.Binary.Structures.html#1852" class="Module">IsDecEquivalence</a> <a id="1745" href="Relation.Binary.Bundles.html#1680" class="Field">isDecEquivalence</a> <a id="1762" class="Keyword">public</a>
<a id="1773" class="Keyword">using</a> <a id="1779" class="Symbol">(</a><a id="1780" href="Relation.Binary.Structures.html#1949" class="Field Operator">_≟_</a><a id="1783" class="Symbol">;</a> <a id="1785" href="Relation.Binary.Structures.html#1915" class="Field">isEquivalence</a><a id="1798" class="Symbol">)</a>
<a id="DecSetoid.setoid"></a><a id="1803" href="Relation.Binary.Bundles.html#1803" class="Function">setoid</a> <a id="1810" class="Symbol">:</a> <a id="1812" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="1819" href="Relation.Binary.Bundles.html#1558" class="Bound">c</a> <a id="1821" href="Relation.Binary.Bundles.html#1560" class="Bound">ℓ</a>
<a id="1825" href="Relation.Binary.Bundles.html#1803" class="Function">setoid</a> <a id="1832" class="Symbol">=</a> <a id="1834" class="Keyword">record</a>
<a id="1845" class="Symbol">{</a> <a id="1847" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="1861" class="Symbol">=</a> <a id="1863" href="Relation.Binary.Structures.html#1915" class="Function">isEquivalence</a>
<a id="1881" class="Symbol">}</a>
<a id="1886" class="Keyword">open</a> <a id="1891" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="1898" href="Relation.Binary.Bundles.html#1803" class="Function">setoid</a> <a id="1905" class="Keyword">public</a>
<a id="1916" class="Keyword">hiding</a> <a id="1923" class="Symbol">(</a><a id="1924" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a><a id="1931" class="Symbol">;</a> <a id="1933" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a><a id="1936" class="Symbol">;</a> <a id="1938" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a><a id="1951" class="Symbol">)</a>
<a id="1954" class="Comment">------------------------------------------------------------------------</a>
<a id="2027" class="Comment">-- Preorders</a>
<a id="2040" class="Comment">------------------------------------------------------------------------</a>
<a id="2114" class="Keyword">record</a> <a id="Preorder"></a><a id="2121" href="Relation.Binary.Bundles.html#2121" class="Record">Preorder</a> <a id="2130" href="Relation.Binary.Bundles.html#2130" class="Bound">c</a> <a id="2132" href="Relation.Binary.Bundles.html#2132" class="Bound">ℓ₁</a> <a id="2135" href="Relation.Binary.Bundles.html#2135" class="Bound">ℓ₂</a> <a id="2138" class="Symbol">:</a> <a id="2140" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2144" class="Symbol">(</a><a id="2145" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="2149" class="Symbol">(</a><a id="2150" href="Relation.Binary.Bundles.html#2130" class="Bound">c</a> <a id="2152" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2154" href="Relation.Binary.Bundles.html#2132" class="Bound">ℓ₁</a> <a id="2157" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2159" href="Relation.Binary.Bundles.html#2135" class="Bound">ℓ₂</a><a id="2161" class="Symbol">))</a> <a id="2164" class="Keyword">where</a>
<a id="2172" class="Keyword">infix</a> <a id="2178" class="Number">4</a> <a id="2180" href="Relation.Binary.Bundles.html#2223" class="Field Operator">_≈_</a> <a id="2184" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a>
<a id="2190" class="Keyword">field</a>
<a id="Preorder.Carrier"></a><a id="2200" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a> <a id="2211" class="Symbol">:</a> <a id="2213" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2217" href="Relation.Binary.Bundles.html#2130" class="Bound">c</a>
<a id="Preorder._≈_"></a><a id="2223" href="Relation.Binary.Bundles.html#2223" class="Field Operator">_≈_</a> <a id="2234" class="Symbol">:</a> <a id="2236" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2240" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a> <a id="2248" href="Relation.Binary.Bundles.html#2132" class="Bound">ℓ₁</a> <a id="2252" class="Comment">-- The underlying equality.</a>
<a id="Preorder._≲_"></a><a id="2284" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a> <a id="2295" class="Symbol">:</a> <a id="2297" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2301" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a> <a id="2309" href="Relation.Binary.Bundles.html#2135" class="Bound">ℓ₂</a> <a id="2313" class="Comment">-- The relation.</a>
<a id="Preorder.isPreorder"></a><a id="2334" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a> <a id="2345" class="Symbol">:</a> <a id="2347" href="Relation.Binary.Structures.html#2191" class="Record">IsPreorder</a> <a id="2358" href="Relation.Binary.Bundles.html#2223" class="Field Operator">_≈_</a> <a id="2362" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a>
<a id="2369" class="Keyword">open</a> <a id="2374" href="Relation.Binary.Structures.html#2191" class="Module">IsPreorder</a> <a id="2385" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a> <a id="2396" class="Keyword">public</a>
<a id="2407" class="Keyword">hiding</a> <a id="2414" class="Symbol">(</a><a id="2415" class="Keyword">module</a> <a id="2422" href="Relation.Binary.Structures.html#2430" class="Module">Eq</a><a id="2424" class="Symbol">)</a>
<a id="2429" class="Keyword">module</a> <a id="Preorder.Eq"></a><a id="2436" href="Relation.Binary.Bundles.html#2436" class="Module">Eq</a> <a id="2439" class="Keyword">where</a>
<a id="Preorder.Eq.setoid"></a><a id="2449" href="Relation.Binary.Bundles.html#2449" class="Function">setoid</a> <a id="2456" class="Symbol">:</a> <a id="2458" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2465" href="Relation.Binary.Bundles.html#2130" class="Bound">c</a> <a id="2467" href="Relation.Binary.Bundles.html#2132" class="Bound">ℓ₁</a>
<a id="2474" href="Relation.Binary.Bundles.html#2449" class="Function">setoid</a> <a id="2481" class="Symbol">=</a> <a id="2483" class="Keyword">record</a>
<a id="2496" class="Symbol">{</a> <a id="2498" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="2512" class="Symbol">=</a> <a id="2514" href="Relation.Binary.Structures.html#2256" class="Function">isEquivalence</a>
<a id="2534" class="Symbol">}</a>
<a id="2541" class="Keyword">open</a> <a id="2546" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="2553" href="Relation.Binary.Bundles.html#2449" class="Function">setoid</a> <a id="2560" class="Keyword">public</a>
<a id="2570" class="Keyword">infix</a> <a id="2576" class="Number">4</a> <a id="2578" href="Relation.Binary.Bundles.html#2584" class="Function Operator">_⋦_</a>
<a id="Preorder._⋦_"></a><a id="2584" href="Relation.Binary.Bundles.html#2584" class="Function Operator">_⋦_</a> <a id="2588" class="Symbol">:</a> <a id="2590" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2594" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a> <a id="2602" class="Symbol">_</a>
<a id="2606" href="Relation.Binary.Bundles.html#2606" class="Bound">x</a> <a id="2608" href="Relation.Binary.Bundles.html#2584" class="Function Operator">⋦</a> <a id="2610" href="Relation.Binary.Bundles.html#2610" class="Bound">y</a> <a id="2612" class="Symbol">=</a> <a id="2614" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬</a> <a id="2616" class="Symbol">(</a><a id="2617" href="Relation.Binary.Bundles.html#2606" class="Bound">x</a> <a id="2619" href="Relation.Binary.Bundles.html#2284" class="Field Operator">≲</a> <a id="2621" href="Relation.Binary.Bundles.html#2610" class="Bound">y</a><a id="2622" class="Symbol">)</a>
<a id="2627" class="Keyword">infix</a> <a id="2633" class="Number">4</a> <a id="2635" href="Relation.Binary.Bundles.html#2641" class="Function Operator">_≳_</a>
<a id="Preorder._≳_"></a><a id="2641" href="Relation.Binary.Bundles.html#2641" class="Function Operator">_≳_</a> <a id="2645" class="Symbol">=</a> <a id="2647" href="Function.Base.html#1638" class="Function">flip</a> <a id="2652" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a>
<a id="2659" class="Keyword">infix</a> <a id="2665" class="Number">4</a> <a id="2667" href="Relation.Binary.Bundles.html#2673" class="Function Operator">_⋧_</a>
<a id="Preorder._⋧_"></a><a id="2673" href="Relation.Binary.Bundles.html#2673" class="Function Operator">_⋧_</a> <a id="2677" class="Symbol">=</a> <a id="2679" href="Function.Base.html#1638" class="Function">flip</a> <a id="2684" href="Relation.Binary.Bundles.html#2584" class="Function Operator">_⋦_</a>
<a id="2691" class="Comment">-- Deprecated.</a>
<a id="2708" class="Keyword">infix</a> <a id="2714" class="Number">4</a> <a id="2716" href="Relation.Binary.Bundles.html#2722" class="Function Operator">_∼_</a>
<a id="Preorder._∼_"></a><a id="2722" href="Relation.Binary.Bundles.html#2722" class="Function Operator">_∼_</a> <a id="2726" class="Symbol">=</a> <a id="2728" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a>
<a id="2734" class="Symbol">{-#</a> <a id="2738" class="Keyword">WARNING_ON_USAGE</a> <a id="2755" class="Pragma">_∼_</a>
<a id="2761" class="String">&quot;Warning: _∼_ was deprecated in v2.0.
