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<html><head><meta charset="utf-8"><title>Data.Unit.Properties</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">-- Properties of the unit type</a>
<a id="137" class="Comment">------------------------------------------------------------------------</a>
<a id="211" class="Symbol">{-#</a> <a id="215" class="Keyword">OPTIONS</a> <a id="223" class="Pragma">--cubical-compatible</a> <a id="244" class="Pragma">--safe</a> <a id="251" class="Symbol">#-}</a>
<a id="256" class="Comment">-- Disabled to prevent warnings from deprecation warnings for _≤_</a>
<a id="322" class="Symbol">{-#</a> <a id="326" class="Keyword">OPTIONS</a> <a id="334" class="Pragma">--warn=noUserWarning</a> <a id="355" class="Symbol">#-}</a>
<a id="360" class="Keyword">module</a> <a id="367" href="Data.Unit.Properties.html" class="Module">Data.Unit.Properties</a> <a id="388" class="Keyword">where</a>
<a id="395" class="Keyword">open</a> <a id="400" class="Keyword">import</a> <a id="407" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a>
<a id="421" class="Keyword">open</a> <a id="426" class="Keyword">import</a> <a id="433" href="Data.Unit.Base.html" class="Module">Data.Unit.Base</a>
<a id="448" class="Keyword">open</a> <a id="453" class="Keyword">import</a> <a id="460" href="Level.html" class="Module">Level</a> <a id="466" class="Keyword">using</a> <a id="472" class="Symbol">(</a><a id="473" href="Level.html#521" class="Function">0ℓ</a><a id="475" class="Symbol">)</a>
<a id="477" class="Keyword">open</a> <a id="482" class="Keyword">import</a> <a id="489" href="Relation.Nullary.html" class="Module">Relation.Nullary</a>
<a id="506" class="Keyword">open</a> <a id="511" class="Keyword">import</a> <a id="518" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="534" class="Keyword">hiding</a> <a id="541" class="Symbol">(</a><a id="542" href="Relation.Binary.Definitions.html#5074" class="Function">Irrelevant</a><a id="552" class="Symbol">)</a>
<a id="554" class="Keyword">open</a> <a id="559" class="Keyword">import</a> <a id="566" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a>
<a id="605" class="Comment">------------------------------------------------------------------------</a>
<a id="678" class="Comment">-- Irrelevancy</a>
<a id="⊤-irrelevant"></a><a id="694" href="Data.Unit.Properties.html#694" class="Function">⊤-irrelevant</a> <a id="707" class="Symbol">:</a> <a id="709" href="Relation.Nullary.html#2049" class="Function">Irrelevant</a> <a id="720" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a>
<a id="722" href="Data.Unit.Properties.html#694" class="Function">⊤-irrelevant</a> <a id="735" class="Symbol">_</a> <a id="737" class="Symbol">_</a> <a id="739" class="Symbol">=</a> <a id="741" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a>
<a id="747" class="Comment">------------------------------------------------------------------------</a>
<a id="820" class="Comment">-- Equality</a>
<a id="833" class="Keyword">infix</a> <a id="839" class="Number">4</a> <a id="841" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a>
<a id="_≟_"></a><a id="846" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a> <a id="850" class="Symbol">:</a> <a id="852" href="Relation.Binary.Definitions.html#4584" class="Function">Decidable</a> <a id="862" class="Symbol">{</a><a id="863" class="Argument">A</a> <a id="865" class="Symbol">=</a> <a id="867" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a><a id="868" class="Symbol">}</a> <a id="870" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="874" class="Symbol">_</a> <a id="876" href="Data.Unit.Properties.html#846" class="Function Operator">≟</a> <a id="878" class="Symbol">_</a> <a id="880" class="Symbol">=</a> <a id="882" href="Relation.Nullary.html#1657" class="InductiveConstructor">yes</a> <a id="886" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a>
