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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="Level.html" class="Module">Level</a>
<a id="399" class="Keyword">open</a> <a id="404" class="Keyword">import</a> <a id="411" href="Relation.Nullary.html" class="Module">Relation.Nullary</a> <a id="428" class="Keyword">using</a> <a id="434" class="Symbol">(</a><a id="435" href="Relation.Nullary.html#665" class="Function Operator">¬_</a><a id="437" class="Symbol">)</a>
<a id="439" class="Keyword">open</a> <a id="444" class="Keyword">import</a> <a id="451" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a>
<a id="472" class="Keyword">open</a> <a id="477" class="Keyword">import</a> <a id="484" href="Relation.Binary.Definitions.html" class="Module">Relation.Binary.Definitions</a>
<a id="512" class="Keyword">open</a> <a id="517" class="Keyword">import</a> <a id="524" href="Relation.Binary.Structures.html" class="Module">Relation.Binary.Structures</a>
<a id="552" class="Comment">------------------------------------------------------------------------</a>
<a id="625" class="Comment">-- Setoids</a>
<a id="636" class="Comment">------------------------------------------------------------------------</a>
<a id="710" class="Keyword">record</a> <a id="PartialSetoid"></a><a id="717" href="Relation.Binary.Bundles.html#717" class="Record">PartialSetoid</a> <a id="731" href="Relation.Binary.Bundles.html#731" class="Bound">a</a> <a id="733" href="Relation.Binary.Bundles.html#733" class="Bound">ℓ</a> <a id="735" class="Symbol">:</a> <a id="737" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="741" class="Symbol">(</a><a id="742" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="746" class="Symbol">(</a><a id="747" href="Relation.Binary.Bundles.html#731" class="Bound">a</a> <a id="749" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="751" href="Relation.Binary.Bundles.html#733" class="Bound">ℓ</a><a id="752" class="Symbol">))</a> <a id="755" class="Keyword">where</a>
<a id="763" class="Keyword">field</a>
<a id="PartialSetoid.Carrier"></a><a id="773" href="Relation.Binary.Bundles.html#773" class="Field">Carrier</a> <a id="794" class="Symbol">:</a> <a id="796" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="800" href="Relation.Binary.Bundles.html#731" class="Bound">a</a>
<a id="PartialSetoid._≈_"></a><a id="806" href="Relation.Binary.Bundles.html#806" class="Field Operator">_≈_</a> <a id="827" class="Symbol">:</a> <a id="829" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="833" href="Relation.Binary.Bundles.html#773" class="Field">Carrier</a> <a id="841" href="Relation.Binary.Bundles.html#733" class="Bound">ℓ</a>
<a id="PartialSetoid.isPartialEquivalence"></a><a id="847" href="Relation.Binary.Bundles.html#847" class="Field">isPartialEquivalence</a> <a id="868" class="Symbol">:</a> <a id="870" href="Relation.Binary.Structures.html#1128" class="Record">IsPartialEquivalence</a> <a id="891" href="Relation.Binary.Bundles.html#806" class="Field Operator">_≈_</a>
<a id="898" class="Keyword">open</a> <a id="903" href="Relation.Binary.Structures.html#1128" class="Module">IsPartialEquivalence</a> <a id="924" href="Relation.Binary.Bundles.html#847" class="Field">isPartialEquivalence</a> <a id="945" class="Keyword">public</a>
<a id="955" class="Keyword">infix</a> <a id="961" class="Number">4</a> <a id="963" href="Relation.Binary.Bundles.html#969" class="Function Operator">_≉_</a>
<a id="PartialSetoid._≉_"></a><a id="969" href="Relation.Binary.Bundles.html#969" class="Function Operator">_≉_</a> <a id="973" class="Symbol">:</a> <a id="975" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="979" href="Relation.Binary.Bundles.html#773" class="Field">Carrier</a> <a id="987" class="Symbol">_</a>
<a id="991" href="Relation.Binary.Bundles.html#991" class="Bound">x</a> <a id="993" href="Relation.Binary.Bundles.html#969" class="Function Operator">≉</a> <a id="995" href="Relation.Binary.Bundles.html#995" class="Bound">y</a> <a id="997" class="Symbol">=</a> <a id="999" href="Relation.Nullary.html#665" class="Function Operator">¬</a> <a id="1001" class="Symbol">(</a><a id="1002" href="Relation.Binary.Bundles.html#991" class="Bound">x</a> <a id="1004" href="Relation.Binary.Bundles.html#806" class="Field Operator">≈</a> <a id="1006" href="Relation.Binary.Bundles.html#995" class="Bound">y</a><a id="1007" class="Symbol">)</a>
<a id="1011" class="Keyword">record</a> <a id="Setoid"></a><a id="1018" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="1025" href="Relation.Binary.Bundles.html#1025" class="Bound">c</a> <a id="1027" href="Relation.Binary.Bundles.html#1027" class="Bound">ℓ</a> <a id="1029" class="Symbol">:</a> <a id="1031" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1035" class="Symbol">(</a><a id="1036" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="1040" class="Symbol">(</a><a id="1041" href="Relation.Binary.Bundles.html#1025" class="Bound">c</a> <a id="1043" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1045" href="Relation.Binary.Bundles.html#1027" class="Bound">ℓ</a><a id="1046" class="Symbol">))</a> <a id="1049" class="Keyword">where</a>
<a id="1057" class="Keyword">infix</a> <a id="1063" class="Number">4</a> <a id="1065" href="Relation.Binary.Bundles.html#1107" class="Field Operator">_≈_</a>
<a id="1071" class="Keyword">field</a>
<a id="Setoid.Carrier"></a><a id="1081" href="Relation.Binary.Bundles.html#1081" class="Field">Carrier</a> <a id="1095" class="Symbol">:</a> <a id="1097" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1101" href="Relation.Binary.Bundles.html#1025" class="Bound">c</a>
<a id="Setoid._≈_"></a><a id="1107" href="Relation.Binary.Bundles.html#1107" class="Field Operator">_≈_</a> <a id="1121" class="Symbol">:</a> <a id="1123" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1127" href="Relation.Binary.Bundles.html#1081" class="Field">Carrier</a> <a id="1135" href="Relation.Binary.Bundles.html#1027" class="Bound">ℓ</a>
<a id="Setoid.isEquivalence"></a><a id="1141" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="1155" class="Symbol">:</a> <a id="1157" href="Relation.Binary.Structures.html#1531" class="Record">IsEquivalence</a> <a id="1171" href="Relation.Binary.Bundles.html#1107" class="Field Operator">_≈_</a>
<a id="1178" class="Keyword">open</a> <a id="1183" href="Relation.Binary.Structures.html#1531" class="Module">IsEquivalence</a> <a id="1197" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="1211" class="Keyword">public</a>
<a id="Setoid.partialSetoid"></a><a id="1221" href="Relation.Binary.Bundles.html#1221" class="Function">partialSetoid</a> <a id="1235" class="Symbol">:</a> <a id="1237" href="Relation.Binary.Bundles.html#717" class="Record">PartialSetoid</a> <a id="1251" href="Relation.Binary.Bundles.html#1025" class="Bound">c</a> <a id="1253" href="Relation.Binary.Bundles.html#1027" class="Bound">ℓ</a>
<a id="1257" href="Relation.Binary.Bundles.html#1221" class="Function">partialSetoid</a> <a id="1271" class="Symbol">=</a> <a id="1273" class="Keyword">record</a>
<a id="1284" class="Symbol">{</a> <a id="1286" href="Relation.Binary.Bundles.html#847" class="Field">isPartialEquivalence</a> <a id="1307" class="Symbol">=</a> <a id="1309" href="Relation.Binary.Structures.html#1706" class="Function">isPartialEquivalence</a>
<a id="1334" class="Symbol">}</a>