Please use _≲_ instead. &quot;</a>
<a id="2829" class="Symbol">#-}</a>
<a id="2835" class="Keyword">record</a> <a id="TotalPreorder"></a><a id="2842" href="Relation.Binary.Bundles.html#2842" class="Record">TotalPreorder</a> <a id="2856" href="Relation.Binary.Bundles.html#2856" class="Bound">c</a> <a id="2858" href="Relation.Binary.Bundles.html#2858" class="Bound">ℓ₁</a> <a id="2861" href="Relation.Binary.Bundles.html#2861" class="Bound">ℓ₂</a> <a id="2864" class="Symbol">:</a> <a id="2866" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2870" class="Symbol">(</a><a id="2871" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="2875" class="Symbol">(</a><a id="2876" href="Relation.Binary.Bundles.html#2856" class="Bound">c</a> <a id="2878" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2880" href="Relation.Binary.Bundles.html#2858" class="Bound">ℓ₁</a> <a id="2883" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2885" href="Relation.Binary.Bundles.html#2861" class="Bound">ℓ₂</a><a id="2887" class="Symbol">))</a> <a id="2890" class="Keyword">where</a>
<a id="2898" class="Keyword">infix</a> <a id="2904" class="Number">4</a> <a id="2906" href="Relation.Binary.Bundles.html#2954" class="Field Operator">_≈_</a> <a id="2910" href="Relation.Binary.Bundles.html#3020" class="Field Operator">_≲_</a>
<a id="2916" class="Keyword">field</a>
<a id="TotalPreorder.Carrier"></a><a id="2926" href="Relation.Binary.Bundles.html#2926" class="Field">Carrier</a> <a id="2942" class="Symbol">:</a> <a id="2944" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2948" href="Relation.Binary.Bundles.html#2856" class="Bound">c</a>
<a id="TotalPreorder._≈_"></a><a id="2954" href="Relation.Binary.Bundles.html#2954" class="Field Operator">_≈_</a> <a id="2970" class="Symbol">:</a> <a id="2972" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="2976" href="Relation.Binary.Bundles.html#2926" class="Field">Carrier</a> <a id="2984" href="Relation.Binary.Bundles.html#2858" class="Bound">ℓ₁</a> <a id="2988" class="Comment">-- The underlying equality.</a>
<a id="TotalPreorder._≲_"></a><a id="3020" href="Relation.Binary.Bundles.html#3020" class="Field Operator">_≲_</a> <a id="3036" class="Symbol">:</a> <a id="3038" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3042" href="Relation.Binary.Bundles.html#2926" class="Field">Carrier</a> <a id="3050" href="Relation.Binary.Bundles.html#2861" class="Bound">ℓ₂</a> <a id="3054" class="Comment">-- The relation.</a>
<a id="TotalPreorder.isTotalPreorder"></a><a id="3075" href="Relation.Binary.Bundles.html#3075" class="Field">isTotalPreorder</a> <a id="3091" class="Symbol">:</a> <a id="3093" href="Relation.Binary.Structures.html#3186" class="Record">IsTotalPreorder</a> <a id="3109" href="Relation.Binary.Bundles.html#2954" class="Field Operator">_≈_</a> <a id="3113" href="Relation.Binary.Bundles.html#3020" class="Field Operator">_≲_</a>
<a id="3120" class="Keyword">open</a> <a id="3125" href="Relation.Binary.Structures.html#3186" class="Module">IsTotalPreorder</a> <a id="3141" href="Relation.Binary.Bundles.html#3075" class="Field">isTotalPreorder</a> <a id="3157" class="Keyword">public</a>
<a id="3168" class="Keyword">using</a> <a id="3174" class="Symbol">(</a><a id="3175" href="Relation.Binary.Structures.html#3288" class="Field">total</a><a id="3180" class="Symbol">;</a> <a id="3182" href="Relation.Binary.Structures.html#3256" class="Field">isPreorder</a><a id="3192" class="Symbol">)</a>
<a id="TotalPreorder.preorder"></a><a id="3197" href="Relation.Binary.Bundles.html#3197" class="Function">preorder</a> <a id="3206" class="Symbol">:</a> <a id="3208" href="Relation.Binary.Bundles.html#2121" class="Record">Preorder</a> <a id="3217" href="Relation.Binary.Bundles.html#2856" class="Bound">c</a> <a id="3219" href="Relation.Binary.Bundles.html#2858" class="Bound">ℓ₁</a> <a id="3222" href="Relation.Binary.Bundles.html#2861" class="Bound">ℓ₂</a>
<a id="3227" href="Relation.Binary.Bundles.html#3197" class="Function">preorder</a> <a id="3236" class="Symbol">=</a> <a id="3238" class="Keyword">record</a>
<a id="3249" class="Symbol">{</a> <a id="3251" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a> <a id="3262" class="Symbol">=</a> <a id="3264" href="Relation.Binary.Structures.html#3256" class="Function">isPreorder</a>
<a id="3279" class="Symbol">}</a>
<a id="3284" class="Keyword">open</a> <a id="3289" href="Relation.Binary.Bundles.html#2121" class="Module">Preorder</a> <a id="3298" href="Relation.Binary.Bundles.html#3197" class="Function">preorder</a> <a id="3307" class="Keyword">public</a>
<a id="3318" class="Keyword">hiding</a> <a id="3325" class="Symbol">(</a><a id="3326" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a><a id="3333" class="Symbol">;</a> <a id="3335" href="Relation.Binary.Bundles.html#2223" class="Field Operator">_≈_</a><a id="3338" class="Symbol">;</a> <a id="3340" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a><a id="3343" class="Symbol">;</a> <a id="3345" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a><a id="3355" class="Symbol">)</a>
<a id="3358" class="Comment">------------------------------------------------------------------------</a>
<a id="3431" class="Comment">-- Partial orders</a>
<a id="3449" class="Comment">------------------------------------------------------------------------</a>
<a id="3523" class="Keyword">record</a> <a id="Poset"></a><a id="3530" href="Relation.Binary.Bundles.html#3530" class="Record">Poset</a> <a id="3536" href="Relation.Binary.Bundles.html#3536" class="Bound">c</a> <a id="3538" href="Relation.Binary.Bundles.html#3538" class="Bound">ℓ₁</a> <a id="3541" href="Relation.Binary.Bundles.html#3541" class="Bound">ℓ₂</a> <a id="3544" class="Symbol">:</a> <a id="3546" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3550" class="Symbol">(</a><a id="3551" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="3555" class="Symbol">(</a><a id="3556" href="Relation.Binary.Bundles.html#3536" class="Bound">c</a> <a id="3558" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="3560" href="Relation.Binary.Bundles.html#3538" class="Bound">ℓ₁</a> <a id="3563" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="3565" href="Relation.Binary.Bundles.html#3541" class="Bound">ℓ₂</a><a id="3567" class="Symbol">))</a> <a id="3570" class="Keyword">where</a>
<a id="3578" class="Keyword">infix</a> <a id="3584" class="Number">4</a> <a id="3586" href="Relation.Binary.Bundles.html#3633" class="Field Operator">_≈_</a> <a id="3590" href="Relation.Binary.Bundles.html#3669" class="Field Operator">_≤_</a>
<a id="3596" class="Keyword">field</a>
<a id="Poset.Carrier"></a><a id="3606" href="Relation.Binary.Bundles.html#3606" class="Field">Carrier</a> <a id="3621" class="Symbol">:</a> <a id="3623" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="3627" href="Relation.Binary.Bundles.html#3536" class="Bound">c</a>
<a id="Poset._≈_"></a><a id="3633" href="Relation.Binary.Bundles.html#3633" class="Field Operator">_≈_</a> <a id="3648" class="Symbol">:</a> <a id="3650" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3654" href="Relation.Binary.Bundles.html#3606" class="Field">Carrier</a> <a id="3662" href="Relation.Binary.Bundles.html#3538" class="Bound">ℓ₁</a>
<a id="Poset._≤_"></a><a id="3669" href="Relation.Binary.Bundles.html#3669" class="Field Operator">_≤_</a> <a id="3684" class="Symbol">:</a> <a id="3686" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="3690" href="Relation.Binary.Bundles.html#3606" class="Field">Carrier</a> <a id="3698" href="Relation.Binary.Bundles.html#3541" class="Bound">ℓ₂</a>
<a id="Poset.isPartialOrder"></a><a id="3705" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a> <a id="3720" class="Symbol">:</a> <a id="3722" href="Relation.Binary.Structures.html#3522" class="Record">IsPartialOrder</a> <a id="3737" href="Relation.Binary.Bundles.html#3633" class="Field Operator">_≈_</a> <a id="3741" href="Relation.Binary.Bundles.html#3669" class="Field Operator">_≤_</a>
<a id="3748" class="Keyword">open</a> <a id="3753" href="Relation.Binary.Structures.html#3522" class="Module">IsPartialOrder</a> <a id="3768" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a> <a id="3783" class="Keyword">public</a>
<a id="3794" class="Keyword">using</a> <a id="3800" class="Symbol">(</a><a id="3801" href="Relation.Binary.Structures.html#3623" class="Field">antisym</a><a id="3808" class="Symbol">;</a> <a id="3810" href="Relation.Binary.Structures.html#3591" class="Field">isPreorder</a><a id="3820" class="Symbol">)</a>
<a id="Poset.preorder"></a><a id="3825" href="Relation.Binary.Bundles.html#3825" class="Function">preorder</a> <a id="3834" class="Symbol">:</a> <a id="3836" href="Relation.Binary.Bundles.html#2121" class="Record">Preorder</a> <a id="3845" href="Relation.Binary.Bundles.html#3536" class="Bound">c</a> <a id="3847" href="Relation.Binary.Bundles.html#3538" class="Bound">ℓ₁</a> <a id="3850" href="Relation.Binary.Bundles.html#3541" class="Bound">ℓ₂</a>