<a id="≡-setoid"></a><a id="892" href="Data.Unit.Properties.html#892" class="Function">≡-setoid</a> <a id="901" class="Symbol">:</a> <a id="903" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="910" href="Level.html#521" class="Function">0ℓ</a> <a id="913" href="Level.html#521" class="Function">0ℓ</a>
<a id="916" href="Data.Unit.Properties.html#892" class="Function">≡-setoid</a> <a id="925" class="Symbol">=</a> <a id="927" href="Relation.Binary.PropositionalEquality.Properties.html#3981" class="Function">setoid</a> <a id="934" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a>
<a id="≡-decSetoid"></a><a id="937" href="Data.Unit.Properties.html#937" class="Function">≡-decSetoid</a> <a id="949" class="Symbol">:</a> <a id="951" href="Relation.Binary.Bundles.html#1400" class="Record">DecSetoid</a> <a id="961" href="Level.html#521" class="Function">0ℓ</a> <a id="964" href="Level.html#521" class="Function">0ℓ</a>
<a id="967" href="Data.Unit.Properties.html#937" class="Function">≡-decSetoid</a> <a id="979" class="Symbol">=</a> <a id="981" href="Relation.Binary.PropositionalEquality.Properties.html#4112" class="Function">decSetoid</a> <a id="991" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a>
<a id="996" class="Comment">------------------------------------------------------------------------</a>
<a id="1069" class="Comment">-- Relational properties</a>
<a id="≡-total"></a><a id="1095" href="Data.Unit.Properties.html#1095" class="Function">≡-total</a> <a id="1103" class="Symbol">:</a> <a id="1105" href="Relation.Binary.Definitions.html#2593" class="Function">Total</a> <a id="1111" class="Symbol">{</a><a id="1112" class="Argument">A</a> <a id="1114" class="Symbol">=</a> <a id="1116" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a><a id="1117" class="Symbol">}</a> <a id="1119" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1123" href="Data.Unit.Properties.html#1095" class="Function">≡-total</a> <a id="1131" class="Symbol">_</a> <a id="1133" class="Symbol">_</a> <a id="1135" class="Symbol">=</a> <a id="1137" href="Data.Sum.Base.html#793" class="InductiveConstructor">inj₁</a> <a id="1142" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a>
<a id="≡-antisym"></a><a id="1148" href="Data.Unit.Properties.html#1148" class="Function">≡-antisym</a> <a id="1158" class="Symbol">:</a> <a id="1160" href="Relation.Binary.Definitions.html#2091" class="Function">Antisymmetric</a> <a id="1174" class="Symbol">{</a><a id="1175" class="Argument">A</a> <a id="1177" class="Symbol">=</a> <a id="1179" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a><a id="1180" class="Symbol">}</a> <a id="1182" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="1186" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1190" href="Data.Unit.Properties.html#1148" class="Function">≡-antisym</a> <a id="1200" href="Data.Unit.Properties.html#1200" class="Bound">eq</a> <a id="1203" class="Symbol">_</a> <a id="1205" class="Symbol">=</a> <a id="1207" href="Data.Unit.Properties.html#1200" class="Bound">eq</a>
<a id="1211" class="Comment">------------------------------------------------------------------------</a>
<a id="1284" class="Comment">-- Structures</a>
<a id="≡-isPreorder"></a><a id="1299" href="Data.Unit.Properties.html#1299" class="Function">≡-isPreorder</a> <a id="1312" class="Symbol">:</a> <a id="1314" href="Relation.Binary.Structures.html#2172" class="Record">IsPreorder</a> <a id="1325" class="Symbol">{</a><a id="1326" class="Argument">A</a> <a id="1328" class="Symbol">=</a> <a id="1330" href="Agda.Builtin.Unit.html#158" class="Record">⊤</a><a id="1331" class="Symbol">}</a> <a id="1333" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="1337" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1341" href="Data.Unit.Properties.html#1299" class="Function">≡-isPreorder</a> <a id="1354" class="Symbol">=</a> <a id="1356" class="Keyword">record</a>