<a id="1339" class="Keyword">open</a> <a id="1344" href="Relation.Binary.Bundles.html#717" class="Module">PartialSetoid</a> <a id="1358" href="Relation.Binary.Bundles.html#1221" class="Function">partialSetoid</a> <a id="1372" class="Keyword">public</a> <a id="1379" class="Keyword">using</a> <a id="1385" class="Symbol">(</a><a id="1386" href="Relation.Binary.Bundles.html#969" class="Function Operator">_≉_</a><a id="1389" class="Symbol">)</a>
<a id="1393" class="Keyword">record</a> <a id="DecSetoid"></a><a id="1400" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="1410" href="Relation.Binary.Bundles.html#1410" class="Bound">c</a> <a id="1412" href="Relation.Binary.Bundles.html#1412" class="Bound">ℓ</a> <a id="1414" class="Symbol">:</a> <a id="1416" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1420" class="Symbol">(</a><a id="1421" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="1425" class="Symbol">(</a><a id="1426" href="Relation.Binary.Bundles.html#1410" class="Bound">c</a> <a id="1428" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1430" href="Relation.Binary.Bundles.html#1412" class="Bound">ℓ</a><a id="1431" class="Symbol">))</a> <a id="1434" class="Keyword">where</a>
<a id="1442" class="Keyword">infix</a> <a id="1448" class="Number">4</a> <a id="1450" href="Relation.Binary.Bundles.html#1495" class="Field Operator">_≈_</a>
<a id="1456" class="Keyword">field</a>
<a id="DecSetoid.Carrier"></a><a id="1466" href="Relation.Binary.Bundles.html#1466" class="Field">Carrier</a> <a id="1483" class="Symbol">:</a> <a id="1485" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1489" href="Relation.Binary.Bundles.html#1410" class="Bound">c</a>
<a id="DecSetoid._≈_"></a><a id="1495" href="Relation.Binary.Bundles.html#1495" class="Field Operator">_≈_</a> <a id="1512" class="Symbol">:</a> <a id="1514" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="1518" href="Relation.Binary.Bundles.html#1466" class="Field">Carrier</a> <a id="1526" href="Relation.Binary.Bundles.html#1412" class="Bound">ℓ</a>
<a id="DecSetoid.isDecEquivalence"></a><a id="1532" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="1549" class="Symbol">:</a> <a id="1551" href="Relation.Binary.Structures.html#1833" class="Record">IsDecEquivalence</a> <a id="1568" href="Relation.Binary.Bundles.html#1495" class="Field Operator">_≈_</a>
<a id="1575" class="Keyword">open</a> <a id="1580" href="Relation.Binary.Structures.html#1833" class="Module">IsDecEquivalence</a> <a id="1597" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="1614" class="Keyword">public</a>
<a id="DecSetoid.setoid"></a><a id="1624" href="Relation.Binary.Bundles.html#1624" class="Function">setoid</a> <a id="1631" class="Symbol">:</a> <a id="1633" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="1640" href="Relation.Binary.Bundles.html#1410" class="Bound">c</a> <a id="1642" href="Relation.Binary.Bundles.html#1412" class="Bound">ℓ</a>
<a id="1646" href="Relation.Binary.Bundles.html#1624" class="Function">setoid</a> <a id="1653" class="Symbol">=</a> <a id="1655" class="Keyword">record</a>
<a id="1666" class="Symbol">{</a> <a id="1668" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="1682" class="Symbol">=</a> <a id="1684" href="Relation.Binary.Structures.html#1896" class="Function">isEquivalence</a>
<a id="1702" class="Symbol">}</a>
<a id="1707" class="Keyword">open</a> <a id="1712" href="Relation.Binary.Bundles.html#1018" class="Module">Setoid</a> <a id="1719" href="Relation.Binary.Bundles.html#1624" class="Function">setoid</a> <a id="1726" class="Keyword">public</a> <a id="1733" class="Keyword">using</a> <a id="1739" class="Symbol">(</a><a id="1740" href="Relation.Binary.Bundles.html#1221" class="Function">partialSetoid</a><a id="1753" class="Symbol">;</a> <a id="1755" href="Relation.Binary.Bundles.html#969" class="Function Operator">_≉_</a><a id="1758" class="Symbol">)</a>
<a id="1762" class="Comment">------------------------------------------------------------------------</a>
<a id="1835" class="Comment">-- Preorders</a>
<a id="1848" class="Comment">------------------------------------------------------------------------</a>
<a id="1922" class="Keyword">record</a> <a id="Preorder"></a><a id="1929" href="Relation.Binary.Bundles.html#1929" class="Record">Preorder</a> <a id="1938" href="Relation.Binary.Bundles.html#1938" class="Bound">c</a> <a id="1940" href="Relation.Binary.Bundles.html#1940" class="Bound">ℓ₁</a> <a id="1943" href="Relation.Binary.Bundles.html#1943" class="Bound">ℓ₂</a> <a id="1946" class="Symbol">:</a> <a id="1948" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1952" class="Symbol">(</a><a id="1953" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="1957" class="Symbol">(</a><a id="1958" href="Relation.Binary.Bundles.html#1938" class="Bound">c</a> <a id="1960" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1962" href="Relation.Binary.Bundles.html#1940" class="Bound">ℓ₁</a> <a id="1965" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1967" href="Relation.Binary.Bundles.html#1943" class="Bound">ℓ₂</a><a id="1969" class="Symbol">))</a> <a id="1972" class="Keyword">where</a>
<a id="1980" class="Keyword">infix</a> <a id="1986" class="Number">4</a> <a id="1988" href="Relation.Binary.Bundles.html#2031" class="Field Operator">_≈_</a> <a id="1992" href="Relation.Binary.Bundles.html#2092" class="Field Operator">_∼_</a>
<a id="1998" class="Keyword">field</a>
<a id="Preorder.Carrier"></a><a id="2008" href="Relation.Binary.Bundles.html#2008" class="Field">Carrier</a> <a id="2019" class="Symbol">:</a> <a id="2021" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="2025" href="Relation.Binary.Bundles.html#1938" class="Bound">c</a>
<a id="Preorder._≈_"></a><a id="2031" href="Relation.Binary.Bundles.html#2031" class="Field Operator">_≈_</a> <a id="2042" class="Symbol">:</a> <a id="2044" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2048" href="Relation.Binary.Bundles.html#2008" class="Field">Carrier</a> <a id="2056" href="Relation.Binary.Bundles.html#1940" class="Bound">ℓ₁</a> <a id="2060" class="Comment">-- The underlying equality.</a>
<a id="Preorder._∼_"></a><a id="2092" href="Relation.Binary.Bundles.html#2092" class="Field Operator">_∼_</a> <a id="2103" class="Symbol">:</a> <a id="2105" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2109" href="Relation.Binary.Bundles.html#2008" class="Field">Carrier</a> <a id="2117" href="Relation.Binary.Bundles.html#1943" class="Bound">ℓ₂</a> <a id="2121" class="Comment">-- The relation.</a>
<a id="Preorder.isPreorder"></a><a id="2142" href="Relation.Binary.Bundles.html#2142" class="Field">isPreorder</a> <a id="2153" class="Symbol">:</a> <a id="2155" href="Relation.Binary.Structures.html#2172" class="Record">IsPreorder</a> <a id="2166" href="Relation.Binary.Bundles.html#2031" class="Field Operator">_≈_</a> <a id="2170" href="Relation.Binary.Bundles.html#2092" class="Field Operator">_∼_</a>
<a id="2177" class="Keyword">open</a> <a id="2182" href="Relation.Binary.Structures.html#2172" class="Module">IsPreorder</a> <a id="2193" href="Relation.Binary.Bundles.html#2142" class="Field">isPreorder</a> <a id="2204" class="Keyword">public</a>
<a id="2215" class="Keyword">hiding</a> <a id="2222" class="Symbol">(</a><a id="2223" class="Keyword">module</a> <a id="2230" href="Relation.Binary.Structures.html#2411" class="Module">Eq</a><a id="2232" class="Symbol">)</a>
<a id="2237" class="Keyword">module</a> <a id="Preorder.Eq"></a><a id="2244" href="Relation.Binary.Bundles.html#2244" class="Module">Eq</a> <a id="2247" class="Keyword">where</a>