<a id="3855" href="Relation.Binary.Bundles.html#3825" class="Function">preorder</a> <a id="3864" class="Symbol">=</a> <a id="3866" class="Keyword">record</a>
<a id="3877" class="Symbol">{</a> <a id="3879" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a> <a id="3890" class="Symbol">=</a> <a id="3892" href="Relation.Binary.Structures.html#3591" class="Function">isPreorder</a>
<a id="3907" class="Symbol">}</a>
<a id="3912" class="Keyword">open</a> <a id="3917" href="Relation.Binary.Bundles.html#2121" class="Module">Preorder</a> <a id="3926" href="Relation.Binary.Bundles.html#3825" class="Function">preorder</a> <a id="3935" class="Keyword">public</a>
<a id="3946" class="Keyword">hiding</a> <a id="3953" class="Symbol">(</a><a id="3954" href="Relation.Binary.Bundles.html#2200" class="Field">Carrier</a><a id="3961" class="Symbol">;</a> <a id="3963" href="Relation.Binary.Bundles.html#2223" class="Field Operator">_≈_</a><a id="3966" class="Symbol">;</a> <a id="3968" href="Relation.Binary.Bundles.html#2284" class="Field Operator">_≲_</a><a id="3971" class="Symbol">;</a> <a id="3973" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a><a id="3983" class="Symbol">)</a>
<a id="3989" class="Keyword">renaming</a>
<a id="4002" class="Symbol">(</a> <a id="4004" href="Relation.Binary.Bundles.html#2584" class="Function Operator">_⋦_</a> <a id="4008" class="Symbol">to</a> <a id="4011" class="Function Operator">_≰_</a><a id="4014" class="Symbol">;</a> <a id="4016" href="Relation.Binary.Bundles.html#2641" class="Function Operator">_≳_</a> <a id="4020" class="Symbol">to</a> <a id="4023" class="Function Operator">_≥_</a><a id="4026" class="Symbol">;</a> <a id="4028" href="Relation.Binary.Bundles.html#2673" class="Function Operator">_⋧_</a> <a id="4032" class="Symbol">to</a> <a id="4035" class="Function Operator">_≱_</a>
<a id="4043" class="Symbol">;</a> <a id="4045" href="Relation.Binary.Structures.html#2517" class="Function">≲-respˡ-≈</a> <a id="4055" class="Symbol">to</a> <a id="4058" class="Function">≤-respˡ-≈</a>
<a id="4072" class="Symbol">;</a> <a id="4074" href="Relation.Binary.Structures.html#2607" class="Function">≲-respʳ-≈</a> <a id="4084" class="Symbol">to</a> <a id="4087" class="Function">≤-respʳ-≈</a>
<a id="4101" class="Symbol">;</a> <a id="4103" href="Relation.Binary.Structures.html#2688" class="Function">≲-resp-≈</a> <a id="4113" class="Symbol">to</a> <a id="4116" class="Function">≤-resp-≈</a>
<a id="4129" class="Symbol">)</a>
<a id="4133" class="Keyword">record</a> <a id="DecPoset"></a><a id="4140" href="Relation.Binary.Bundles.html#4140" class="Record">DecPoset</a> <a id="4149" href="Relation.Binary.Bundles.html#4149" class="Bound">c</a> <a id="4151" href="Relation.Binary.Bundles.html#4151" class="Bound">ℓ₁</a> <a id="4154" href="Relation.Binary.Bundles.html#4154" class="Bound">ℓ₂</a> <a id="4157" class="Symbol">:</a> <a id="4159" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4163" class="Symbol">(</a><a id="4164" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="4168" class="Symbol">(</a><a id="4169" href="Relation.Binary.Bundles.html#4149" class="Bound">c</a> <a id="4171" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4173" href="Relation.Binary.Bundles.html#4151" class="Bound">ℓ₁</a> <a id="4176" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4178" href="Relation.Binary.Bundles.html#4154" class="Bound">ℓ₂</a><a id="4180" class="Symbol">))</a> <a id="4183" class="Keyword">where</a>
<a id="4191" class="Keyword">infix</a> <a id="4197" class="Number">4</a> <a id="4199" href="Relation.Binary.Bundles.html#4249" class="Field Operator">_≈_</a> <a id="4203" href="Relation.Binary.Bundles.html#4288" class="Field Operator">_≤_</a>
<a id="4209" class="Keyword">field</a>
<a id="DecPoset.Carrier"></a><a id="4219" href="Relation.Binary.Bundles.html#4219" class="Field">Carrier</a> <a id="4237" class="Symbol">:</a> <a id="4239" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4243" href="Relation.Binary.Bundles.html#4149" class="Bound">c</a>
<a id="DecPoset._≈_"></a><a id="4249" href="Relation.Binary.Bundles.html#4249" class="Field Operator">_≈_</a> <a id="4267" class="Symbol">:</a> <a id="4269" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="4273" href="Relation.Binary.Bundles.html#4219" class="Field">Carrier</a> <a id="4281" href="Relation.Binary.Bundles.html#4151" class="Bound">ℓ₁</a>
<a id="DecPoset._≤_"></a><a id="4288" href="Relation.Binary.Bundles.html#4288" class="Field Operator">_≤_</a> <a id="4306" class="Symbol">:</a> <a id="4308" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="4312" href="Relation.Binary.Bundles.html#4219" class="Field">Carrier</a> <a id="4320" href="Relation.Binary.Bundles.html#4154" class="Bound">ℓ₂</a>
<a id="DecPoset.isDecPartialOrder"></a><a id="4327" href="Relation.Binary.Bundles.html#4327" class="Field">isDecPartialOrder</a> <a id="4345" class="Symbol">:</a> <a id="4347" href="Relation.Binary.Structures.html#3809" class="Record">IsDecPartialOrder</a> <a id="4365" href="Relation.Binary.Bundles.html#4249" class="Field Operator">_≈_</a> <a id="4369" href="Relation.Binary.Bundles.html#4288" class="Field Operator">_≤_</a>
<a id="4376" class="Keyword">private</a> <a id="4384" class="Keyword">module</a> <a id="DecPoset.DPO"></a><a id="4391" href="Relation.Binary.Bundles.html#4391" class="Module">DPO</a> <a id="4395" class="Symbol">=</a> <a id="4397" href="Relation.Binary.Structures.html#3809" class="Module">IsDecPartialOrder</a> <a id="4415" href="Relation.Binary.Bundles.html#4327" class="Field">isDecPartialOrder</a>
<a id="4436" class="Keyword">open</a> <a id="4441" href="Relation.Binary.Bundles.html#4391" class="Module">DPO</a> <a id="4445" class="Keyword">public</a>
<a id="4456" class="Keyword">using</a> <a id="4462" class="Symbol">(</a><a id="4463" href="Relation.Binary.Structures.html#3940" class="Function Operator">_≟_</a><a id="4466" class="Symbol">;</a> <a id="4468" href="Relation.Binary.Structures.html#3975" class="Function Operator">_≤?_</a><a id="4472" class="Symbol">;</a> <a id="4474" href="Relation.Binary.Structures.html#3900" class="Function">isPartialOrder</a><a id="4488" class="Symbol">)</a>
<a id="DecPoset.poset"></a><a id="4493" href="Relation.Binary.Bundles.html#4493" class="Function">poset</a> <a id="4499" class="Symbol">:</a> <a id="4501" href="Relation.Binary.Bundles.html#3530" class="Record">Poset</a> <a id="4507" href="Relation.Binary.Bundles.html#4149" class="Bound">c</a> <a id="4509" href="Relation.Binary.Bundles.html#4151" class="Bound">ℓ₁</a> <a id="4512" href="Relation.Binary.Bundles.html#4154" class="Bound">ℓ₂</a>
<a id="4517" href="Relation.Binary.Bundles.html#4493" class="Function">poset</a> <a id="4523" class="Symbol">=</a> <a id="4525" class="Keyword">record</a>
<a id="4536" class="Symbol">{</a> <a id="4538" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a> <a id="4553" class="Symbol">=</a> <a id="4555" href="Relation.Binary.Structures.html#3900" class="Function">isPartialOrder</a>
<a id="4574" class="Symbol">}</a>
<a id="4579" class="Keyword">open</a> <a id="4584" href="Relation.Binary.Bundles.html#3530" class="Module">Poset</a> <a id="4590" href="Relation.Binary.Bundles.html#4493" class="Function">poset</a> <a id="4596" class="Keyword">public</a>
<a id="4607" class="Keyword">hiding</a> <a id="4614" class="Symbol">(</a><a id="4615" href="Relation.Binary.Bundles.html#3606" class="Field">Carrier</a><a id="4622" class="Symbol">;</a> <a id="4624" href="Relation.Binary.Bundles.html#3633" class="Field Operator">_≈_</a><a id="4627" class="Symbol">;</a> <a id="4629" href="Relation.Binary.Bundles.html#3669" class="Field Operator">_≤_</a><a id="4632" class="Symbol">;</a> <a id="4634" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a><a id="4648" class="Symbol">;</a> <a id="4650" class="Keyword">module</a> <a id="4657" href="Relation.Binary.Bundles.html#2436" class="Module">Eq</a><a id="4659" class="Symbol">)</a>
<a id="4664" class="Keyword">module</a> <a id="DecPoset.Eq"></a><a id="4671" href="Relation.Binary.Bundles.html#4671" class="Module">Eq</a> <a id="4674" class="Keyword">where</a>
<a id="DecPoset.Eq.decSetoid"></a><a id="4684" href="Relation.Binary.Bundles.html#4684" class="Function">decSetoid</a> <a id="4694" class="Symbol">:</a> <a id="4696" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a> <a id="4706" href="Relation.Binary.Bundles.html#4149" class="Bound">c</a> <a id="4708" href="Relation.Binary.Bundles.html#4151" class="Bound">ℓ₁</a>
<a id="4715" href="Relation.Binary.Bundles.html#4684" class="Function">decSetoid</a> <a id="4725" class="Symbol">=</a> <a id="4727" class="Keyword">record</a>
<a id="4740" class="Symbol">{</a> <a id="4742" href="Relation.Binary.Bundles.html#1680" class="Field">isDecEquivalence</a> <a id="4759" class="Symbol">=</a> <a id="4761" href="Relation.Binary.Structures.html#4098" class="Function">DPO.Eq.isDecEquivalence</a>