<a id="1365" class="Symbol">{</a> <a id="1367" href="Relation.Binary.Structures.html#2237" class="Field">isEquivalence</a> <a id="1381" class="Symbol">=</a> <a id="1383" href="Relation.Binary.PropositionalEquality.Properties.html#3436" class="Function">isEquivalence</a>
<a id="1399" class="Symbol">;</a> <a id="1401" href="Relation.Binary.Structures.html#2340" class="Field">reflexive</a> <a id="1415" class="Symbol">=</a> <a id="1417" class="Symbol">λ</a> <a id="1419" href="Data.Unit.Properties.html#1419" class="Bound">x</a> <a id="1421" class="Symbol">→</a> <a id="1423" href="Data.Unit.Properties.html#1419" class="Bound">x</a>
<a id="1427" class="Symbol">;</a> <a id="1429" href="Relation.Binary.Structures.html#2370" class="Field">trans</a> <a id="1443" class="Symbol">=</a> <a id="1445" href="Relation.Binary.PropositionalEquality.Core.html#1738" class="Function">trans</a>
<a id="1453" class="Symbol">}</a>
<a id="≡-isPartialOrder"></a><a id="1456" href="Data.Unit.Properties.html#1456" class="Function">≡-isPartialOrder</a> <a id="1473" class="Symbol">:</a> <a id="1475" href="Relation.Binary.Structures.html#3183" class="Record">IsPartialOrder</a> <a id="1490" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="1494" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1498" href="Data.Unit.Properties.html#1456" class="Function">≡-isPartialOrder</a> <a id="1515" class="Symbol">=</a> <a id="1517" class="Keyword">record</a>
<a id="1526" class="Symbol">{</a> <a id="1528" href="Relation.Binary.Structures.html#3252" class="Field">isPreorder</a> <a id="1539" class="Symbol">=</a> <a id="1541" href="Data.Unit.Properties.html#1299" class="Function">≡-isPreorder</a>
<a id="1556" class="Symbol">;</a> <a id="1558" href="Relation.Binary.Structures.html#3284" class="Field">antisym</a> <a id="1569" class="Symbol">=</a> <a id="1571" href="Data.Unit.Properties.html#1148" class="Function">≡-antisym</a>
<a id="1583" class="Symbol">}</a>
<a id="≡-isTotalOrder"></a><a id="1586" href="Data.Unit.Properties.html#1586" class="Function">≡-isTotalOrder</a> <a id="1601" class="Symbol">:</a> <a id="1603" href="Relation.Binary.Structures.html#5306" class="Record">IsTotalOrder</a> <a id="1616" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="1620" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1624" href="Data.Unit.Properties.html#1586" class="Function">≡-isTotalOrder</a> <a id="1639" class="Symbol">=</a> <a id="1641" class="Keyword">record</a>
<a id="1650" class="Symbol">{</a> <a id="1652" href="Relation.Binary.Structures.html#5373" class="Field">isPartialOrder</a> <a id="1667" class="Symbol">=</a> <a id="1669" href="Data.Unit.Properties.html#1456" class="Function">≡-isPartialOrder</a>
<a id="1688" class="Symbol">;</a> <a id="1690" href="Relation.Binary.Structures.html#5413" class="Field">total</a> <a id="1705" class="Symbol">=</a> <a id="1707" href="Data.Unit.Properties.html#1095" class="Function">≡-total</a>
<a id="1717" class="Symbol">}</a>
<a id="≡-isDecTotalOrder"></a><a id="1720" href="Data.Unit.Properties.html#1720" class="Function">≡-isDecTotalOrder</a> <a id="1738" class="Symbol">:</a> <a id="1740" href="Relation.Binary.Structures.html#5623" class="Record">IsDecTotalOrder</a> <a id="1756" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="1760" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a>
<a id="1764" href="Data.Unit.Properties.html#1720" class="Function">≡-isDecTotalOrder</a> <a id="1782" class="Symbol">=</a> <a id="1784" class="Keyword">record</a>
<a id="1793" class="Symbol">{</a> <a id="1795" href="Relation.Binary.Structures.html#5712" class="Field">isTotalOrder</a> <a id="1808" class="Symbol">=</a> <a id="1810" href="Data.Unit.Properties.html#1586" class="Function">≡-isTotalOrder</a>
<a id="1827" class="Symbol">;</a> <a id="1829" href="Relation.Binary.Structures.html#5748" class="Field Operator">_≟_</a> <a id="1842" class="Symbol">=</a> <a id="1844" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a>