<a id="Preorder.Eq.setoid"></a><a id="2257" href="Relation.Binary.Bundles.html#2257" class="Function">setoid</a> <a id="2264" class="Symbol">:</a> <a id="2266" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="2273" href="Relation.Binary.Bundles.html#1938" class="Bound">c</a> <a id="2275" href="Relation.Binary.Bundles.html#1940" class="Bound">ℓ₁</a>
<a id="2282" href="Relation.Binary.Bundles.html#2257" class="Function">setoid</a> <a id="2289" class="Symbol">=</a> <a id="2291" class="Keyword">record</a>
<a id="2304" class="Symbol">{</a> <a id="2306" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="2320" class="Symbol">=</a> <a id="2322" href="Relation.Binary.Structures.html#2237" class="Function">isEquivalence</a>
<a id="2342" class="Symbol">}</a>
<a id="2349" class="Keyword">open</a> <a id="2354" href="Relation.Binary.Bundles.html#1018" class="Module">Setoid</a> <a id="2361" href="Relation.Binary.Bundles.html#2257" class="Function">setoid</a> <a id="2368" class="Keyword">public</a>
<a id="2377" class="Keyword">record</a> <a id="TotalPreorder"></a><a id="2384" href="Relation.Binary.Bundles.html#2384" class="Record">TotalPreorder</a> <a id="2398" href="Relation.Binary.Bundles.html#2398" class="Bound">c</a> <a id="2400" href="Relation.Binary.Bundles.html#2400" class="Bound">ℓ₁</a> <a id="2403" href="Relation.Binary.Bundles.html#2403" class="Bound">ℓ₂</a> <a id="2406" class="Symbol">:</a> <a id="2408" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="2412" class="Symbol">(</a><a id="2413" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="2417" class="Symbol">(</a><a id="2418" href="Relation.Binary.Bundles.html#2398" class="Bound">c</a> <a id="2420" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="2422" href="Relation.Binary.Bundles.html#2400" class="Bound">ℓ₁</a> <a id="2425" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="2427" href="Relation.Binary.Bundles.html#2403" class="Bound">ℓ₂</a><a id="2429" class="Symbol">))</a> <a id="2432" class="Keyword">where</a>
<a id="2440" class="Keyword">infix</a> <a id="2446" class="Number">4</a> <a id="2448" href="Relation.Binary.Bundles.html#2496" class="Field Operator">_≈_</a> <a id="2452" href="Relation.Binary.Bundles.html#2562" class="Field Operator">_≲_</a>
<a id="2458" class="Keyword">field</a>
<a id="TotalPreorder.Carrier"></a><a id="2468" href="Relation.Binary.Bundles.html#2468" class="Field">Carrier</a> <a id="2484" class="Symbol">:</a> <a id="2486" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="2490" href="Relation.Binary.Bundles.html#2398" class="Bound">c</a>
<a id="TotalPreorder._≈_"></a><a id="2496" href="Relation.Binary.Bundles.html#2496" class="Field Operator">_≈_</a> <a id="2512" class="Symbol">:</a> <a id="2514" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2518" href="Relation.Binary.Bundles.html#2468" class="Field">Carrier</a> <a id="2526" href="Relation.Binary.Bundles.html#2400" class="Bound">ℓ₁</a> <a id="2530" class="Comment">-- The underlying equality.</a>
<a id="TotalPreorder._≲_"></a><a id="2562" href="Relation.Binary.Bundles.html#2562" class="Field Operator">_≲_</a> <a id="2578" class="Symbol">:</a> <a id="2580" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="2584" href="Relation.Binary.Bundles.html#2468" class="Field">Carrier</a> <a id="2592" href="Relation.Binary.Bundles.html#2403" class="Bound">ℓ₂</a> <a id="2596" class="Comment">-- The relation.</a>
<a id="TotalPreorder.isTotalPreorder"></a><a id="2617" href="Relation.Binary.Bundles.html#2617" class="Field">isTotalPreorder</a> <a id="2633" class="Symbol">:</a> <a id="2635" href="Relation.Binary.Structures.html#2742" class="Record">IsTotalPreorder</a> <a id="2651" href="Relation.Binary.Bundles.html#2496" class="Field Operator">_≈_</a> <a id="2655" href="Relation.Binary.Bundles.html#2562" class="Field Operator">_≲_</a>
<a id="2662" class="Keyword">open</a> <a id="2667" href="Relation.Binary.Structures.html#2742" class="Module">IsTotalPreorder</a> <a id="2683" href="Relation.Binary.Bundles.html#2617" class="Field">isTotalPreorder</a> <a id="2699" class="Keyword">public</a>
<a id="2710" class="Keyword">hiding</a> <a id="2717" class="Symbol">(</a><a id="2718" class="Keyword">module</a> <a id="2725" href="Relation.Binary.Structures.html#2411" class="Module">Eq</a><a id="2727" class="Symbol">)</a>
<a id="TotalPreorder.preorder"></a><a id="2732" href="Relation.Binary.Bundles.html#2732" class="Function">preorder</a> <a id="2741" class="Symbol">:</a> <a id="2743" href="Relation.Binary.Bundles.html#1929" class="Record">Preorder</a> <a id="2752" href="Relation.Binary.Bundles.html#2398" class="Bound">c</a> <a id="2754" href="Relation.Binary.Bundles.html#2400" class="Bound">ℓ₁</a> <a id="2757" href="Relation.Binary.Bundles.html#2403" class="Bound">ℓ₂</a>
<a id="2762" href="Relation.Binary.Bundles.html#2732" class="Function">preorder</a> <a id="2771" class="Symbol">=</a> <a id="2773" class="Keyword">record</a> <a id="2780" class="Symbol">{</a> <a id="2782" href="Relation.Binary.Bundles.html#2142" class="Field">isPreorder</a> <a id="2793" class="Symbol">=</a> <a id="2795" href="Relation.Binary.Structures.html#2812" class="Function">isPreorder</a> <a id="2806" class="Symbol">}</a>
<a id="2811" class="Keyword">open</a> <a id="2816" href="Relation.Binary.Bundles.html#1929" class="Module">Preorder</a> <a id="2825" href="Relation.Binary.Bundles.html#2732" class="Function">preorder</a> <a id="2834" class="Keyword">public</a>
<a id="2845" class="Keyword">using</a> <a id="2851" class="Symbol">(</a><a id="2852" class="Keyword">module</a> <a id="2859" href="Relation.Binary.Bundles.html#2244" class="Module">Eq</a><a id="2861" class="Symbol">)</a>
<a id="2865" class="Comment">------------------------------------------------------------------------</a>
<a id="2938" class="Comment">-- Partial orders</a>
<a id="2956" class="Comment">------------------------------------------------------------------------</a>
<a id="3030" class="Keyword">record</a> <a id="Poset"></a><a id="3037" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="3043" href="Relation.Binary.Bundles.html#3043" class="Bound">c</a> <a id="3045" href="Relation.Binary.Bundles.html#3045" class="Bound">ℓ₁</a> <a id="3048" href="Relation.Binary.Bundles.html#3048" class="Bound">ℓ₂</a> <a id="3051" class="Symbol">:</a> <a id="3053" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="3057" class="Symbol">(</a><a id="3058" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="3062" class="Symbol">(</a><a id="3063" href="Relation.Binary.Bundles.html#3043" class="Bound">c</a> <a id="3065" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="3067" href="Relation.Binary.Bundles.html#3045" class="Bound">ℓ₁</a> <a id="3070" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="3072" href="Relation.Binary.Bundles.html#3048" class="Bound">ℓ₂</a><a id="3074" class="Symbol">))</a> <a id="3077" class="Keyword">where</a>
<a id="3085" class="Keyword">infix</a> <a id="3091" class="Number">4</a> <a id="3093" href="Relation.Binary.Bundles.html#3140" class="Field Operator">_≈_</a> <a id="3097" href="Relation.Binary.Bundles.html#3176" class="Field Operator">_≤_</a>
<a id="3103" class="Keyword">field</a>
<a id="Poset.Carrier"></a><a id="3113" href="Relation.Binary.Bundles.html#3113" class="Field">Carrier</a> <a id="3128" class="Symbol">:</a> <a id="3130" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="3134" href="Relation.Binary.Bundles.html#3043" class="Bound">c</a>