<a id="4791" class="Symbol">}</a>
<a id="4798" class="Keyword">open</a> <a id="4803" href="Relation.Binary.Bundles.html#1548" class="Module">DecSetoid</a> <a id="4813" href="Relation.Binary.Bundles.html#4684" class="Function">decSetoid</a> <a id="4823" class="Keyword">public</a>
<a id="4832" class="Keyword">record</a> <a id="StrictPartialOrder"></a><a id="4839" href="Relation.Binary.Bundles.html#4839" class="Record">StrictPartialOrder</a> <a id="4858" href="Relation.Binary.Bundles.html#4858" class="Bound">c</a> <a id="4860" href="Relation.Binary.Bundles.html#4860" class="Bound">ℓ₁</a> <a id="4863" href="Relation.Binary.Bundles.html#4863" class="Bound">ℓ₂</a> <a id="4866" class="Symbol">:</a> <a id="4868" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4872" class="Symbol">(</a><a id="4873" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="4877" class="Symbol">(</a><a id="4878" href="Relation.Binary.Bundles.html#4858" class="Bound">c</a> <a id="4880" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4882" href="Relation.Binary.Bundles.html#4860" class="Bound">ℓ₁</a> <a id="4885" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4887" href="Relation.Binary.Bundles.html#4863" class="Bound">ℓ₂</a><a id="4889" class="Symbol">))</a> <a id="4892" class="Keyword">where</a>
<a id="4900" class="Keyword">infix</a> <a id="4906" class="Number">4</a> <a id="4908" href="Relation.Binary.Bundles.html#4961" class="Field Operator">_≈_</a> <a id="4912" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a>
<a id="4918" class="Keyword">field</a>
<a id="StrictPartialOrder.Carrier"></a><a id="4928" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a> <a id="4949" class="Symbol">:</a> <a id="4951" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="4955" href="Relation.Binary.Bundles.html#4858" class="Bound">c</a>
<a id="StrictPartialOrder._≈_"></a><a id="4961" href="Relation.Binary.Bundles.html#4961" class="Field Operator">_≈_</a> <a id="4982" class="Symbol">:</a> <a id="4984" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="4988" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a> <a id="4996" href="Relation.Binary.Bundles.html#4860" class="Bound">ℓ₁</a>
<a id="StrictPartialOrder._&lt;_"></a><a id="5003" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a> <a id="5024" class="Symbol">:</a> <a id="5026" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5030" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a> <a id="5038" href="Relation.Binary.Bundles.html#4863" class="Bound">ℓ₂</a>
<a id="StrictPartialOrder.isStrictPartialOrder"></a><a id="5045" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a> <a id="5066" class="Symbol">:</a> <a id="5068" href="Relation.Binary.Structures.html#4298" class="Record">IsStrictPartialOrder</a> <a id="5089" href="Relation.Binary.Bundles.html#4961" class="Field Operator">_≈_</a> <a id="5093" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a>
<a id="5100" class="Keyword">open</a> <a id="5105" href="Relation.Binary.Structures.html#4298" class="Module">IsStrictPartialOrder</a> <a id="5126" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a> <a id="5147" class="Keyword">public</a>
<a id="5158" class="Keyword">hiding</a> <a id="5165" class="Symbol">(</a><a id="5166" class="Keyword">module</a> <a id="5173" href="Relation.Binary.Structures.html#4526" class="Module">Eq</a><a id="5175" class="Symbol">)</a>
<a id="5180" class="Keyword">module</a> <a id="StrictPartialOrder.Eq"></a><a id="5187" href="Relation.Binary.Bundles.html#5187" class="Module">Eq</a> <a id="5190" class="Keyword">where</a>
<a id="StrictPartialOrder.Eq.setoid"></a><a id="5200" href="Relation.Binary.Bundles.html#5200" class="Function">setoid</a> <a id="5207" class="Symbol">:</a> <a id="5209" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="5216" href="Relation.Binary.Bundles.html#4858" class="Bound">c</a> <a id="5218" href="Relation.Binary.Bundles.html#4860" class="Bound">ℓ₁</a>
<a id="5225" href="Relation.Binary.Bundles.html#5200" class="Function">setoid</a> <a id="5232" class="Symbol">=</a> <a id="5234" class="Keyword">record</a>
<a id="5247" class="Symbol">{</a> <a id="5249" href="Relation.Binary.Bundles.html#1203" class="Field">isEquivalence</a> <a id="5263" class="Symbol">=</a> <a id="5265" href="Relation.Binary.Structures.html#4373" class="Function">isEquivalence</a>
<a id="5285" class="Symbol">}</a>
<a id="5292" class="Keyword">open</a> <a id="5297" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="5304" href="Relation.Binary.Bundles.html#5200" class="Function">setoid</a> <a id="5311" class="Keyword">public</a>
<a id="5321" class="Keyword">infix</a> <a id="5327" class="Number">4</a> <a id="5329" href="Relation.Binary.Bundles.html#5335" class="Function Operator">_≮_</a>
<a id="StrictPartialOrder._≮_"></a><a id="5335" href="Relation.Binary.Bundles.html#5335" class="Function Operator">_≮_</a> <a id="5339" class="Symbol">:</a> <a id="5341" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5345" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a> <a id="5353" class="Symbol">_</a>
<a id="5357" href="Relation.Binary.Bundles.html#5357" class="Bound">x</a> <a id="5359" href="Relation.Binary.Bundles.html#5335" class="Function Operator">≮</a> <a id="5361" href="Relation.Binary.Bundles.html#5361" class="Bound">y</a> <a id="5363" class="Symbol">=</a> <a id="5365" href="Relation.Nullary.Negation.Core.html#698" class="Function Operator">¬</a> <a id="5367" class="Symbol">(</a><a id="5368" href="Relation.Binary.Bundles.html#5357" class="Bound">x</a> <a id="5370" href="Relation.Binary.Bundles.html#5003" class="Field Operator">&lt;</a> <a id="5372" href="Relation.Binary.Bundles.html#5361" class="Bound">y</a><a id="5373" class="Symbol">)</a>
<a id="5378" class="Keyword">infix</a> <a id="5384" class="Number">4</a> <a id="5386" href="Relation.Binary.Bundles.html#5392" class="Function Operator">_&gt;_</a>
<a id="StrictPartialOrder._&gt;_"></a><a id="5392" href="Relation.Binary.Bundles.html#5392" class="Function Operator">_&gt;_</a> <a id="5396" class="Symbol">=</a> <a id="5398" href="Function.Base.html#1638" class="Function">flip</a> <a id="5403" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a>
<a id="5410" class="Keyword">infix</a> <a id="5416" class="Number">4</a> <a id="5418" href="Relation.Binary.Bundles.html#5424" class="Function Operator">_≯_</a>
<a id="StrictPartialOrder._≯_"></a><a id="5424" href="Relation.Binary.Bundles.html#5424" class="Function Operator">_≯_</a> <a id="5428" class="Symbol">=</a> <a id="5430" href="Function.Base.html#1638" class="Function">flip</a> <a id="5435" href="Relation.Binary.Bundles.html#5335" class="Function Operator">_≮_</a>
<a id="5441" class="Keyword">record</a> <a id="DecStrictPartialOrder"></a><a id="5448" href="Relation.Binary.Bundles.html#5448" class="Record">DecStrictPartialOrder</a> <a id="5470" href="Relation.Binary.Bundles.html#5470" class="Bound">c</a> <a id="5472" href="Relation.Binary.Bundles.html#5472" class="Bound">ℓ₁</a> <a id="5475" href="Relation.Binary.Bundles.html#5475" class="Bound">ℓ₂</a> <a id="5478" class="Symbol">:</a> <a id="5480" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="5484" class="Symbol">(</a><a id="5485" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="5489" class="Symbol">(</a><a id="5490" href="Relation.Binary.Bundles.html#5470" class="Bound">c</a> <a id="5492" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="5494" href="Relation.Binary.Bundles.html#5472" class="Bound">ℓ₁</a> <a id="5497" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="5499" href="Relation.Binary.Bundles.html#5475" class="Bound">ℓ₂</a><a id="5501" class="Symbol">))</a> <a id="5504" class="Keyword">where</a>
<a id="5512" class="Keyword">infix</a> <a id="5518" class="Number">4</a> <a id="5520" href="Relation.Binary.Bundles.html#5576" class="Field Operator">_≈_</a> <a id="5524" href="Relation.Binary.Bundles.html#5621" class="Field Operator">_&lt;_</a>
<a id="5530" class="Keyword">field</a>
<a id="DecStrictPartialOrder.Carrier"></a><a id="5540" href="Relation.Binary.Bundles.html#5540" class="Field">Carrier</a> <a id="5564" class="Symbol">:</a> <a id="5566" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="5570" href="Relation.Binary.Bundles.html#5470" class="Bound">c</a>
<a id="DecStrictPartialOrder._≈_"></a><a id="5576" href="Relation.Binary.Bundles.html#5576" class="Field Operator">_≈_</a> <a id="5600" class="Symbol">:</a> <a id="5602" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5606" href="Relation.Binary.Bundles.html#5540" class="Field">Carrier</a> <a id="5614" href="Relation.Binary.Bundles.html#5472" class="Bound">ℓ₁</a>