<a id="1850" class="Symbol">;</a> <a id="1852" href="Relation.Binary.Structures.html#5781" class="Field Operator">_≤?_</a> <a id="1865" class="Symbol">=</a> <a id="1867" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a>
<a id="1873" class="Symbol">}</a>
<a id="1876" class="Comment">------------------------------------------------------------------------</a>
<a id="1949" class="Comment">-- Bundles</a>
<a id="≡-poset"></a><a id="1961" href="Data.Unit.Properties.html#1961" class="Function">≡-poset</a> <a id="1969" class="Symbol">:</a> <a id="1971" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="1977" href="Level.html#521" class="Function">0ℓ</a> <a id="1980" href="Level.html#521" class="Function">0ℓ</a> <a id="1983" href="Level.html#521" class="Function">0ℓ</a>
<a id="1986" href="Data.Unit.Properties.html#1961" class="Function">≡-poset</a> <a id="1994" class="Symbol">=</a> <a id="1996" class="Keyword">record</a>
<a id="2005" class="Symbol">{</a> <a id="2007" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="2022" class="Symbol">=</a> <a id="2024" href="Data.Unit.Properties.html#1456" class="Function">≡-isPartialOrder</a>
<a id="2043" class="Symbol">}</a>
<a id="≡-decTotalOrder"></a><a id="2046" href="Data.Unit.Properties.html#2046" class="Function">≡-decTotalOrder</a> <a id="2062" class="Symbol">:</a> <a id="2064" href="Relation.Binary.Bundles.html#6016" class="Record">DecTotalOrder</a> <a id="2078" href="Level.html#521" class="Function">0ℓ</a> <a id="2081" href="Level.html#521" class="Function">0ℓ</a> <a id="2084" href="Level.html#521" class="Function">0ℓ</a>
<a id="2087" href="Data.Unit.Properties.html#2046" class="Function">≡-decTotalOrder</a> <a id="2103" class="Symbol">=</a> <a id="2105" class="Keyword">record</a>
<a id="2114" class="Symbol">{</a> <a id="2116" href="Relation.Binary.Bundles.html#6202" class="Field">isDecTotalOrder</a> <a id="2132" class="Symbol">=</a> <a id="2134" href="Data.Unit.Properties.html#1720" class="Function">≡-isDecTotalOrder</a>
<a id="2154" class="Symbol">}</a>
<a id="2157" class="Comment">------------------------------------------------------------------------</a>
<a id="2230" class="Comment">-- DEPRECATED NAMES</a>
<a id="2250" class="Comment">------------------------------------------------------------------------</a>
<a id="2323" class="Comment">-- Please use the new names as continuing support for the old names is</a>
<a id="2394" class="Comment">-- not guaranteed.</a>
<a id="2414" class="Comment">-- Version 1.2</a>
<a id="≤-reflexive"></a><a id="2430" href="Data.Unit.Properties.html#2430" class="Function">≤-reflexive</a> <a id="2442" class="Symbol">:</a> <a id="2444" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="2448" href="Relation.Binary.Core.html#1263" class="Function Operator">⇒</a> <a id="2450" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="2454" href="Data.Unit.Properties.html#2430" class="Function">≤-reflexive</a> <a id="2466" class="Symbol">_</a> <a id="2468" class="Symbol">=</a> <a id="2470" class="Symbol">_</a>
<a id="2472" class="Symbol">{-#</a> <a id="2476" class="Keyword">WARNING_ON_USAGE</a> <a id="2493" class="Pragma">≤-reflexive</a>
<a id="2505" class="String">&quot;Warning: ≤-reflexive was deprecated in v1.2.
Please use id from Function instead.&quot;</a>
<a id="2589" class="Symbol">#-}</a>
<a id="≤-trans"></a><a id="2593" href="Data.Unit.Properties.html#2593" class="Function">≤-trans</a> <a id="2601" class="Symbol">:</a> <a id="2603" href="Relation.Binary.Definitions.html#1875" class="Function">Transitive</a> <a id="2614" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="2618" href="Data.Unit.Properties.html#2593" class="Function">≤-trans</a> <a id="2626" class="Symbol">_</a> <a id="2628" class="Symbol">_</a> <a id="2630" class="Symbol">=</a> <a id="2632" class="Symbol">_</a>
<a id="2634" class="Symbol">{-#</a> <a id="2638" class="Keyword">WARNING_ON_USAGE</a> <a id="2655" class="Pragma">≤-trans</a>
<a id="2663" class="String">&quot;Warning: ≤-trans was deprecated in v1.2.