<a id="Poset._≈_"></a><a id="3140" href="Relation.Binary.Bundles.html#3140" class="Field Operator">_≈_</a> <a id="3155" class="Symbol">:</a> <a id="3157" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3161" href="Relation.Binary.Bundles.html#3113" class="Field">Carrier</a> <a id="3169" href="Relation.Binary.Bundles.html#3045" class="Bound">ℓ₁</a>
<a id="Poset._≤_"></a><a id="3176" href="Relation.Binary.Bundles.html#3176" class="Field Operator">_≤_</a> <a id="3191" class="Symbol">:</a> <a id="3193" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3197" href="Relation.Binary.Bundles.html#3113" class="Field">Carrier</a> <a id="3205" href="Relation.Binary.Bundles.html#3048" class="Bound">ℓ₂</a>
<a id="Poset.isPartialOrder"></a><a id="3212" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="3227" class="Symbol">:</a> <a id="3229" href="Relation.Binary.Structures.html#3183" class="Record">IsPartialOrder</a> <a id="3244" href="Relation.Binary.Bundles.html#3140" class="Field Operator">_≈_</a> <a id="3248" href="Relation.Binary.Bundles.html#3176" class="Field Operator">_≤_</a>
<a id="3255" class="Keyword">open</a> <a id="3260" href="Relation.Binary.Structures.html#3183" class="Module">IsPartialOrder</a> <a id="3275" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="3290" class="Keyword">public</a>
<a id="3301" class="Keyword">hiding</a> <a id="3308" class="Symbol">(</a><a id="3309" class="Keyword">module</a> <a id="3316" href="Relation.Binary.Structures.html#2411" class="Module">Eq</a><a id="3318" class="Symbol">)</a>
<a id="Poset.preorder"></a><a id="3323" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a> <a id="3332" class="Symbol">:</a> <a id="3334" href="Relation.Binary.Bundles.html#1929" class="Record">Preorder</a> <a id="3343" href="Relation.Binary.Bundles.html#3043" class="Bound">c</a> <a id="3345" href="Relation.Binary.Bundles.html#3045" class="Bound">ℓ₁</a> <a id="3348" href="Relation.Binary.Bundles.html#3048" class="Bound">ℓ₂</a>
<a id="3353" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a> <a id="3362" class="Symbol">=</a> <a id="3364" class="Keyword">record</a>
<a id="3375" class="Symbol">{</a> <a id="3377" href="Relation.Binary.Bundles.html#2142" class="Field">isPreorder</a> <a id="3388" class="Symbol">=</a> <a id="3390" href="Relation.Binary.Structures.html#3252" class="Function">isPreorder</a>
<a id="3405" class="Symbol">}</a>
<a id="3410" class="Keyword">open</a> <a id="3415" href="Relation.Binary.Bundles.html#1929" class="Module">Preorder</a> <a id="3424" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a> <a id="3433" class="Keyword">public</a>
<a id="3444" class="Keyword">using</a> <a id="3450" class="Symbol">(</a><a id="3451" class="Keyword">module</a> <a id="3458" href="Relation.Binary.Bundles.html#2244" class="Module">Eq</a><a id="3460" class="Symbol">)</a>
<a id="3464" class="Keyword">record</a> <a id="DecPoset"></a><a id="3471" href="Relation.Binary.Bundles.html#3471" class="Record">DecPoset</a> <a id="3480" href="Relation.Binary.Bundles.html#3480" class="Bound">c</a> <a id="3482" href="Relation.Binary.Bundles.html#3482" class="Bound">ℓ₁</a> <a id="3485" href="Relation.Binary.Bundles.html#3485" class="Bound">ℓ₂</a> <a id="3488" class="Symbol">:</a> <a id="3490" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="3494" class="Symbol">(</a><a id="3495" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="3499" class="Symbol">(</a><a id="3500" href="Relation.Binary.Bundles.html#3480" class="Bound">c</a> <a id="3502" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="3504" href="Relation.Binary.Bundles.html#3482" class="Bound">ℓ₁</a> <a id="3507" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="3509" href="Relation.Binary.Bundles.html#3485" class="Bound">ℓ₂</a><a id="3511" class="Symbol">))</a> <a id="3514" class="Keyword">where</a>
<a id="3522" class="Keyword">infix</a> <a id="3528" class="Number">4</a> <a id="3530" href="Relation.Binary.Bundles.html#3580" class="Field Operator">_≈_</a> <a id="3534" href="Relation.Binary.Bundles.html#3619" class="Field Operator">_≤_</a>
<a id="3540" class="Keyword">field</a>
<a id="DecPoset.Carrier"></a><a id="3550" href="Relation.Binary.Bundles.html#3550" class="Field">Carrier</a> <a id="3568" class="Symbol">:</a> <a id="3570" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="3574" href="Relation.Binary.Bundles.html#3480" class="Bound">c</a>
<a id="DecPoset._≈_"></a><a id="3580" href="Relation.Binary.Bundles.html#3580" class="Field Operator">_≈_</a> <a id="3598" class="Symbol">:</a> <a id="3600" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3604" href="Relation.Binary.Bundles.html#3550" class="Field">Carrier</a> <a id="3612" href="Relation.Binary.Bundles.html#3482" class="Bound">ℓ₁</a>
<a id="DecPoset._≤_"></a><a id="3619" href="Relation.Binary.Bundles.html#3619" class="Field Operator">_≤_</a> <a id="3637" class="Symbol">:</a> <a id="3639" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="3643" href="Relation.Binary.Bundles.html#3550" class="Field">Carrier</a> <a id="3651" href="Relation.Binary.Bundles.html#3485" class="Bound">ℓ₂</a>
<a id="DecPoset.isDecPartialOrder"></a><a id="3658" href="Relation.Binary.Bundles.html#3658" class="Field">isDecPartialOrder</a> <a id="3676" class="Symbol">:</a> <a id="3678" href="Relation.Binary.Structures.html#3470" class="Record">IsDecPartialOrder</a> <a id="3696" href="Relation.Binary.Bundles.html#3580" class="Field Operator">_≈_</a> <a id="3700" href="Relation.Binary.Bundles.html#3619" class="Field Operator">_≤_</a>
<a id="3707" class="Keyword">private</a>
<a id="3719" class="Keyword">module</a> <a id="DecPoset.DPO"></a><a id="3726" href="Relation.Binary.Bundles.html#3726" class="Module">DPO</a> <a id="3730" class="Symbol">=</a> <a id="3732" href="Relation.Binary.Structures.html#3470" class="Module">IsDecPartialOrder</a> <a id="3750" href="Relation.Binary.Bundles.html#3658" class="Field">isDecPartialOrder</a>
<a id="3770" class="Keyword">open</a> <a id="3775" href="Relation.Binary.Bundles.html#3726" class="Module">DPO</a> <a id="3779" class="Keyword">public</a> <a id="3786" class="Keyword">hiding</a> <a id="3793" class="Symbol">(</a><a id="3794" class="Keyword">module</a> <a id="3801" href="Relation.Binary.Structures.html#3745" class="Module">Eq</a><a id="3803" class="Symbol">)</a>
<a id="DecPoset.poset"></a><a id="3808" href="Relation.Binary.Bundles.html#3808" class="Function">poset</a> <a id="3814" class="Symbol">:</a> <a id="3816" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="3822" href="Relation.Binary.Bundles.html#3480" class="Bound">c</a> <a id="3824" href="Relation.Binary.Bundles.html#3482" class="Bound">ℓ₁</a> <a id="3827" href="Relation.Binary.Bundles.html#3485" class="Bound">ℓ₂</a>
<a id="3832" href="Relation.Binary.Bundles.html#3808" class="Function">poset</a> <a id="3838" class="Symbol">=</a> <a id="3840" class="Keyword">record</a>
<a id="3851" class="Symbol">{</a> <a id="3853" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="3868" class="Symbol">=</a> <a id="3870" href="Relation.Binary.Structures.html#3561" class="Function">isPartialOrder</a>
<a id="3889" class="Symbol">}</a>
<a id="3894" class="Keyword">open</a> <a id="3899" href="Relation.Binary.Bundles.html#3037" class="Module">Poset</a> <a id="3905" href="Relation.Binary.Bundles.html#3808" class="Function">poset</a> <a id="3911" class="Keyword">public</a>
<a id="3922" class="Keyword">using</a> <a id="3928" class="Symbol">(</a><a id="3929" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a><a id="3937" class="Symbol">)</a>