<a id="DecStrictPartialOrder._&lt;_"></a><a id="5621" href="Relation.Binary.Bundles.html#5621" class="Field Operator">_&lt;_</a> <a id="5645" class="Symbol">:</a> <a id="5647" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="5651" href="Relation.Binary.Bundles.html#5540" class="Field">Carrier</a> <a id="5659" href="Relation.Binary.Bundles.html#5475" class="Bound">ℓ₂</a>
<a id="DecStrictPartialOrder.isDecStrictPartialOrder"></a><a id="5666" href="Relation.Binary.Bundles.html#5666" class="Field">isDecStrictPartialOrder</a> <a id="5690" class="Symbol">:</a> <a id="5692" href="Relation.Binary.Structures.html#4782" class="Record">IsDecStrictPartialOrder</a> <a id="5716" href="Relation.Binary.Bundles.html#5576" class="Field Operator">_≈_</a> <a id="5720" href="Relation.Binary.Bundles.html#5621" class="Field Operator">_&lt;_</a>
<a id="5727" class="Keyword">private</a> <a id="5735" class="Keyword">module</a> <a id="DecStrictPartialOrder.DSPO"></a><a id="5742" href="Relation.Binary.Bundles.html#5742" class="Module">DSPO</a> <a id="5747" class="Symbol">=</a> <a id="5749" href="Relation.Binary.Structures.html#4782" class="Module">IsDecStrictPartialOrder</a> <a id="5773" href="Relation.Binary.Bundles.html#5666" class="Field">isDecStrictPartialOrder</a>
<a id="5800" class="Keyword">open</a> <a id="5805" href="Relation.Binary.Bundles.html#5742" class="Module">DSPO</a> <a id="5810" class="Keyword">public</a>
<a id="5821" class="Keyword">using</a> <a id="5827" class="Symbol">(</a><a id="5828" href="Relation.Binary.Structures.html#4972" class="Function Operator">_&lt;?_</a><a id="5832" class="Symbol">;</a> <a id="5834" href="Relation.Binary.Structures.html#4931" class="Function Operator">_≟_</a><a id="5837" class="Symbol">;</a> <a id="5839" href="Relation.Binary.Structures.html#4879" class="Function">isStrictPartialOrder</a><a id="5859" class="Symbol">)</a>
<a id="DecStrictPartialOrder.strictPartialOrder"></a><a id="5864" href="Relation.Binary.Bundles.html#5864" class="Function">strictPartialOrder</a> <a id="5883" class="Symbol">:</a> <a id="5885" href="Relation.Binary.Bundles.html#4839" class="Record">StrictPartialOrder</a> <a id="5904" href="Relation.Binary.Bundles.html#5470" class="Bound">c</a> <a id="5906" href="Relation.Binary.Bundles.html#5472" class="Bound">ℓ₁</a> <a id="5909" href="Relation.Binary.Bundles.html#5475" class="Bound">ℓ₂</a>
<a id="5914" href="Relation.Binary.Bundles.html#5864" class="Function">strictPartialOrder</a> <a id="5933" class="Symbol">=</a> <a id="5935" class="Keyword">record</a>
<a id="5946" class="Symbol">{</a> <a id="5948" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a> <a id="5969" class="Symbol">=</a> <a id="5971" href="Relation.Binary.Structures.html#4879" class="Function">isStrictPartialOrder</a>
<a id="5996" class="Symbol">}</a>
<a id="6001" class="Keyword">open</a> <a id="6006" href="Relation.Binary.Bundles.html#4839" class="Module">StrictPartialOrder</a> <a id="6025" href="Relation.Binary.Bundles.html#5864" class="Function">strictPartialOrder</a> <a id="6044" class="Keyword">public</a>
<a id="6055" class="Keyword">hiding</a> <a id="6062" class="Symbol">(</a><a id="6063" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a><a id="6070" class="Symbol">;</a> <a id="6072" href="Relation.Binary.Bundles.html#4961" class="Field Operator">_≈_</a><a id="6075" class="Symbol">;</a> <a id="6077" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a><a id="6080" class="Symbol">;</a> <a id="6082" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a><a id="6102" class="Symbol">;</a> <a id="6104" class="Keyword">module</a> <a id="6111" href="Relation.Binary.Bundles.html#5187" class="Module">Eq</a><a id="6113" class="Symbol">)</a>
<a id="6118" class="Keyword">module</a> <a id="DecStrictPartialOrder.Eq"></a><a id="6125" href="Relation.Binary.Bundles.html#6125" class="Module">Eq</a> <a id="6128" class="Keyword">where</a>
<a id="DecStrictPartialOrder.Eq.decSetoid"></a><a id="6139" href="Relation.Binary.Bundles.html#6139" class="Function">decSetoid</a> <a id="6149" class="Symbol">:</a> <a id="6151" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a> <a id="6161" href="Relation.Binary.Bundles.html#5470" class="Bound">c</a> <a id="6163" href="Relation.Binary.Bundles.html#5472" class="Bound">ℓ₁</a>
<a id="6170" href="Relation.Binary.Bundles.html#6139" class="Function">decSetoid</a> <a id="6180" class="Symbol">=</a> <a id="6182" class="Keyword">record</a>
<a id="6195" class="Symbol">{</a> <a id="6197" href="Relation.Binary.Bundles.html#1680" class="Field">isDecEquivalence</a> <a id="6214" class="Symbol">=</a> <a id="6216" href="Relation.Binary.Structures.html#5141" class="Function">DSPO.Eq.isDecEquivalence</a>
<a id="6247" class="Symbol">}</a>
<a id="6254" class="Keyword">open</a> <a id="6259" href="Relation.Binary.Bundles.html#1548" class="Module">DecSetoid</a> <a id="6269" href="Relation.Binary.Bundles.html#6139" class="Function">decSetoid</a> <a id="6279" class="Keyword">public</a>
<a id="6288" class="Comment">------------------------------------------------------------------------</a>
<a id="6361" class="Comment">-- Total orders</a>
<a id="6377" class="Comment">------------------------------------------------------------------------</a>
<a id="6451" class="Keyword">record</a> <a id="TotalOrder"></a><a id="6458" href="Relation.Binary.Bundles.html#6458" class="Record">TotalOrder</a> <a id="6469" href="Relation.Binary.Bundles.html#6469" class="Bound">c</a> <a id="6471" href="Relation.Binary.Bundles.html#6471" class="Bound">ℓ₁</a> <a id="6474" href="Relation.Binary.Bundles.html#6474" class="Bound">ℓ₂</a> <a id="6477" class="Symbol">:</a> <a id="6479" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6483" class="Symbol">(</a><a id="6484" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="6488" class="Symbol">(</a><a id="6489" href="Relation.Binary.Bundles.html#6469" class="Bound">c</a> <a id="6491" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="6493" href="Relation.Binary.Bundles.html#6471" class="Bound">ℓ₁</a> <a id="6496" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="6498" href="Relation.Binary.Bundles.html#6474" class="Bound">ℓ₂</a><a id="6500" class="Symbol">))</a> <a id="6503" class="Keyword">where</a>
<a id="6511" class="Keyword">infix</a> <a id="6517" class="Number">4</a> <a id="6519" href="Relation.Binary.Bundles.html#6564" class="Field Operator">_≈_</a> <a id="6523" href="Relation.Binary.Bundles.html#6598" class="Field Operator">_≤_</a>
<a id="6529" class="Keyword">field</a>
<a id="TotalOrder.Carrier"></a><a id="6539" href="Relation.Binary.Bundles.html#6539" class="Field">Carrier</a> <a id="6552" class="Symbol">:</a> <a id="6554" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="6558" href="Relation.Binary.Bundles.html#6469" class="Bound">c</a>
<a id="TotalOrder._≈_"></a><a id="6564" href="Relation.Binary.Bundles.html#6564" class="Field Operator">_≈_</a> <a id="6577" class="Symbol">:</a> <a id="6579" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="6583" href="Relation.Binary.Bundles.html#6539" class="Field">Carrier</a> <a id="6591" href="Relation.Binary.Bundles.html#6471" class="Bound">ℓ₁</a>
<a id="TotalOrder._≤_"></a><a id="6598" href="Relation.Binary.Bundles.html#6598" class="Field Operator">_≤_</a> <a id="6611" class="Symbol">:</a> <a id="6613" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="6617" href="Relation.Binary.Bundles.html#6539" class="Field">Carrier</a> <a id="6625" href="Relation.Binary.Bundles.html#6474" class="Bound">ℓ₂</a>
<a id="TotalOrder.isTotalOrder"></a><a id="6632" href="Relation.Binary.Bundles.html#6632" class="Field">isTotalOrder</a> <a id="6645" class="Symbol">:</a> <a id="6647" href="Relation.Binary.Structures.html#5508" class="Record">IsTotalOrder</a> <a id="6660" href="Relation.Binary.Bundles.html#6564" class="Field Operator">_≈_</a> <a id="6664" href="Relation.Binary.Bundles.html#6598" class="Field Operator">_≤_</a>
<a id="6671" class="Keyword">open</a> <a id="6676" href="Relation.Binary.Structures.html#5508" class="Module">IsTotalOrder</a> <a id="6689" href="Relation.Binary.Bundles.html#6632" class="Field">isTotalOrder</a> <a id="6702" class="Keyword">public</a>
<a id="6713" class="Keyword">using</a> <a id="6719" class="Symbol">(</a><a id="6720" href="Relation.Binary.Structures.html#5615" class="Field">total</a><a id="6725" class="Symbol">;</a> <a id="6727" href="Relation.Binary.Structures.html#5575" class="Field">isPartialOrder</a><a id="6741" class="Symbol">;</a> <a id="6743" href="Relation.Binary.Structures.html#5690" class="Function">isTotalPreorder</a><a id="6758" class="Symbol">)</a>
<a id="TotalOrder.poset"></a><a id="6763" href="Relation.Binary.Bundles.html#6763" class="Function">poset</a> <a id="6769" class="Symbol">:</a> <a id="6771" href="Relation.Binary.Bundles.html#3530" class="Record">Poset</a> <a id="6777" href="Relation.Binary.Bundles.html#6469" class="Bound">c</a> <a id="6779" href="Relation.Binary.Bundles.html#6471" class="Bound">ℓ₁</a> <a id="6782" href="Relation.Binary.Bundles.html#6474" class="Bound">ℓ₂</a>
