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<html><head><meta charset="utf-8"><title>Data.Unit.Polymorphic.Properties</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
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<a id="74" class="Comment">-- The Agda standard library</a>
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<a id="103" class="Comment">--</a>
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<a id="106" class="Comment">-- Properties of the polymorphic unit type</a>
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<a id="149" class="Comment">-- Defines Decidable Equality and Decidable Ordering as well</a>
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<a id="210" class="Comment">------------------------------------------------------------------------</a>
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<a id="284" class="Symbol">{-#</a> <a id="288" class="Keyword">OPTIONS</a> <a id="296" class="Pragma">--cubical-compatible</a> <a id="317" class="Pragma">--safe</a> <a id="324" class="Symbol">#-}</a>
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<a id="329" class="Keyword">module</a> <a id="336" href="Data.Unit.Polymorphic.Properties.html" class="Module">Data.Unit.Polymorphic.Properties</a> <a id="369" class="Keyword">where</a>
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<a id="376" class="Keyword">open</a> <a id="381" class="Keyword">import</a> <a id="388" href="Level.html" class="Module">Level</a>
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<a id="394" class="Keyword">open</a> <a id="399" class="Keyword">import</a> <a id="406" href="Function.Bundles.html" class="Module">Function.Bundles</a> <a id="423" class="Keyword">using</a> <a id="429" class="Symbol">(</a><a id="430" href="Function.Bundles.html#12340" class="Function Operator">_↔_</a><a id="433" class="Symbol">;</a> <a id="435" href="Function.Bundles.html#14187" class="Function">mk↔</a><a id="438" class="Symbol">)</a>
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<a id="440" class="Keyword">open</a> <a id="445" class="Keyword">import</a> <a id="452" href="Data.Product.Base.html" class="Module">Data.Product.Base</a> <a id="470" class="Keyword">using</a> <a id="476" class="Symbol">(</a><a id="477" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="480" class="Symbol">)</a>
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<a id="482" class="Keyword">open</a> <a id="487" class="Keyword">import</a> <a id="494" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a> <a id="508" class="Keyword">using</a> <a id="514" class="Symbol">(</a><a id="515" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a><a id="519" class="Symbol">)</a>
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<a id="521" class="Keyword">open</a> <a id="526" class="Keyword">import</a> <a id="533" href="Data.Unit.Base.html" class="Module">Data.Unit.Base</a> <a id="548" class="Keyword">renaming</a> <a id="557" class="Symbol">(</a><a id="558" href="Agda.Builtin.Unit.html#175" class="Record">⊤</a> <a id="560" class="Symbol">to</a> <a id="563" class="Record">⊤*</a><a id="565" class="Symbol">)</a>
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<a id="567" class="Keyword">open</a> <a id="572" class="Keyword">import</a> <a id="579" href="Data.Unit.Polymorphic.Base.html" class="Module">Data.Unit.Polymorphic.Base</a> <a id="606" class="Keyword">using</a> <a id="612" class="Symbol">(</a><a id="613" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a><a id="614" class="Symbol">;</a> <a id="616" href="Data.Unit.Polymorphic.Base.html#533" class="Function">tt</a><a id="618" class="Symbol">)</a>
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<a id="620" class="Keyword">open</a> <a id="625" class="Keyword">import</a> <a id="632" href="Relation.Nullary.html" class="Module">Relation.Nullary</a>
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<a id="649" class="Keyword">open</a> <a id="654" class="Keyword">import</a> <a id="661" href="Relation.Binary.Bundles.html" class="Module">Relation.Binary.Bundles</a>
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<a id="687" class="Keyword">using</a> <a id="693" class="Symbol">(</a><a id="694" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="700" class="Symbol">;</a> <a id="702" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a><a id="711" class="Symbol">;</a> <a id="713" href="Relation.Binary.Bundles.html#2121" class="Record">Preorder</a><a id="721" class="Symbol">;</a> <a id="723" href="Relation.Binary.Bundles.html#3530" class="Record">Poset</a><a id="728" class="Symbol">;</a> <a id="730" href="Relation.Binary.Bundles.html#6458" class="Record">TotalOrder</a><a id="740" class="Symbol">;</a> <a id="742" href="Relation.Binary.Bundles.html#7041" class="Record">DecTotalOrder</a><a id="755" class="Symbol">)</a>