<a id="3942" class="Keyword">module</a> <a id="DecPoset.Eq"></a><a id="3949" href="Relation.Binary.Bundles.html#3949" class="Module">Eq</a> <a id="3952" class="Keyword">where</a>
<a id="DecPoset.Eq.decSetoid"></a><a id="3962" href="Relation.Binary.Bundles.html#3962" class="Function">decSetoid</a> <a id="3972" class="Symbol">:</a> <a id="3974" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="3984" href="Relation.Binary.Bundles.html#3480" class="Bound">c</a> <a id="3986" href="Relation.Binary.Bundles.html#3482" class="Bound">ℓ₁</a>
<a id="3993" href="Relation.Binary.Bundles.html#3962" class="Function">decSetoid</a> <a id="4003" class="Symbol">=</a> <a id="4005" class="Keyword">record</a>
<a id="4018" class="Symbol">{</a> <a id="4020" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="4037" class="Symbol">=</a> <a id="4039" href="Relation.Binary.Structures.html#3759" class="Function">DPO.Eq.isDecEquivalence</a>
<a id="4069" class="Symbol">}</a>
<a id="4076" class="Keyword">open</a> <a id="4081" href="Relation.Binary.Bundles.html#1400" class="Module">DecSetoid</a> <a id="4091" href="Relation.Binary.Bundles.html#3962" class="Function">decSetoid</a> <a id="4101" class="Keyword">public</a>
<a id="4110" class="Keyword">record</a> <a id="StrictPartialOrder"></a><a id="4117" href="Relation.Binary.Bundles.html#4117" class="Record">StrictPartialOrder</a> <a id="4136" href="Relation.Binary.Bundles.html#4136" class="Bound">c</a> <a id="4138" href="Relation.Binary.Bundles.html#4138" class="Bound">ℓ₁</a> <a id="4141" href="Relation.Binary.Bundles.html#4141" class="Bound">ℓ₂</a> <a id="4144" class="Symbol">:</a> <a id="4146" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="4150" class="Symbol">(</a><a id="4151" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="4155" class="Symbol">(</a><a id="4156" href="Relation.Binary.Bundles.html#4136" class="Bound">c</a> <a id="4158" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="4160" href="Relation.Binary.Bundles.html#4138" class="Bound">ℓ₁</a> <a id="4163" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="4165" href="Relation.Binary.Bundles.html#4141" class="Bound">ℓ₂</a><a id="4167" class="Symbol">))</a> <a id="4170" class="Keyword">where</a>
<a id="4178" class="Keyword">infix</a> <a id="4184" class="Number">4</a> <a id="4186" href="Relation.Binary.Bundles.html#4239" class="Field Operator">_≈_</a> <a id="4190" href="Relation.Binary.Bundles.html#4281" class="Field Operator">_&lt;_</a>
<a id="4196" class="Keyword">field</a>
<a id="StrictPartialOrder.Carrier"></a><a id="4206" href="Relation.Binary.Bundles.html#4206" class="Field">Carrier</a> <a id="4227" class="Symbol">:</a> <a id="4229" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="4233" href="Relation.Binary.Bundles.html#4136" class="Bound">c</a>
<a id="StrictPartialOrder._≈_"></a><a id="4239" href="Relation.Binary.Bundles.html#4239" class="Field Operator">_≈_</a> <a id="4260" class="Symbol">:</a> <a id="4262" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="4266" href="Relation.Binary.Bundles.html#4206" class="Field">Carrier</a> <a id="4274" href="Relation.Binary.Bundles.html#4138" class="Bound">ℓ₁</a>
<a id="StrictPartialOrder._&lt;_"></a><a id="4281" href="Relation.Binary.Bundles.html#4281" class="Field Operator">_&lt;_</a> <a id="4302" class="Symbol">:</a> <a id="4304" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="4308" href="Relation.Binary.Bundles.html#4206" class="Field">Carrier</a> <a id="4316" href="Relation.Binary.Bundles.html#4141" class="Bound">ℓ₂</a>
<a id="StrictPartialOrder.isStrictPartialOrder"></a><a id="4323" href="Relation.Binary.Bundles.html#4323" class="Field">isStrictPartialOrder</a> <a id="4344" class="Symbol">:</a> <a id="4346" href="Relation.Binary.Structures.html#3959" class="Record">IsStrictPartialOrder</a> <a id="4367" href="Relation.Binary.Bundles.html#4239" class="Field Operator">_≈_</a> <a id="4371" href="Relation.Binary.Bundles.html#4281" class="Field Operator">_&lt;_</a>
<a id="4378" class="Keyword">open</a> <a id="4383" href="Relation.Binary.Structures.html#3959" class="Module">IsStrictPartialOrder</a> <a id="4404" href="Relation.Binary.Bundles.html#4323" class="Field">isStrictPartialOrder</a> <a id="4425" class="Keyword">public</a>
<a id="4436" class="Keyword">hiding</a> <a id="4443" class="Symbol">(</a><a id="4444" class="Keyword">module</a> <a id="4451" href="Relation.Binary.Structures.html#4187" class="Module">Eq</a><a id="4453" class="Symbol">)</a>
<a id="4458" class="Keyword">module</a> <a id="StrictPartialOrder.Eq"></a><a id="4465" href="Relation.Binary.Bundles.html#4465" class="Module">Eq</a> <a id="4468" class="Keyword">where</a>
<a id="StrictPartialOrder.Eq.setoid"></a><a id="4478" href="Relation.Binary.Bundles.html#4478" class="Function">setoid</a> <a id="4485" class="Symbol">:</a> <a id="4487" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="4494" href="Relation.Binary.Bundles.html#4136" class="Bound">c</a> <a id="4496" href="Relation.Binary.Bundles.html#4138" class="Bound">ℓ₁</a>
<a id="4503" href="Relation.Binary.Bundles.html#4478" class="Function">setoid</a> <a id="4510" class="Symbol">=</a> <a id="4512" class="Keyword">record</a>
<a id="4525" class="Symbol">{</a> <a id="4527" href="Relation.Binary.Bundles.html#1141" class="Field">isEquivalence</a> <a id="4541" class="Symbol">=</a> <a id="4543" href="Relation.Binary.Structures.html#4034" class="Function">isEquivalence</a>
<a id="4563" class="Symbol">}</a>
<a id="4570" class="Keyword">open</a> <a id="4575" href="Relation.Binary.Bundles.html#1018" class="Module">Setoid</a> <a id="4582" href="Relation.Binary.Bundles.html#4478" class="Function">setoid</a> <a id="4589" class="Keyword">public</a>
<a id="4598" class="Keyword">record</a> <a id="DecStrictPartialOrder"></a><a id="4605" href="Relation.Binary.Bundles.html#4605" class="Record">DecStrictPartialOrder</a> <a id="4627" href="Relation.Binary.Bundles.html#4627" class="Bound">c</a> <a id="4629" href="Relation.Binary.Bundles.html#4629" class="Bound">ℓ₁</a> <a id="4632" href="Relation.Binary.Bundles.html#4632" class="Bound">ℓ₂</a> <a id="4635" class="Symbol">:</a> <a id="4637" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="4641" class="Symbol">(</a><a id="4642" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="4646" class="Symbol">(</a><a id="4647" href="Relation.Binary.Bundles.html#4627" class="Bound">c</a> <a id="4649" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="4651" href="Relation.Binary.Bundles.html#4629" class="Bound">ℓ₁</a> <a id="4654" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="4656" href="Relation.Binary.Bundles.html#4632" class="Bound">ℓ₂</a><a id="4658" class="Symbol">))</a> <a id="4661" class="Keyword">where</a>
<a id="4669" class="Keyword">infix</a> <a id="4675" class="Number">4</a> <a id="4677" href="Relation.Binary.Bundles.html#4733" class="Field Operator">_≈_</a> <a id="4681" href="Relation.Binary.Bundles.html#4778" class="Field Operator">_&lt;_</a>
<a id="4687" class="Keyword">field</a>
<a id="DecStrictPartialOrder.Carrier"></a><a id="4697" href="Relation.Binary.Bundles.html#4697" class="Field">Carrier</a> <a id="4721" class="Symbol">:</a> <a id="4723" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="4727" href="Relation.Binary.Bundles.html#4627" class="Bound">c</a>