<a id="6787" href="Relation.Binary.Bundles.html#6763" class="Function">poset</a> <a id="6793" class="Symbol">=</a> <a id="6795" class="Keyword">record</a>
<a id="6806" class="Symbol">{</a> <a id="6808" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a> <a id="6823" class="Symbol">=</a> <a id="6825" href="Relation.Binary.Structures.html#5575" class="Function">isPartialOrder</a>
<a id="6844" class="Symbol">}</a>
<a id="6849" class="Keyword">open</a> <a id="6854" href="Relation.Binary.Bundles.html#3530" class="Module">Poset</a> <a id="6860" href="Relation.Binary.Bundles.html#6763" class="Function">poset</a> <a id="6866" class="Keyword">public</a>
<a id="6877" class="Keyword">hiding</a> <a id="6884" class="Symbol">(</a><a id="6885" href="Relation.Binary.Bundles.html#3606" class="Field">Carrier</a><a id="6892" class="Symbol">;</a> <a id="6894" href="Relation.Binary.Bundles.html#3633" class="Field Operator">_≈_</a><a id="6897" class="Symbol">;</a> <a id="6899" href="Relation.Binary.Bundles.html#3669" class="Field Operator">_≤_</a><a id="6902" class="Symbol">;</a> <a id="6904" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a><a id="6918" class="Symbol">)</a>
<a id="TotalOrder.totalPreorder"></a><a id="6923" href="Relation.Binary.Bundles.html#6923" class="Function">totalPreorder</a> <a id="6937" class="Symbol">:</a> <a id="6939" href="Relation.Binary.Bundles.html#2842" class="Record">TotalPreorder</a> <a id="6953" href="Relation.Binary.Bundles.html#6469" class="Bound">c</a> <a id="6955" href="Relation.Binary.Bundles.html#6471" class="Bound">ℓ₁</a> <a id="6958" href="Relation.Binary.Bundles.html#6474" class="Bound">ℓ₂</a>
<a id="6963" href="Relation.Binary.Bundles.html#6923" class="Function">totalPreorder</a> <a id="6977" class="Symbol">=</a> <a id="6979" class="Keyword">record</a>
<a id="6990" class="Symbol">{</a> <a id="6992" href="Relation.Binary.Bundles.html#3075" class="Field">isTotalPreorder</a> <a id="7008" class="Symbol">=</a> <a id="7010" href="Relation.Binary.Structures.html#5690" class="Function">isTotalPreorder</a>
<a id="7030" class="Symbol">}</a>
<a id="7034" class="Keyword">record</a> <a id="DecTotalOrder"></a><a id="7041" href="Relation.Binary.Bundles.html#7041" class="Record">DecTotalOrder</a> <a id="7055" href="Relation.Binary.Bundles.html#7055" class="Bound">c</a> <a id="7057" href="Relation.Binary.Bundles.html#7057" class="Bound">ℓ₁</a> <a id="7060" href="Relation.Binary.Bundles.html#7060" class="Bound">ℓ₂</a> <a id="7063" class="Symbol">:</a> <a id="7065" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="7069" class="Symbol">(</a><a id="7070" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="7074" class="Symbol">(</a><a id="7075" href="Relation.Binary.Bundles.html#7055" class="Bound">c</a> <a id="7077" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="7079" href="Relation.Binary.Bundles.html#7057" class="Bound">ℓ₁</a> <a id="7082" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="7084" href="Relation.Binary.Bundles.html#7060" class="Bound">ℓ₂</a><a id="7086" class="Symbol">))</a> <a id="7089" class="Keyword">where</a>
<a id="7097" class="Keyword">infix</a> <a id="7103" class="Number">4</a> <a id="7105" href="Relation.Binary.Bundles.html#7153" class="Field Operator">_≈_</a> <a id="7109" href="Relation.Binary.Bundles.html#7190" class="Field Operator">_≤_</a>
<a id="7115" class="Keyword">field</a>
<a id="DecTotalOrder.Carrier"></a><a id="7125" href="Relation.Binary.Bundles.html#7125" class="Field">Carrier</a> <a id="7141" class="Symbol">:</a> <a id="7143" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="7147" href="Relation.Binary.Bundles.html#7055" class="Bound">c</a>
<a id="DecTotalOrder._≈_"></a><a id="7153" href="Relation.Binary.Bundles.html#7153" class="Field Operator">_≈_</a> <a id="7169" class="Symbol">:</a> <a id="7171" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="7175" href="Relation.Binary.Bundles.html#7125" class="Field">Carrier</a> <a id="7183" href="Relation.Binary.Bundles.html#7057" class="Bound">ℓ₁</a>
<a id="DecTotalOrder._≤_"></a><a id="7190" href="Relation.Binary.Bundles.html#7190" class="Field Operator">_≤_</a> <a id="7206" class="Symbol">:</a> <a id="7208" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="7212" href="Relation.Binary.Bundles.html#7125" class="Field">Carrier</a> <a id="7220" href="Relation.Binary.Bundles.html#7060" class="Bound">ℓ₂</a>
<a id="DecTotalOrder.isDecTotalOrder"></a><a id="7227" href="Relation.Binary.Bundles.html#7227" class="Field">isDecTotalOrder</a> <a id="7243" class="Symbol">:</a> <a id="7245" href="Relation.Binary.Structures.html#5825" class="Record">IsDecTotalOrder</a> <a id="7261" href="Relation.Binary.Bundles.html#7153" class="Field Operator">_≈_</a> <a id="7265" href="Relation.Binary.Bundles.html#7190" class="Field Operator">_≤_</a>
<a id="7272" class="Keyword">private</a> <a id="7280" class="Keyword">module</a> <a id="DecTotalOrder.DTO"></a><a id="7287" href="Relation.Binary.Bundles.html#7287" class="Module">DTO</a> <a id="7291" class="Symbol">=</a> <a id="7293" href="Relation.Binary.Structures.html#5825" class="Module">IsDecTotalOrder</a> <a id="7309" href="Relation.Binary.Bundles.html#7227" class="Field">isDecTotalOrder</a>
<a id="7328" class="Keyword">open</a> <a id="7333" href="Relation.Binary.Bundles.html#7287" class="Module">DTO</a> <a id="7337" class="Keyword">public</a>
<a id="7348" class="Keyword">using</a> <a id="7354" class="Symbol">(</a><a id="7355" href="Relation.Binary.Structures.html#5950" class="Function Operator">_≟_</a><a id="7358" class="Symbol">;</a> <a id="7360" href="Relation.Binary.Structures.html#5983" class="Function Operator">_≤?_</a><a id="7364" class="Symbol">;</a> <a id="7366" href="Relation.Binary.Structures.html#5914" class="Function">isTotalOrder</a><a id="7378" class="Symbol">;</a> <a id="7380" href="Relation.Binary.Structures.html#6079" class="Function">isDecPartialOrder</a><a id="7397" class="Symbol">)</a>
<a id="DecTotalOrder.totalOrder"></a><a id="7402" href="Relation.Binary.Bundles.html#7402" class="Function">totalOrder</a> <a id="7413" class="Symbol">:</a> <a id="7415" href="Relation.Binary.Bundles.html#6458" class="Record">TotalOrder</a> <a id="7426" href="Relation.Binary.Bundles.html#7055" class="Bound">c</a> <a id="7428" href="Relation.Binary.Bundles.html#7057" class="Bound">ℓ₁</a> <a id="7431" href="Relation.Binary.Bundles.html#7060" class="Bound">ℓ₂</a>
<a id="7436" href="Relation.Binary.Bundles.html#7402" class="Function">totalOrder</a> <a id="7447" class="Symbol">=</a> <a id="7449" class="Keyword">record</a>
<a id="7460" class="Symbol">{</a> <a id="7462" href="Relation.Binary.Bundles.html#6632" class="Field">isTotalOrder</a> <a id="7475" class="Symbol">=</a> <a id="7477" href="Relation.Binary.Structures.html#5914" class="Function">isTotalOrder</a>
<a id="7494" class="Symbol">}</a>
<a id="7499" class="Keyword">open</a> <a id="7504" href="Relation.Binary.Bundles.html#6458" class="Module">TotalOrder</a> <a id="7515" href="Relation.Binary.Bundles.html#7402" class="Function">totalOrder</a> <a id="7526" class="Keyword">public</a>
<a id="7537" class="Keyword">hiding</a> <a id="7544" class="Symbol">(</a><a id="7545" href="Relation.Binary.Bundles.html#6539" class="Field">Carrier</a><a id="7552" class="Symbol">;</a> <a id="7554" href="Relation.Binary.Bundles.html#6564" class="Field Operator">_≈_</a><a id="7557" class="Symbol">;</a> <a id="7559" href="Relation.Binary.Bundles.html#6598" class="Field Operator">_≤_</a><a id="7562" class="Symbol">;</a> <a id="7564" href="Relation.Binary.Bundles.html#6632" class="Field">isTotalOrder</a><a id="7576" class="Symbol">;</a> <a id="7578" class="Keyword">module</a> <a id="7585" href="Relation.Binary.Bundles.html#2436" class="Module">Eq</a><a id="7587" class="Symbol">)</a>
<a id="DecTotalOrder.decPoset"></a><a id="7592" href="Relation.Binary.Bundles.html#7592" class="Function">decPoset</a> <a id="7601" class="Symbol">:</a> <a id="7603" href="Relation.Binary.Bundles.html#4140" class="Record">DecPoset</a> <a id="7612" href="Relation.Binary.Bundles.html#7055" class="Bound">c</a> <a id="7614" href="Relation.Binary.Bundles.html#7057" class="Bound">ℓ₁</a> <a id="7617" href="Relation.Binary.Bundles.html#7060" class="Bound">ℓ₂</a>
<a id="7622" href="Relation.Binary.Bundles.html#7592" class="Function">decPoset</a> <a id="7631" class="Symbol">=</a> <a id="7633" class="Keyword">record</a>
<a id="7644" class="Symbol">{</a> <a id="7646" href="Relation.Binary.Bundles.html#4327" class="Field">isDecPartialOrder</a> <a id="7664" class="Symbol">=</a> <a id="7666" href="Relation.Binary.Structures.html#6079" class="Function">isDecPartialOrder</a>
<a id="7688" class="Symbol">}</a>
<a id="7693" class="Keyword">open</a> <a id="7698" href="Relation.Binary.Bundles.html#4140" class="Module">DecPoset</a> <a id="7707" href="Relation.Binary.Bundles.html#7592" class="Function">decPoset</a> <a id="7716" class="Keyword">public</a>