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<a id="757" class="Keyword">open</a> <a id="762" class="Keyword">import</a> <a id="769" href="Relation.Binary.Structures.html" class="Module">Relation.Binary.Structures</a>
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<a id="798" class="Keyword">using</a> <a id="804" class="Symbol">(</a><a id="805" href="Relation.Binary.Structures.html#2191" class="Record">IsPreorder</a><a id="815" class="Symbol">;</a> <a id="817" href="Relation.Binary.Structures.html#3522" class="Record">IsPartialOrder</a><a id="831" class="Symbol">;</a> <a id="833" href="Relation.Binary.Structures.html#5508" class="Record">IsTotalOrder</a><a id="845" class="Symbol">;</a> <a id="847" href="Relation.Binary.Structures.html#5825" class="Record">IsDecTotalOrder</a><a id="862" class="Symbol">)</a>
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<a id="864" class="Keyword">open</a> <a id="869" class="Keyword">import</a> <a id="876" href="Relation.Binary.Definitions.html" class="Module">Relation.Binary.Definitions</a>
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<a id="906" class="Keyword">using</a> <a id="912" class="Symbol">(</a><a id="913" href="Relation.Binary.Definitions.html#6161" class="Function">Decidable</a><a id="922" class="Symbol">;</a> <a id="924" href="Relation.Binary.Definitions.html#2319" class="Function">Antisymmetric</a><a id="937" class="Symbol">;</a> <a id="939" href="Relation.Binary.Definitions.html#2910" class="Function">Total</a><a id="944" class="Symbol">)</a>
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<a id="946" class="Keyword">open</a> <a id="951" class="Keyword">import</a> <a id="958" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a>
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<a id="997" class="Keyword">private</a>
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<a id="1007" class="Keyword">variable</a>
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<a id="1020" href="Data.Unit.Polymorphic.Properties.html#1020" class="Generalizable">ℓ</a> <a id="1022" class="Symbol">:</a> <a id="1024" href="Agda.Primitive.html#742" class="Postulate">Level</a>
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<a id="1031" class="Comment">------------------------------------------------------------------------</a>
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<a id="1104" class="Comment">-- Equality</a>
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<a id="1116" class="Comment">------------------------------------------------------------------------</a>
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<a id="1190" class="Keyword">infix</a> <a id="1196" class="Number">4</a> <a id="1198" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">_≟_</a>
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<a id="_≟_"></a><a id="1203" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">_≟_</a> <a id="1207" class="Symbol">:</a> <a id="1209" href="Relation.Binary.Definitions.html#6161" class="Function">Decidable</a> <a id="1219" class="Symbol">{</a><a id="1220" class="Argument">A</a> <a id="1222" class="Symbol">=</a> <a id="1224" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="1226" class="Symbol">{</a><a id="1227" href="Data.Unit.Polymorphic.Properties.html#1020" class="Generalizable">ℓ</a><a id="1228" class="Symbol">}}</a> <a id="1231" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="1235" class="Symbol">_</a> <a id="1237" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">≟</a> <a id="1239" class="Symbol">_</a> <a id="1241" class="Symbol">=</a> <a id="1243" href="Relation.Nullary.Decidable.Core.html#1618" class="InductiveConstructor">yes</a> <a id="1247" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
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<a id="≡-setoid"></a><a id="1253" href="Data.Unit.Polymorphic.Properties.html#1253" class="Function">≡-setoid</a> <a id="1262" class="Symbol">:</a> <a id="1264" class="Symbol">∀</a> <a id="1266" href="Data.Unit.Polymorphic.Properties.html#1266" class="Bound">ℓ</a> <a id="1268" class="Symbol">→</a> <a id="1270" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="1277" href="Data.Unit.Polymorphic.Properties.html#1266" class="Bound">ℓ</a> <a id="1279" href="Data.Unit.Polymorphic.Properties.html#1266" class="Bound">ℓ</a>