Please use trans from Relation.Binary.PropositionalEquality instead.&quot;</a>
<a id="2775" class="Symbol">#-}</a>
<a id="≤-antisym"></a><a id="2779" href="Data.Unit.Properties.html#2779" class="Function">≤-antisym</a> <a id="2789" class="Symbol">:</a> <a id="2791" href="Relation.Binary.Definitions.html#2091" class="Function">Antisymmetric</a> <a id="2805" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="2809" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="2813" href="Data.Unit.Properties.html#2779" class="Function">≤-antisym</a> <a id="2824" class="Symbol">_</a> <a id="2826" class="Symbol">_</a> <a id="2828" class="Symbol">=</a> <a id="2830" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a>
<a id="2835" class="Symbol">{-#</a> <a id="2839" class="Keyword">WARNING_ON_USAGE</a> <a id="2856" class="Pragma">≤-antisym</a>
<a id="2866" class="String">&quot;Warning: ≤-antisym was deprecated in v1.2.
Please use ≡-antisym instead.&quot;</a>
<a id="2941" class="Symbol">#-}</a>
<a id="≤-total"></a><a id="2945" href="Data.Unit.Properties.html#2945" class="Function">≤-total</a> <a id="2953" class="Symbol">:</a> <a id="2955" href="Relation.Binary.Definitions.html#2593" class="Function">Total</a> <a id="2961" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="2965" href="Data.Unit.Properties.html#2945" class="Function">≤-total</a> <a id="2973" class="Symbol">_</a> <a id="2975" class="Symbol">_</a> <a id="2977" class="Symbol">=</a> <a id="2979" href="Data.Sum.Base.html#793" class="InductiveConstructor">inj₁</a> <a id="2984" class="Symbol">_</a>
<a id="2986" class="Symbol">{-#</a> <a id="2990" class="Keyword">WARNING_ON_USAGE</a> <a id="3007" class="Pragma">≤-total</a>
<a id="3015" class="String">&quot;Warning: ≤-total was deprecated in v1.2.
Please use ≡-total instead.&quot;</a>
<a id="3086" class="Symbol">#-}</a>
<a id="3090" class="Keyword">infix</a> <a id="3096" class="Number">4</a> <a id="3098" href="Data.Unit.Properties.html#3103" class="Function Operator">_≤?_</a>
<a id="_≤?_"></a><a id="3103" href="Data.Unit.Properties.html#3103" class="Function Operator">_≤?_</a> <a id="3108" class="Symbol">:</a> <a id="3110" href="Relation.Binary.Definitions.html#4584" class="Function">Decidable</a> <a id="3120" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="3124" class="Symbol">_</a> <a id="3126" href="Data.Unit.Properties.html#3103" class="Function Operator">≤?</a> <a id="3129" class="Symbol">_</a> <a id="3131" class="Symbol">=</a> <a id="3133" href="Relation.Nullary.html#1657" class="InductiveConstructor">yes</a> <a id="3137" class="Symbol">_</a>
<a id="3139" class="Symbol">{-#</a> <a id="3143" class="Keyword">WARNING_ON_USAGE</a> <a id="3160" class="Pragma">_≤?_</a>
<a id="3165" class="String">&quot;Warning: _≤?_ was deprecated in v1.2.
Please use _≟_ instead.&quot;</a>
<a id="3230" class="Symbol">#-}</a>
<a id="≤-isPreorder"></a><a id="3234" href="Data.Unit.Properties.html#3234" class="Function">≤-isPreorder</a> <a id="3247" class="Symbol">:</a> <a id="3249" href="Relation.Binary.Structures.html#2172" class="Record">IsPreorder</a> <a id="3260" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="3264" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="3268" href="Data.Unit.Properties.html#3234" class="Function">≤-isPreorder</a> <a id="3281" class="Symbol">=</a> <a id="3283" class="Keyword">record</a>
<a id="3292" class="Symbol">{</a> <a id="3294" href="Relation.Binary.Structures.html#2237" class="Field">isEquivalence</a> <a id="3308" class="Symbol">=</a> <a id="3310" href="Relation.Binary.PropositionalEquality.Properties.html#3436" class="Function">isEquivalence</a>
<a id="3326" class="Symbol">;</a> <a id="3328" href="Relation.Binary.Structures.html#2340" class="Field">reflexive</a> <a id="3342" class="Symbol">=</a> <a id="3344" href="Data.Unit.Properties.html#2430" class="Function">≤-reflexive</a>
<a id="3358" class="Symbol">;</a> <a id="3360" href="Relation.Binary.Structures.html#2370" class="Field">trans</a> <a id="3374" class="Symbol">=</a> <a id="3376" href="Data.Unit.Properties.html#2593" class="Function">≤-trans</a>
<a id="3386" class="Symbol">}</a>
<a id="3388" class="Symbol">{-#</a> <a id="3392" class="Keyword">WARNING_ON_USAGE</a> <a id="3409" class="Pragma">≤-isPreorder</a>
<a id="3422" class="String">&quot;Warning: ≤-isPreorder was deprecated in v1.2.