<a id="7727" class="Keyword">using</a> <a id="7733" class="Symbol">(</a><a id="7734" class="Keyword">module</a> <a id="7741" href="Relation.Binary.Bundles.html#4671" class="Module">Eq</a><a id="7743" class="Symbol">)</a>
<a id="7747" class="Comment">-- Note that these orders are decidable. The current implementation</a>
<a id="7815" class="Comment">-- of `Trichotomous` subsumes irreflexivity and asymmetry. Any reasonable</a>
<a id="7889" class="Comment">-- definition capturing these three properties implies decidability</a>
<a id="7957" class="Comment">-- as `Trichotomous` necessarily separates out the equality case.</a>
<a id="8024" class="Keyword">record</a> <a id="StrictTotalOrder"></a><a id="8031" href="Relation.Binary.Bundles.html#8031" class="Record">StrictTotalOrder</a> <a id="8048" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a> <a id="8050" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a> <a id="8053" href="Relation.Binary.Bundles.html#8053" class="Bound">ℓ₂</a> <a id="8056" class="Symbol">:</a> <a id="8058" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="8062" class="Symbol">(</a><a id="8063" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="8067" class="Symbol">(</a><a id="8068" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a> <a id="8070" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="8072" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a> <a id="8075" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="8077" href="Relation.Binary.Bundles.html#8053" class="Bound">ℓ₂</a><a id="8079" class="Symbol">))</a> <a id="8082" class="Keyword">where</a>
<a id="8090" class="Keyword">infix</a> <a id="8096" class="Number">4</a> <a id="8098" href="Relation.Binary.Bundles.html#8149" class="Field Operator">_≈_</a> <a id="8102" href="Relation.Binary.Bundles.html#8189" class="Field Operator">_&lt;_</a>
<a id="8108" class="Keyword">field</a>
<a id="StrictTotalOrder.Carrier"></a><a id="8118" href="Relation.Binary.Bundles.html#8118" class="Field">Carrier</a> <a id="8137" class="Symbol">:</a> <a id="8139" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="8143" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a>
<a id="StrictTotalOrder._≈_"></a><a id="8149" href="Relation.Binary.Bundles.html#8149" class="Field Operator">_≈_</a> <a id="8168" class="Symbol">:</a> <a id="8170" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="8174" href="Relation.Binary.Bundles.html#8118" class="Field">Carrier</a> <a id="8182" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a>
<a id="StrictTotalOrder._&lt;_"></a><a id="8189" href="Relation.Binary.Bundles.html#8189" class="Field Operator">_&lt;_</a> <a id="8208" class="Symbol">:</a> <a id="8210" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="8214" href="Relation.Binary.Bundles.html#8118" class="Field">Carrier</a> <a id="8222" href="Relation.Binary.Bundles.html#8053" class="Bound">ℓ₂</a>
<a id="StrictTotalOrder.isStrictTotalOrder"></a><a id="8229" href="Relation.Binary.Bundles.html#8229" class="Field">isStrictTotalOrder</a> <a id="8248" class="Symbol">:</a> <a id="8250" href="Relation.Binary.Structures.html#6732" class="Record">IsStrictTotalOrder</a> <a id="8269" href="Relation.Binary.Bundles.html#8149" class="Field Operator">_≈_</a> <a id="8273" href="Relation.Binary.Bundles.html#8189" class="Field Operator">_&lt;_</a>
<a id="8280" class="Keyword">open</a> <a id="8285" href="Relation.Binary.Structures.html#6732" class="Module">IsStrictTotalOrder</a> <a id="8304" href="Relation.Binary.Bundles.html#8229" class="Field">isStrictTotalOrder</a> <a id="8323" class="Keyword">public</a>
<a id="8334" class="Keyword">using</a>
<a id="8344" class="Symbol">(</a> <a id="8346" href="Relation.Binary.Structures.html#7102" class="Function Operator">_≟_</a><a id="8349" class="Symbol">;</a> <a id="8351" href="Relation.Binary.Structures.html#7150" class="Function Operator">_&lt;?_</a><a id="8355" class="Symbol">;</a> <a id="8357" href="Relation.Binary.Structures.html#6857" class="Field">compare</a><a id="8364" class="Symbol">;</a> <a id="8366" href="Relation.Binary.Structures.html#6805" class="Field">isStrictPartialOrder</a>
<a id="8391" class="Symbol">;</a> <a id="8393" href="Relation.Binary.Structures.html#7200" class="Function">isDecStrictPartialOrder</a><a id="8416" class="Symbol">;</a> <a id="8418" href="Relation.Binary.Structures.html#7691" class="Function">isDecEquivalence</a>
<a id="8439" class="Symbol">)</a>
<a id="StrictTotalOrder.strictPartialOrder"></a><a id="8444" href="Relation.Binary.Bundles.html#8444" class="Function">strictPartialOrder</a> <a id="8463" class="Symbol">:</a> <a id="8465" href="Relation.Binary.Bundles.html#4839" class="Record">StrictPartialOrder</a> <a id="8484" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a> <a id="8486" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a> <a id="8489" href="Relation.Binary.Bundles.html#8053" class="Bound">ℓ₂</a>
<a id="8494" href="Relation.Binary.Bundles.html#8444" class="Function">strictPartialOrder</a> <a id="8513" class="Symbol">=</a> <a id="8515" class="Keyword">record</a>
<a id="8526" class="Symbol">{</a> <a id="8528" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a> <a id="8549" class="Symbol">=</a> <a id="8551" href="Relation.Binary.Structures.html#6805" class="Function">isStrictPartialOrder</a>
<a id="8576" class="Symbol">}</a>
<a id="8581" class="Keyword">open</a> <a id="8586" href="Relation.Binary.Bundles.html#4839" class="Module">StrictPartialOrder</a> <a id="8605" href="Relation.Binary.Bundles.html#8444" class="Function">strictPartialOrder</a> <a id="8624" class="Keyword">public</a>
<a id="8635" class="Keyword">hiding</a> <a id="8642" class="Symbol">(</a><a id="8643" href="Relation.Binary.Bundles.html#4928" class="Field">Carrier</a><a id="8650" class="Symbol">;</a> <a id="8652" href="Relation.Binary.Bundles.html#4961" class="Field Operator">_≈_</a><a id="8655" class="Symbol">;</a> <a id="8657" href="Relation.Binary.Bundles.html#5003" class="Field Operator">_&lt;_</a><a id="8660" class="Symbol">;</a> <a id="8662" href="Relation.Binary.Bundles.html#5045" class="Field">isStrictPartialOrder</a><a id="8682" class="Symbol">;</a> <a id="8684" class="Keyword">module</a> <a id="8691" href="Relation.Binary.Bundles.html#5187" class="Module">Eq</a><a id="8693" class="Symbol">)</a>
<a id="StrictTotalOrder.decStrictPartialOrder"></a><a id="8698" href="Relation.Binary.Bundles.html#8698" class="Function">decStrictPartialOrder</a> <a id="8720" class="Symbol">:</a> <a id="8722" href="Relation.Binary.Bundles.html#5448" class="Record">DecStrictPartialOrder</a> <a id="8744" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a> <a id="8746" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a> <a id="8749" href="Relation.Binary.Bundles.html#8053" class="Bound">ℓ₂</a>
<a id="8754" href="Relation.Binary.Bundles.html#8698" class="Function">decStrictPartialOrder</a> <a id="8776" class="Symbol">=</a> <a id="8778" class="Keyword">record</a>
<a id="8789" class="Symbol">{</a> <a id="8791" href="Relation.Binary.Bundles.html#5666" class="Field">isDecStrictPartialOrder</a> <a id="8815" class="Symbol">=</a> <a id="8817" href="Relation.Binary.Structures.html#7200" class="Function">isDecStrictPartialOrder</a>
<a id="8845" class="Symbol">}</a>
<a id="8850" class="Keyword">open</a> <a id="8855" href="Relation.Binary.Bundles.html#5448" class="Module">DecStrictPartialOrder</a> <a id="8877" href="Relation.Binary.Bundles.html#8698" class="Function">decStrictPartialOrder</a> <a id="8899" class="Keyword">public</a>
<a id="8910" class="Keyword">using</a> <a id="8916" class="Symbol">(</a><a id="8917" class="Keyword">module</a> <a id="8924" href="Relation.Binary.Bundles.html#6125" class="Module">Eq</a><a id="8926" class="Symbol">)</a>
<a id="StrictTotalOrder.decSetoid"></a><a id="8931" href="Relation.Binary.Bundles.html#8931" class="Function">decSetoid</a> <a id="8941" class="Symbol">:</a> <a id="8943" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a> <a id="8953" href="Relation.Binary.Bundles.html#8048" class="Bound">c</a> <a id="8955" href="Relation.Binary.Bundles.html#8050" class="Bound">ℓ₁</a>
<a id="8960" href="Relation.Binary.Bundles.html#8931" class="Function">decSetoid</a> <a id="8970" class="Symbol">=</a> <a id="8972" class="Keyword">record</a>
<a id="8983" class="Symbol">{</a> <a id="8985" href="Relation.Binary.Bundles.html#1680" class="Field">isDecEquivalence</a> <a id="9002" class="Symbol">=</a> <a id="9004" href="Relation.Binary.Bundles.html#1680" class="Function">Eq.isDecEquivalence</a>
<a id="9028" class="Symbol">}</a>
<a id="9032" class="Symbol">{-#</a> <a id="9036" class="Keyword">WARNING_ON_USAGE</a> <a id="9053" class="Pragma">decSetoid</a>
<a id="9065" class="String">&quot;Warning: decSetoid was deprecated in v1.3.