<a id="DecStrictPartialOrder._≈_"></a><a id="4733" href="Relation.Binary.Bundles.html#4733" class="Field Operator">_≈_</a> <a id="4757" class="Symbol">:</a> <a id="4759" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="4763" href="Relation.Binary.Bundles.html#4697" class="Field">Carrier</a> <a id="4771" href="Relation.Binary.Bundles.html#4629" class="Bound">ℓ₁</a>
<a id="DecStrictPartialOrder._&lt;_"></a><a id="4778" href="Relation.Binary.Bundles.html#4778" class="Field Operator">_&lt;_</a> <a id="4802" class="Symbol">:</a> <a id="4804" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="4808" href="Relation.Binary.Bundles.html#4697" class="Field">Carrier</a> <a id="4816" href="Relation.Binary.Bundles.html#4632" class="Bound">ℓ₂</a>
<a id="DecStrictPartialOrder.isDecStrictPartialOrder"></a><a id="4823" href="Relation.Binary.Bundles.html#4823" class="Field">isDecStrictPartialOrder</a> <a id="4847" class="Symbol">:</a> <a id="4849" href="Relation.Binary.Structures.html#4580" class="Record">IsDecStrictPartialOrder</a> <a id="4873" href="Relation.Binary.Bundles.html#4733" class="Field Operator">_≈_</a> <a id="4877" href="Relation.Binary.Bundles.html#4778" class="Field Operator">_&lt;_</a>
<a id="4884" class="Keyword">private</a>
<a id="4896" class="Keyword">module</a> <a id="DecStrictPartialOrder.DSPO"></a><a id="4903" href="Relation.Binary.Bundles.html#4903" class="Module">DSPO</a> <a id="4908" class="Symbol">=</a> <a id="4910" href="Relation.Binary.Structures.html#4580" class="Module">IsDecStrictPartialOrder</a> <a id="4934" href="Relation.Binary.Bundles.html#4823" class="Field">isDecStrictPartialOrder</a>
<a id="4960" class="Keyword">open</a> <a id="4965" href="Relation.Binary.Bundles.html#4903" class="Module">DSPO</a> <a id="4970" class="Keyword">public</a> <a id="4977" class="Keyword">hiding</a> <a id="4984" class="Symbol">(</a><a id="4985" class="Keyword">module</a> <a id="4992" href="Relation.Binary.Structures.html#4925" class="Module">Eq</a><a id="4994" class="Symbol">)</a>
<a id="DecStrictPartialOrder.strictPartialOrder"></a><a id="4999" href="Relation.Binary.Bundles.html#4999" class="Function">strictPartialOrder</a> <a id="5018" class="Symbol">:</a> <a id="5020" href="Relation.Binary.Bundles.html#4117" class="Record">StrictPartialOrder</a> <a id="5039" href="Relation.Binary.Bundles.html#4627" class="Bound">c</a> <a id="5041" href="Relation.Binary.Bundles.html#4629" class="Bound">ℓ₁</a> <a id="5044" href="Relation.Binary.Bundles.html#4632" class="Bound">ℓ₂</a>
<a id="5049" href="Relation.Binary.Bundles.html#4999" class="Function">strictPartialOrder</a> <a id="5068" class="Symbol">=</a> <a id="5070" class="Keyword">record</a>
<a id="5081" class="Symbol">{</a> <a id="5083" href="Relation.Binary.Bundles.html#4323" class="Field">isStrictPartialOrder</a> <a id="5104" class="Symbol">=</a> <a id="5106" href="Relation.Binary.Structures.html#4677" class="Function">isStrictPartialOrder</a>
<a id="5131" class="Symbol">}</a>
<a id="5136" class="Keyword">module</a> <a id="DecStrictPartialOrder.Eq"></a><a id="5143" href="Relation.Binary.Bundles.html#5143" class="Module">Eq</a> <a id="5146" class="Keyword">where</a>
<a id="DecStrictPartialOrder.Eq.decSetoid"></a><a id="5157" href="Relation.Binary.Bundles.html#5157" class="Function">decSetoid</a> <a id="5167" class="Symbol">:</a> <a id="5169" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="5179" href="Relation.Binary.Bundles.html#4627" class="Bound">c</a> <a id="5181" href="Relation.Binary.Bundles.html#4629" class="Bound">ℓ₁</a>
<a id="5188" href="Relation.Binary.Bundles.html#5157" class="Function">decSetoid</a> <a id="5198" class="Symbol">=</a> <a id="5200" class="Keyword">record</a>
<a id="5213" class="Symbol">{</a> <a id="5215" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="5232" class="Symbol">=</a> <a id="5234" href="Relation.Binary.Structures.html#4939" class="Function">DSPO.Eq.isDecEquivalence</a>
<a id="5265" class="Symbol">}</a>
<a id="5272" class="Keyword">open</a> <a id="5277" href="Relation.Binary.Bundles.html#1400" class="Module">DecSetoid</a> <a id="5287" href="Relation.Binary.Bundles.html#5157" class="Function">decSetoid</a> <a id="5297" class="Keyword">public</a>
<a id="5306" class="Comment">------------------------------------------------------------------------</a>
<a id="5379" class="Comment">-- Total orders</a>
<a id="5395" class="Comment">------------------------------------------------------------------------</a>
<a id="5469" class="Keyword">record</a> <a id="TotalOrder"></a><a id="5476" href="Relation.Binary.Bundles.html#5476" class="Record">TotalOrder</a> <a id="5487" href="Relation.Binary.Bundles.html#5487" class="Bound">c</a> <a id="5489" href="Relation.Binary.Bundles.html#5489" class="Bound">ℓ₁</a> <a id="5492" href="Relation.Binary.Bundles.html#5492" class="Bound">ℓ₂</a> <a id="5495" class="Symbol">:</a> <a id="5497" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="5501" class="Symbol">(</a><a id="5502" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="5506" class="Symbol">(</a><a id="5507" href="Relation.Binary.Bundles.html#5487" class="Bound">c</a> <a id="5509" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="5511" href="Relation.Binary.Bundles.html#5489" class="Bound">ℓ₁</a> <a id="5514" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="5516" href="Relation.Binary.Bundles.html#5492" class="Bound">ℓ₂</a><a id="5518" class="Symbol">))</a> <a id="5521" class="Keyword">where</a>
<a id="5529" class="Keyword">infix</a> <a id="5535" class="Number">4</a> <a id="5537" href="Relation.Binary.Bundles.html#5582" class="Field Operator">_≈_</a> <a id="5541" href="Relation.Binary.Bundles.html#5616" class="Field Operator">_≤_</a>
<a id="5547" class="Keyword">field</a>
<a id="TotalOrder.Carrier"></a><a id="5557" href="Relation.Binary.Bundles.html#5557" class="Field">Carrier</a> <a id="5570" class="Symbol">:</a> <a id="5572" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="5576" href="Relation.Binary.Bundles.html#5487" class="Bound">c</a>
<a id="TotalOrder._≈_"></a><a id="5582" href="Relation.Binary.Bundles.html#5582" class="Field Operator">_≈_</a> <a id="5595" class="Symbol">:</a> <a id="5597" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="5601" href="Relation.Binary.Bundles.html#5557" class="Field">Carrier</a> <a id="5609" href="Relation.Binary.Bundles.html#5489" class="Bound">ℓ₁</a>
<a id="TotalOrder._≤_"></a><a id="5616" href="Relation.Binary.Bundles.html#5616" class="Field Operator">_≤_</a> <a id="5629" class="Symbol">:</a> <a id="5631" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="5635" href="Relation.Binary.Bundles.html#5557" class="Field">Carrier</a> <a id="5643" href="Relation.Binary.Bundles.html#5492" class="Bound">ℓ₂</a>
<a id="TotalOrder.isTotalOrder"></a><a id="5650" href="Relation.Binary.Bundles.html#5650" class="Field">isTotalOrder</a> <a id="5663" class="Symbol">:</a> <a id="5665" href="Relation.Binary.Structures.html#5306" class="Record">IsTotalOrder</a> <a id="5678" href="Relation.Binary.Bundles.html#5582" class="Field Operator">_≈_</a> <a id="5682" href="Relation.Binary.Bundles.html#5616" class="Field Operator">_≤_</a>
<a id="5689" class="Keyword">open</a> <a id="5694" href="Relation.Binary.Structures.html#5306" class="Module">IsTotalOrder</a> <a id="5707" href="Relation.Binary.Bundles.html#5650" class="Field">isTotalOrder</a> <a id="5720" class="Keyword">public</a>
<a id="5731" class="Keyword">hiding</a> <a id="5738" class="Symbol">(</a><a id="5739" class="Keyword">module</a> <a id="5746" href="Relation.Binary.Structures.html#2411" class="Module">Eq</a><a id="5748" class="Symbol">)</a>