Please use ≡-isPreorder instead.&quot;</a>
<a id="3503" class="Symbol">#-}</a>
<a id="≤-isPartialOrder"></a><a id="3507" href="Data.Unit.Properties.html#3507" class="Function">≤-isPartialOrder</a> <a id="3524" class="Symbol">:</a> <a id="3526" href="Relation.Binary.Structures.html#3183" class="Record">IsPartialOrder</a> <a id="3541" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="3545" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="3549" href="Data.Unit.Properties.html#3507" class="Function">≤-isPartialOrder</a> <a id="3566" class="Symbol">=</a> <a id="3568" class="Keyword">record</a>
<a id="3577" class="Symbol">{</a> <a id="3579" href="Relation.Binary.Structures.html#3252" class="Field">isPreorder</a> <a id="3590" class="Symbol">=</a> <a id="3592" href="Data.Unit.Properties.html#3234" class="Function">≤-isPreorder</a>
<a id="3607" class="Symbol">;</a> <a id="3609" href="Relation.Binary.Structures.html#3284" class="Field">antisym</a> <a id="3620" class="Symbol">=</a> <a id="3622" href="Data.Unit.Properties.html#2779" class="Function">≤-antisym</a>
<a id="3634" class="Symbol">}</a>
<a id="3636" class="Symbol">{-#</a> <a id="3640" class="Keyword">WARNING_ON_USAGE</a> <a id="3657" class="Pragma">≤-isPartialOrder</a>
<a id="3674" class="String">&quot;Warning: ≤-isPartialOrder was deprecated in v1.2.
Please use ≡-isPartialOrder instead.&quot;</a>
<a id="3763" class="Symbol">#-}</a>
<a id="≤-isTotalOrder"></a><a id="3767" href="Data.Unit.Properties.html#3767" class="Function">≤-isTotalOrder</a> <a id="3782" class="Symbol">:</a> <a id="3784" href="Relation.Binary.Structures.html#5306" class="Record">IsTotalOrder</a> <a id="3797" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="3801" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="3805" href="Data.Unit.Properties.html#3767" class="Function">≤-isTotalOrder</a> <a id="3820" class="Symbol">=</a> <a id="3822" class="Keyword">record</a>
<a id="3831" class="Symbol">{</a> <a id="3833" href="Relation.Binary.Structures.html#5373" class="Field">isPartialOrder</a> <a id="3848" class="Symbol">=</a> <a id="3850" href="Data.Unit.Properties.html#3507" class="Function">≤-isPartialOrder</a>
<a id="3869" class="Symbol">;</a> <a id="3871" href="Relation.Binary.Structures.html#5413" class="Field">total</a> <a id="3886" class="Symbol">=</a> <a id="3888" href="Data.Unit.Properties.html#2945" class="Function">≤-total</a>
<a id="3898" class="Symbol">}</a>
<a id="3900" class="Symbol">{-#</a> <a id="3904" class="Keyword">WARNING_ON_USAGE</a> <a id="3921" class="Pragma">≤-isTotalOrder</a>
<a id="3936" class="String">&quot;Warning: ≤-isTotalOrder was deprecated in v1.2.