Please use Eq.decSetoid instead.&quot;</a>
<a id="9147" class="Symbol">#-}</a>
<a id="9153" class="Keyword">record</a> <a id="DenseLinearOrder"></a><a id="9160" href="Relation.Binary.Bundles.html#9160" class="Record">DenseLinearOrder</a> <a id="9177" href="Relation.Binary.Bundles.html#9177" class="Bound">c</a> <a id="9179" href="Relation.Binary.Bundles.html#9179" class="Bound">ℓ₁</a> <a id="9182" href="Relation.Binary.Bundles.html#9182" class="Bound">ℓ₂</a> <a id="9185" class="Symbol">:</a> <a id="9187" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9191" class="Symbol">(</a><a id="9192" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="9196" class="Symbol">(</a><a id="9197" href="Relation.Binary.Bundles.html#9177" class="Bound">c</a> <a id="9199" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9201" href="Relation.Binary.Bundles.html#9179" class="Bound">ℓ₁</a> <a id="9204" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9206" href="Relation.Binary.Bundles.html#9182" class="Bound">ℓ₂</a><a id="9208" class="Symbol">))</a> <a id="9211" class="Keyword">where</a>
<a id="9219" class="Keyword">infix</a> <a id="9225" class="Number">4</a> <a id="9227" href="Relation.Binary.Bundles.html#9278" class="Field Operator">_≈_</a> <a id="9231" href="Relation.Binary.Bundles.html#9318" class="Field Operator">_&lt;_</a>
<a id="9237" class="Keyword">field</a>
<a id="DenseLinearOrder.Carrier"></a><a id="9247" href="Relation.Binary.Bundles.html#9247" class="Field">Carrier</a> <a id="9266" class="Symbol">:</a> <a id="9268" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9272" href="Relation.Binary.Bundles.html#9177" class="Bound">c</a>
<a id="DenseLinearOrder._≈_"></a><a id="9278" href="Relation.Binary.Bundles.html#9278" class="Field Operator">_≈_</a> <a id="9297" class="Symbol">:</a> <a id="9299" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="9303" href="Relation.Binary.Bundles.html#9247" class="Field">Carrier</a> <a id="9311" href="Relation.Binary.Bundles.html#9179" class="Bound">ℓ₁</a>
<a id="DenseLinearOrder._&lt;_"></a><a id="9318" href="Relation.Binary.Bundles.html#9318" class="Field Operator">_&lt;_</a> <a id="9337" class="Symbol">:</a> <a id="9339" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="9343" href="Relation.Binary.Bundles.html#9247" class="Field">Carrier</a> <a id="9351" href="Relation.Binary.Bundles.html#9182" class="Bound">ℓ₂</a>
<a id="DenseLinearOrder.isDenseLinearOrder"></a><a id="9358" href="Relation.Binary.Bundles.html#9358" class="Field">isDenseLinearOrder</a> <a id="9377" class="Symbol">:</a> <a id="9379" href="Relation.Binary.Structures.html#7974" class="Record">IsDenseLinearOrder</a> <a id="9398" href="Relation.Binary.Bundles.html#9278" class="Field Operator">_≈_</a> <a id="9402" href="Relation.Binary.Bundles.html#9318" class="Field Operator">_&lt;_</a>
<a id="9409" class="Keyword">open</a> <a id="9414" href="Relation.Binary.Structures.html#7974" class="Module">IsDenseLinearOrder</a> <a id="9433" href="Relation.Binary.Bundles.html#9358" class="Field">isDenseLinearOrder</a> <a id="9452" class="Keyword">public</a>
<a id="9463" class="Keyword">using</a> <a id="9469" class="Symbol">(</a><a id="9470" href="Relation.Binary.Structures.html#8047" class="Field">isStrictTotalOrder</a><a id="9488" class="Symbol">;</a> <a id="9490" href="Relation.Binary.Structures.html#8095" class="Field">dense</a><a id="9495" class="Symbol">)</a>
<a id="DenseLinearOrder.strictTotalOrder"></a><a id="9500" href="Relation.Binary.Bundles.html#9500" class="Function">strictTotalOrder</a> <a id="9517" class="Symbol">:</a> <a id="9519" href="Relation.Binary.Bundles.html#8031" class="Record">StrictTotalOrder</a> <a id="9536" href="Relation.Binary.Bundles.html#9177" class="Bound">c</a> <a id="9538" href="Relation.Binary.Bundles.html#9179" class="Bound">ℓ₁</a> <a id="9541" href="Relation.Binary.Bundles.html#9182" class="Bound">ℓ₂</a>
<a id="9546" href="Relation.Binary.Bundles.html#9500" class="Function">strictTotalOrder</a> <a id="9563" class="Symbol">=</a> <a id="9565" class="Keyword">record</a>
<a id="9576" class="Symbol">{</a> <a id="9578" href="Relation.Binary.Bundles.html#8229" class="Field">isStrictTotalOrder</a> <a id="9597" class="Symbol">=</a> <a id="9599" href="Relation.Binary.Structures.html#8047" class="Function">isStrictTotalOrder</a>
<a id="9622" class="Symbol">}</a>
<a id="9627" class="Keyword">open</a> <a id="9632" href="Relation.Binary.Bundles.html#8031" class="Module">StrictTotalOrder</a> <a id="9649" href="Relation.Binary.Bundles.html#9500" class="Function">strictTotalOrder</a> <a id="9666" class="Keyword">public</a>
<a id="9677" class="Keyword">hiding</a> <a id="9684" class="Symbol">(</a><a id="9685" href="Relation.Binary.Bundles.html#8118" class="Field">Carrier</a><a id="9692" class="Symbol">;</a> <a id="9694" href="Relation.Binary.Bundles.html#8149" class="Field Operator">_≈_</a><a id="9697" class="Symbol">;</a> <a id="9699" href="Relation.Binary.Bundles.html#8189" class="Field Operator">_&lt;_</a><a id="9702" class="Symbol">;</a> <a id="9704" href="Relation.Binary.Bundles.html#8229" class="Field">isStrictTotalOrder</a><a id="9722" class="Symbol">)</a>
<a id="9726" class="Comment">------------------------------------------------------------------------</a>
<a id="9799" class="Comment">-- Apartness relations</a>
<a id="9822" class="Comment">------------------------------------------------------------------------</a>
<a id="9896" class="Keyword">record</a> <a id="ApartnessRelation"></a><a id="9903" href="Relation.Binary.Bundles.html#9903" class="Record">ApartnessRelation</a> <a id="9921" href="Relation.Binary.Bundles.html#9921" class="Bound">c</a> <a id="9923" href="Relation.Binary.Bundles.html#9923" class="Bound">ℓ₁</a> <a id="9926" href="Relation.Binary.Bundles.html#9926" class="Bound">ℓ₂</a> <a id="9929" class="Symbol">:</a> <a id="9931" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="9935" class="Symbol">(</a><a id="9936" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="9940" class="Symbol">(</a><a id="9941" href="Relation.Binary.Bundles.html#9921" class="Bound">c</a> <a id="9943" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9945" href="Relation.Binary.Bundles.html#9923" class="Bound">ℓ₁</a> <a id="9948" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="9950" href="Relation.Binary.Bundles.html#9926" class="Bound">ℓ₂</a><a id="9952" class="Symbol">))</a> <a id="9955" class="Keyword">where</a>
<a id="9963" class="Keyword">infix</a> <a id="9969" class="Number">4</a> <a id="9971" href="Relation.Binary.Bundles.html#10023" class="Field Operator">_≈_</a> <a id="9975" href="Relation.Binary.Bundles.html#10064" class="Field Operator">_#_</a>
<a id="9981" class="Keyword">field</a>
<a id="ApartnessRelation.Carrier"></a><a id="9991" href="Relation.Binary.Bundles.html#9991" class="Field">Carrier</a> <a id="10011" class="Symbol">:</a> <a id="10013" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="10017" href="Relation.Binary.Bundles.html#9921" class="Bound">c</a>
<a id="ApartnessRelation._≈_"></a><a id="10023" href="Relation.Binary.Bundles.html#10023" class="Field Operator">_≈_</a> <a id="10043" class="Symbol">:</a> <a id="10045" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="10049" href="Relation.Binary.Bundles.html#9991" class="Field">Carrier</a> <a id="10057" href="Relation.Binary.Bundles.html#9923" class="Bound">ℓ₁</a>
<a id="ApartnessRelation._#_"></a><a id="10064" href="Relation.Binary.Bundles.html#10064" class="Field Operator">_#_</a> <a id="10084" class="Symbol">:</a> <a id="10086" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="10090" href="Relation.Binary.Bundles.html#9991" class="Field">Carrier</a> <a id="10098" href="Relation.Binary.Bundles.html#9926" class="Bound">ℓ₂</a>
<a id="ApartnessRelation.isApartnessRelation"></a><a id="10105" href="Relation.Binary.Bundles.html#10105" class="Field">isApartnessRelation</a> <a id="10125" class="Symbol">:</a> <a id="10127" href="Relation.Binary.Structures.html#8358" class="Record">IsApartnessRelation</a> <a id="10147" href="Relation.Binary.Bundles.html#10023" class="Field Operator">_≈_</a> <a id="10151" href="Relation.Binary.Bundles.html#10064" class="Field Operator">_#_</a>
<a id="10158" class="Keyword">open</a> <a id="10163" href="Relation.Binary.Structures.html#8358" class="Module">IsApartnessRelation</a> <a id="10183" href="Relation.Binary.Bundles.html#10105" class="Field">isApartnessRelation</a> <a id="10203" class="Keyword">public</a>
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