<a id="TotalOrder.poset"></a><a id="5753" href="Relation.Binary.Bundles.html#5753" class="Function">poset</a> <a id="5759" class="Symbol">:</a> <a id="5761" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="5767" href="Relation.Binary.Bundles.html#5487" class="Bound">c</a> <a id="5769" href="Relation.Binary.Bundles.html#5489" class="Bound">ℓ₁</a> <a id="5772" href="Relation.Binary.Bundles.html#5492" class="Bound">ℓ₂</a>
<a id="5777" href="Relation.Binary.Bundles.html#5753" class="Function">poset</a> <a id="5783" class="Symbol">=</a> <a id="5785" class="Keyword">record</a>
<a id="5796" class="Symbol">{</a> <a id="5798" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="5813" class="Symbol">=</a> <a id="5815" href="Relation.Binary.Structures.html#5373" class="Function">isPartialOrder</a>
<a id="5834" class="Symbol">}</a>
<a id="5839" class="Keyword">open</a> <a id="5844" href="Relation.Binary.Bundles.html#3037" class="Module">Poset</a> <a id="5850" href="Relation.Binary.Bundles.html#5753" class="Function">poset</a> <a id="5856" class="Keyword">public</a>
<a id="5867" class="Keyword">using</a> <a id="5873" class="Symbol">(</a><a id="5874" class="Keyword">module</a> <a id="5881" href="Relation.Binary.Bundles.html#2244" class="Module">Eq</a><a id="5883" class="Symbol">;</a> <a id="5885" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a><a id="5893" class="Symbol">)</a>
<a id="TotalOrder.totalPreorder"></a><a id="5898" href="Relation.Binary.Bundles.html#5898" class="Function">totalPreorder</a> <a id="5912" class="Symbol">:</a> <a id="5914" href="Relation.Binary.Bundles.html#2384" class="Record">TotalPreorder</a> <a id="5928" href="Relation.Binary.Bundles.html#5487" class="Bound">c</a> <a id="5930" href="Relation.Binary.Bundles.html#5489" class="Bound">ℓ₁</a> <a id="5933" href="Relation.Binary.Bundles.html#5492" class="Bound">ℓ₂</a>
<a id="5938" href="Relation.Binary.Bundles.html#5898" class="Function">totalPreorder</a> <a id="5952" class="Symbol">=</a> <a id="5954" class="Keyword">record</a>
<a id="5965" class="Symbol">{</a> <a id="5967" href="Relation.Binary.Bundles.html#2617" class="Field">isTotalPreorder</a> <a id="5983" class="Symbol">=</a> <a id="5985" href="Relation.Binary.Structures.html#5488" class="Function">isTotalPreorder</a>
<a id="6005" class="Symbol">}</a>
<a id="6009" class="Keyword">record</a> <a id="DecTotalOrder"></a><a id="6016" href="Relation.Binary.Bundles.html#6016" class="Record">DecTotalOrder</a> <a id="6030" href="Relation.Binary.Bundles.html#6030" class="Bound">c</a> <a id="6032" href="Relation.Binary.Bundles.html#6032" class="Bound">ℓ₁</a> <a id="6035" href="Relation.Binary.Bundles.html#6035" class="Bound">ℓ₂</a> <a id="6038" class="Symbol">:</a> <a id="6040" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="6044" class="Symbol">(</a><a id="6045" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="6049" class="Symbol">(</a><a id="6050" href="Relation.Binary.Bundles.html#6030" class="Bound">c</a> <a id="6052" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="6054" href="Relation.Binary.Bundles.html#6032" class="Bound">ℓ₁</a> <a id="6057" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="6059" href="Relation.Binary.Bundles.html#6035" class="Bound">ℓ₂</a><a id="6061" class="Symbol">))</a> <a id="6064" class="Keyword">where</a>
<a id="6072" class="Keyword">infix</a> <a id="6078" class="Number">4</a> <a id="6080" href="Relation.Binary.Bundles.html#6128" class="Field Operator">_≈_</a> <a id="6084" href="Relation.Binary.Bundles.html#6165" class="Field Operator">_≤_</a>
<a id="6090" class="Keyword">field</a>
<a id="DecTotalOrder.Carrier"></a><a id="6100" href="Relation.Binary.Bundles.html#6100" class="Field">Carrier</a> <a id="6116" class="Symbol">:</a> <a id="6118" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="6122" href="Relation.Binary.Bundles.html#6030" class="Bound">c</a>
<a id="DecTotalOrder._≈_"></a><a id="6128" href="Relation.Binary.Bundles.html#6128" class="Field Operator">_≈_</a> <a id="6144" class="Symbol">:</a> <a id="6146" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="6150" href="Relation.Binary.Bundles.html#6100" class="Field">Carrier</a> <a id="6158" href="Relation.Binary.Bundles.html#6032" class="Bound">ℓ₁</a>
<a id="DecTotalOrder._≤_"></a><a id="6165" href="Relation.Binary.Bundles.html#6165" class="Field Operator">_≤_</a> <a id="6181" class="Symbol">:</a> <a id="6183" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="6187" href="Relation.Binary.Bundles.html#6100" class="Field">Carrier</a> <a id="6195" href="Relation.Binary.Bundles.html#6035" class="Bound">ℓ₂</a>
<a id="DecTotalOrder.isDecTotalOrder"></a><a id="6202" href="Relation.Binary.Bundles.html#6202" class="Field">isDecTotalOrder</a> <a id="6218" class="Symbol">:</a> <a id="6220" href="Relation.Binary.Structures.html#5623" class="Record">IsDecTotalOrder</a> <a id="6236" href="Relation.Binary.Bundles.html#6128" class="Field Operator">_≈_</a> <a id="6240" href="Relation.Binary.Bundles.html#6165" class="Field Operator">_≤_</a>
<a id="6247" class="Keyword">private</a>
<a id="6259" class="Keyword">module</a> <a id="DecTotalOrder.DTO"></a><a id="6266" href="Relation.Binary.Bundles.html#6266" class="Module">DTO</a> <a id="6270" class="Symbol">=</a> <a id="6272" href="Relation.Binary.Structures.html#5623" class="Module">IsDecTotalOrder</a> <a id="6288" href="Relation.Binary.Bundles.html#6202" class="Field">isDecTotalOrder</a>
<a id="6306" class="Keyword">open</a> <a id="6311" href="Relation.Binary.Bundles.html#6266" class="Module">DTO</a> <a id="6315" class="Keyword">public</a> <a id="6322" class="Keyword">hiding</a> <a id="6329" class="Symbol">(</a><a id="6330" class="Keyword">module</a> <a id="6337" href="Relation.Binary.Structures.html#6057" class="Module">Eq</a><a id="6339" class="Symbol">)</a>
<a id="DecTotalOrder.totalOrder"></a><a id="6344" href="Relation.Binary.Bundles.html#6344" class="Function">totalOrder</a> <a id="6355" class="Symbol">:</a> <a id="6357" href="Relation.Binary.Bundles.html#5476" class="Record">TotalOrder</a> <a id="6368" href="Relation.Binary.Bundles.html#6030" class="Bound">c</a> <a id="6370" href="Relation.Binary.Bundles.html#6032" class="Bound">ℓ₁</a> <a id="6373" href="Relation.Binary.Bundles.html#6035" class="Bound">ℓ₂</a>
<a id="6378" href="Relation.Binary.Bundles.html#6344" class="Function">totalOrder</a> <a id="6389" class="Symbol">=</a> <a id="6391" class="Keyword">record</a>
<a id="6402" class="Symbol">{</a> <a id="6404" href="Relation.Binary.Bundles.html#5650" class="Field">isTotalOrder</a> <a id="6417" class="Symbol">=</a> <a id="6419" href="Relation.Binary.Structures.html#5712" class="Function">isTotalOrder</a>
<a id="6436" class="Symbol">}</a>
<a id="6441" class="Keyword">open</a> <a id="6446" href="Relation.Binary.Bundles.html#5476" class="Module">TotalOrder</a> <a id="6457" href="Relation.Binary.Bundles.html#6344" class="Function">totalOrder</a> <a id="6468" class="Keyword">public</a> <a id="6475" class="Keyword">using</a> <a id="6481" class="Symbol">(</a><a id="6482" href="Relation.Binary.Bundles.html#5753" class="Function">poset</a><a id="6487" class="Symbol">;</a> <a id="6489" href="Relation.Binary.Bundles.html#3323" class="Function">preorder</a><a id="6497" class="Symbol">)</a>