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<a id="1281" href="Data.Unit.Polymorphic.Properties.html#1253" class="Function">≡-setoid</a> <a id="1290" class="Symbol">_</a> <a id="1292" class="Symbol">=</a> <a id="1294" href="Relation.Binary.PropositionalEquality.Properties.html#5700" class="Function">setoid</a> <a id="1301" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a>
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<a id="≡-decSetoid"></a><a id="1304" href="Data.Unit.Polymorphic.Properties.html#1304" class="Function">≡-decSetoid</a> <a id="1316" class="Symbol">:</a> <a id="1318" class="Symbol">∀</a> <a id="1320" href="Data.Unit.Polymorphic.Properties.html#1320" class="Bound">ℓ</a> <a id="1322" class="Symbol">→</a> <a id="1324" href="Relation.Binary.Bundles.html#1548" class="Record">DecSetoid</a> <a id="1334" href="Data.Unit.Polymorphic.Properties.html#1320" class="Bound">ℓ</a> <a id="1336" href="Data.Unit.Polymorphic.Properties.html#1320" class="Bound">ℓ</a>
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<a id="1338" href="Data.Unit.Polymorphic.Properties.html#1304" class="Function">≡-decSetoid</a> <a id="1350" class="Symbol">_</a> <a id="1352" class="Symbol">=</a> <a id="1354" href="Relation.Binary.PropositionalEquality.Properties.html#5831" class="Function">decSetoid</a> <a id="1364" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">_≟_</a>
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<a id="1369" class="Comment">------------------------------------------------------------------------</a>
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<a id="1442" class="Comment">-- Ordering</a>
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<a id="1454" class="Comment">------------------------------------------------------------------------</a>
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<a id="≡-total"></a><a id="1528" href="Data.Unit.Polymorphic.Properties.html#1528" class="Function">≡-total</a> <a id="1536" class="Symbol">:</a> <a id="1538" href="Relation.Binary.Definitions.html#2910" class="Function">Total</a> <a id="1544" class="Symbol">{</a><a id="1545" class="Argument">A</a> <a id="1547" class="Symbol">=</a> <a id="1549" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="1551" class="Symbol">{</a><a id="1552" href="Data.Unit.Polymorphic.Properties.html#1020" class="Generalizable">ℓ</a><a id="1553" class="Symbol">}}</a> <a id="1556" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="1560" href="Data.Unit.Polymorphic.Properties.html#1528" class="Function">≡-total</a> <a id="1568" class="Symbol">_</a> <a id="1570" class="Symbol">_</a> <a id="1572" class="Symbol">=</a> <a id="1574" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="1579" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
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<a id="≡-antisym"></a><a id="1585" href="Data.Unit.Polymorphic.Properties.html#1585" class="Function">≡-antisym</a> <a id="1595" class="Symbol">:</a> <a id="1597" href="Relation.Binary.Definitions.html#2319" class="Function">Antisymmetric</a> <a id="1611" class="Symbol">{</a><a id="1612" class="Argument">A</a> <a id="1614" class="Symbol">=</a> <a id="1616" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="1618" class="Symbol">{</a><a id="1619" href="Data.Unit.Polymorphic.Properties.html#1020" class="Generalizable">ℓ</a><a id="1620" class="Symbol">}}</a> <a id="1623" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a> <a id="1627" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="1631" href="Data.Unit.Polymorphic.Properties.html#1585" class="Function">≡-antisym</a> <a id="1641" href="Data.Unit.Polymorphic.Properties.html#1641" class="Bound">p</a> <a id="1643" class="Symbol">_</a> <a id="1645" class="Symbol">=</a> <a id="1647" href="Data.Unit.Polymorphic.Properties.html#1641" class="Bound">p</a>
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<a id="1650" class="Comment">------------------------------------------------------------------------</a>
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<a id="1723" class="Comment">-- Structures</a>