Please use ≡-isTotalOrder instead.&quot;</a>
<a id="4021" class="Symbol">#-}</a>
<a id="≤-isDecTotalOrder"></a><a id="4025" href="Data.Unit.Properties.html#4025" class="Function">≤-isDecTotalOrder</a> <a id="4043" class="Symbol">:</a> <a id="4045" href="Relation.Binary.Structures.html#5623" class="Record">IsDecTotalOrder</a> <a id="4061" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a> <a id="4065" href="Data.Unit.Base.html#1032" class="Record Operator">_≤_</a>
<a id="4069" href="Data.Unit.Properties.html#4025" class="Function">≤-isDecTotalOrder</a> <a id="4087" class="Symbol">=</a> <a id="4089" class="Keyword">record</a>
<a id="4098" class="Symbol">{</a> <a id="4100" href="Relation.Binary.Structures.html#5712" class="Field">isTotalOrder</a> <a id="4113" class="Symbol">=</a> <a id="4115" href="Data.Unit.Properties.html#3767" class="Function">≤-isTotalOrder</a>
<a id="4132" class="Symbol">;</a> <a id="4134" href="Relation.Binary.Structures.html#5748" class="Field Operator">_≟_</a> <a id="4147" class="Symbol">=</a> <a id="4149" href="Data.Unit.Properties.html#846" class="Function Operator">_≟_</a>
<a id="4155" class="Symbol">;</a> <a id="4157" href="Relation.Binary.Structures.html#5781" class="Field Operator">_≤?_</a> <a id="4170" class="Symbol">=</a> <a id="4172" href="Data.Unit.Properties.html#3103" class="Function Operator">_≤?_</a>
<a id="4179" class="Symbol">}</a>
<a id="4181" class="Symbol">{-#</a> <a id="4185" class="Keyword">WARNING_ON_USAGE</a> <a id="4202" class="Pragma">≤-isDecTotalOrder</a>
<a id="4220" class="String">&quot;Warning: ≤-isDecTotalOrder was deprecated in v1.2.
Please use ≡-isDecTotalOrder instead.&quot;</a>
<a id="4311" class="Symbol">#-}</a>
<a id="4316" class="Comment">-- Bundles</a>
<a id="≤-poset"></a><a id="4328" href="Data.Unit.Properties.html#4328" class="Function">≤-poset</a> <a id="4336" class="Symbol">:</a> <a id="4338" href="Relation.Binary.Bundles.html#3037" class="Record">Poset</a> <a id="4344" href="Level.html#521" class="Function">0ℓ</a> <a id="4347" href="Level.html#521" class="Function">0ℓ</a> <a id="4350" href="Level.html#521" class="Function">0ℓ</a>
<a id="4353" href="Data.Unit.Properties.html#4328" class="Function">≤-poset</a> <a id="4361" class="Symbol">=</a> <a id="4363" class="Keyword">record</a>
<a id="4372" class="Symbol">{</a> <a id="4374" href="Relation.Binary.Bundles.html#3212" class="Field">isPartialOrder</a> <a id="4389" class="Symbol">=</a> <a id="4391" href="Data.Unit.Properties.html#3507" class="Function">≤-isPartialOrder</a>
<a id="4410" class="Symbol">}</a>
<a id="4412" class="Symbol">{-#</a> <a id="4416" class="Keyword">WARNING_ON_USAGE</a> <a id="4433" class="Pragma">≤-poset</a>
<a id="4441" class="String">&quot;Warning: ≤-poset was deprecated in v1.2.
Please use ≡-poset instead.&quot;</a>
<a id="4512" class="Symbol">#-}</a>
<a id="≤-decTotalOrder"></a><a id="4516" href="Data.Unit.Properties.html#4516" class="Function">≤-decTotalOrder</a> <a id="4532" class="Symbol">:</a> <a id="4534" href="Relation.Binary.Bundles.html#6016" class="Record">DecTotalOrder</a> <a id="4548" href="Level.html#521" class="Function">0ℓ</a> <a id="4551" href="Level.html#521" class="Function">0ℓ</a> <a id="4554" href="Level.html#521" class="Function">0ℓ</a>
<a id="4557" href="Data.Unit.Properties.html#4516" class="Function">≤-decTotalOrder</a> <a id="4573" class="Symbol">=</a> <a id="4575" class="Keyword">record</a>
<a id="4584" class="Symbol">{</a> <a id="4586" href="Relation.Binary.Bundles.html#6202" class="Field">isDecTotalOrder</a> <a id="4602" class="Symbol">=</a> <a id="4604" href="Data.Unit.Properties.html#4025" class="Function">≤-isDecTotalOrder</a>
<a id="4624" class="Symbol">}</a>
<a id="4626" class="Symbol">{-#</a> <a id="4630" class="Keyword">WARNING_ON_USAGE</a> <a id="4647" class="Pragma">≤-decTotalOrder</a>
<a id="4663" class="String">&quot;Warning: ≤-decTotalOrder was deprecated in v1.2.
Please use ≡-decTotalOrder instead.&quot;</a>
<a id="4750" class="Symbol">#-}</a>
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