<a id="DecTotalOrder.decPoset"></a><a id="6502" href="Relation.Binary.Bundles.html#6502" class="Function">decPoset</a> <a id="6511" class="Symbol">:</a> <a id="6513" href="Relation.Binary.Bundles.html#3471" class="Record">DecPoset</a> <a id="6522" href="Relation.Binary.Bundles.html#6030" class="Bound">c</a> <a id="6524" href="Relation.Binary.Bundles.html#6032" class="Bound">ℓ₁</a> <a id="6527" href="Relation.Binary.Bundles.html#6035" class="Bound">ℓ₂</a>
<a id="6532" href="Relation.Binary.Bundles.html#6502" class="Function">decPoset</a> <a id="6541" class="Symbol">=</a> <a id="6543" class="Keyword">record</a>
<a id="6554" class="Symbol">{</a> <a id="6556" href="Relation.Binary.Bundles.html#3658" class="Field">isDecPartialOrder</a> <a id="6574" class="Symbol">=</a> <a id="6576" href="Relation.Binary.Structures.html#5877" class="Function">isDecPartialOrder</a>
<a id="6598" class="Symbol">}</a>
<a id="6603" class="Keyword">open</a> <a id="6608" href="Relation.Binary.Bundles.html#3471" class="Module">DecPoset</a> <a id="6617" href="Relation.Binary.Bundles.html#6502" class="Function">decPoset</a> <a id="6626" class="Keyword">public</a> <a id="6633" class="Keyword">using</a> <a id="6639" class="Symbol">(</a><a id="6640" class="Keyword">module</a> <a id="6647" href="Relation.Binary.Bundles.html#3949" class="Module">Eq</a><a id="6649" class="Symbol">)</a>
<a id="6653" class="Comment">-- Note that these orders are decidable. The current implementation</a>
<a id="6721" class="Comment">-- of `Trichotomous` subsumes irreflexivity and asymmetry. Any reasonable</a>
<a id="6795" class="Comment">-- definition capturing these three properties implies decidability</a>
<a id="6863" class="Comment">-- as `Trichotomous` necessarily separates out the equality case.</a>
<a id="6930" class="Keyword">record</a> <a id="StrictTotalOrder"></a><a id="6937" href="Relation.Binary.Bundles.html#6937" class="Record">StrictTotalOrder</a> <a id="6954" href="Relation.Binary.Bundles.html#6954" class="Bound">c</a> <a id="6956" href="Relation.Binary.Bundles.html#6956" class="Bound">ℓ₁</a> <a id="6959" href="Relation.Binary.Bundles.html#6959" class="Bound">ℓ₂</a> <a id="6962" class="Symbol">:</a> <a id="6964" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="6968" class="Symbol">(</a><a id="6969" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="6973" class="Symbol">(</a><a id="6974" href="Relation.Binary.Bundles.html#6954" class="Bound">c</a> <a id="6976" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="6978" href="Relation.Binary.Bundles.html#6956" class="Bound">ℓ₁</a> <a id="6981" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="6983" href="Relation.Binary.Bundles.html#6959" class="Bound">ℓ₂</a><a id="6985" class="Symbol">))</a> <a id="6988" class="Keyword">where</a>
<a id="6996" class="Keyword">infix</a> <a id="7002" class="Number">4</a> <a id="7004" href="Relation.Binary.Bundles.html#7055" class="Field Operator">_≈_</a> <a id="7008" href="Relation.Binary.Bundles.html#7095" class="Field Operator">_&lt;_</a>
<a id="7014" class="Keyword">field</a>
<a id="StrictTotalOrder.Carrier"></a><a id="7024" href="Relation.Binary.Bundles.html#7024" class="Field">Carrier</a> <a id="7043" class="Symbol">:</a> <a id="7045" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="7049" href="Relation.Binary.Bundles.html#6954" class="Bound">c</a>
<a id="StrictTotalOrder._≈_"></a><a id="7055" href="Relation.Binary.Bundles.html#7055" class="Field Operator">_≈_</a> <a id="7074" class="Symbol">:</a> <a id="7076" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="7080" href="Relation.Binary.Bundles.html#7024" class="Field">Carrier</a> <a id="7088" href="Relation.Binary.Bundles.html#6956" class="Bound">ℓ₁</a>
<a id="StrictTotalOrder._&lt;_"></a><a id="7095" href="Relation.Binary.Bundles.html#7095" class="Field Operator">_&lt;_</a> <a id="7114" class="Symbol">:</a> <a id="7116" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="7120" href="Relation.Binary.Bundles.html#7024" class="Field">Carrier</a> <a id="7128" href="Relation.Binary.Bundles.html#6959" class="Bound">ℓ₂</a>
<a id="StrictTotalOrder.isStrictTotalOrder"></a><a id="7135" href="Relation.Binary.Bundles.html#7135" class="Field">isStrictTotalOrder</a> <a id="7154" class="Symbol">:</a> <a id="7156" href="Relation.Binary.Structures.html#6548" class="Record">IsStrictTotalOrder</a> <a id="7175" href="Relation.Binary.Bundles.html#7055" class="Field Operator">_≈_</a> <a id="7179" href="Relation.Binary.Bundles.html#7095" class="Field Operator">_&lt;_</a>
<a id="7186" class="Keyword">open</a> <a id="7191" href="Relation.Binary.Structures.html#6548" class="Module">IsStrictTotalOrder</a> <a id="7210" href="Relation.Binary.Bundles.html#7135" class="Field">isStrictTotalOrder</a> <a id="7229" class="Keyword">public</a>
<a id="7240" class="Keyword">hiding</a> <a id="7247" class="Symbol">(</a><a id="7248" class="Keyword">module</a> <a id="7255" href="Relation.Binary.Structures.html#6990" class="Module">Eq</a><a id="7257" class="Symbol">)</a>
<a id="StrictTotalOrder.strictPartialOrder"></a><a id="7262" href="Relation.Binary.Bundles.html#7262" class="Function">strictPartialOrder</a> <a id="7281" class="Symbol">:</a> <a id="7283" href="Relation.Binary.Bundles.html#4117" class="Record">StrictPartialOrder</a> <a id="7302" href="Relation.Binary.Bundles.html#6954" class="Bound">c</a> <a id="7304" href="Relation.Binary.Bundles.html#6956" class="Bound">ℓ₁</a> <a id="7307" href="Relation.Binary.Bundles.html#6959" class="Bound">ℓ₂</a>
<a id="7312" href="Relation.Binary.Bundles.html#7262" class="Function">strictPartialOrder</a> <a id="7331" class="Symbol">=</a> <a id="7333" class="Keyword">record</a>
<a id="7344" class="Symbol">{</a> <a id="7346" href="Relation.Binary.Bundles.html#4323" class="Field">isStrictPartialOrder</a> <a id="7367" class="Symbol">=</a> <a id="7369" href="Relation.Binary.Structures.html#7032" class="Function">isStrictPartialOrder</a>
<a id="7394" class="Symbol">}</a>
<a id="7399" class="Keyword">open</a> <a id="7404" href="Relation.Binary.Bundles.html#4117" class="Module">StrictPartialOrder</a> <a id="7423" href="Relation.Binary.Bundles.html#7262" class="Function">strictPartialOrder</a> <a id="7442" class="Keyword">public</a>
<a id="7453" class="Keyword">using</a> <a id="7459" class="Symbol">(</a><a id="7460" class="Keyword">module</a> <a id="7467" href="Relation.Binary.Bundles.html#4465" class="Module">Eq</a><a id="7469" class="Symbol">)</a>
<a id="StrictTotalOrder.decSetoid"></a><a id="7474" href="Relation.Binary.Bundles.html#7474" class="Function">decSetoid</a> <a id="7484" class="Symbol">:</a> <a id="7486" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="7496" href="Relation.Binary.Bundles.html#6954" class="Bound">c</a> <a id="7498" href="Relation.Binary.Bundles.html#6956" class="Bound">ℓ₁</a>
<a id="7503" href="Relation.Binary.Bundles.html#7474" class="Function">decSetoid</a> <a id="7513" class="Symbol">=</a> <a id="7515" class="Keyword">record</a>
<a id="7526" class="Symbol">{</a> <a id="7528" href="Relation.Binary.Bundles.html#1532" class="Field">isDecEquivalence</a> <a id="7545" class="Symbol">=</a> <a id="7547" href="Relation.Binary.Structures.html#6848" class="Function">isDecEquivalence</a>
<a id="7568" class="Symbol">}</a>
<a id="7572" class="Symbol">{-#</a> <a id="7576" class="Keyword">WARNING_ON_USAGE</a> <a id="7593" class="Pragma">decSetoid</a>
<a id="7605" class="String">&quot;Warning: decSetoid was deprecated in v1.3.
Please use Eq.decSetoid instead.&quot;</a>
<a id="7687" class="Symbol">#-}</a>
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