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<a id="≡-isPreorder"></a><a id="1738" href="Data.Unit.Polymorphic.Properties.html#1738" class="Function">≡-isPreorder</a> <a id="1751" class="Symbol">:</a> <a id="1753" class="Symbol">∀</a> <a id="1755" href="Data.Unit.Polymorphic.Properties.html#1755" class="Bound">ℓ</a> <a id="1757" class="Symbol">→</a> <a id="1759" href="Relation.Binary.Structures.html#2191" class="Record">IsPreorder</a> <a id="1770" class="Symbol">{</a><a id="1771" href="Data.Unit.Polymorphic.Properties.html#1755" class="Bound">ℓ</a><a id="1772" class="Symbol">}</a> <a id="1774" class="Symbol">{_}</a> <a id="1778" class="Symbol">{</a><a id="1779" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a><a id="1780" class="Symbol">}</a> <a id="1782" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a> <a id="1786" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="1790" href="Data.Unit.Polymorphic.Properties.html#1738" class="Function">≡-isPreorder</a> <a id="1803" href="Data.Unit.Polymorphic.Properties.html#1803" class="Bound">ℓ</a> <a id="1805" class="Symbol">=</a> <a id="1807" class="Keyword">record</a>
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<a id="1816" class="Symbol">{</a> <a id="1818" href="Relation.Binary.Structures.html#2256" class="Field">isEquivalence</a> <a id="1832" class="Symbol">=</a> <a id="1834" href="Relation.Binary.PropositionalEquality.Properties.html#5422" class="Function">isEquivalence</a>
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<a id="1850" class="Symbol">;</a> <a id="1852" href="Relation.Binary.Structures.html#2359" class="Field">reflexive</a> <a id="1866" class="Symbol">=</a> <a id="1868" class="Symbol">λ</a> <a id="1870" href="Data.Unit.Polymorphic.Properties.html#1870" class="Bound">x</a> <a id="1872" class="Symbol">→</a> <a id="1874" href="Data.Unit.Polymorphic.Properties.html#1870" class="Bound">x</a>
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<a id="1878" class="Symbol">;</a> <a id="1880" href="Relation.Binary.Structures.html#2389" class="Field">trans</a> <a id="1894" class="Symbol">=</a> <a id="1896" href="Relation.Binary.PropositionalEquality.Core.html#1757" class="Function">trans</a>
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<a id="1904" class="Symbol">}</a>
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<a id="≡-isPartialOrder"></a><a id="1907" href="Data.Unit.Polymorphic.Properties.html#1907" class="Function">≡-isPartialOrder</a> <a id="1924" class="Symbol">:</a> <a id="1926" class="Symbol">∀</a> <a id="1928" href="Data.Unit.Polymorphic.Properties.html#1928" class="Bound">ℓ</a> <a id="1930" class="Symbol">→</a> <a id="1932" href="Relation.Binary.Structures.html#3522" class="Record">IsPartialOrder</a> <a id="1947" class="Symbol">{</a><a id="1948" href="Data.Unit.Polymorphic.Properties.html#1928" class="Bound">ℓ</a><a id="1949" class="Symbol">}</a> <a id="1951" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a> <a id="1955" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="1959" href="Data.Unit.Polymorphic.Properties.html#1907" class="Function">≡-isPartialOrder</a> <a id="1976" href="Data.Unit.Polymorphic.Properties.html#1976" class="Bound">ℓ</a> <a id="1978" class="Symbol">=</a> <a id="1980" class="Keyword">record</a>
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<a id="1989" class="Symbol">{</a> <a id="1991" href="Relation.Binary.Structures.html#3591" class="Field">isPreorder</a> <a id="2002" class="Symbol">=</a> <a id="2004" href="Data.Unit.Polymorphic.Properties.html#1738" class="Function">≡-isPreorder</a> <a id="2017" href="Data.Unit.Polymorphic.Properties.html#1976" class="Bound">ℓ</a>
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<a id="2021" class="Symbol">;</a> <a id="2023" href="Relation.Binary.Structures.html#3623" class="Field">antisym</a> <a id="2034" class="Symbol">=</a> <a id="2036" href="Data.Unit.Polymorphic.Properties.html#1585" class="Function">≡-antisym</a>
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<a id="2048" class="Symbol">}</a>
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<a id="≡-isTotalOrder"></a><a id="2051" href="Data.Unit.Polymorphic.Properties.html#2051" class="Function">≡-isTotalOrder</a> <a id="2066" class="Symbol">:</a> <a id="2068" class="Symbol">∀</a> <a id="2070" href="Data.Unit.Polymorphic.Properties.html#2070" class="Bound">ℓ</a> <a id="2072" class="Symbol">→</a> <a id="2074" href="Relation.Binary.Structures.html#5508" class="Record">IsTotalOrder</a> <a id="2087" class="Symbol">{</a><a id="2088" href="Data.Unit.Polymorphic.Properties.html#2070" class="Bound">ℓ</a><a id="2089" class="Symbol">}</a> <a id="2091" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a> <a id="2095" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="2099" href="Data.Unit.Polymorphic.Properties.html#2051" class="Function">≡-isTotalOrder</a> <a id="2114" href="Data.Unit.Polymorphic.Properties.html#2114" class="Bound">ℓ</a> <a id="2116" class="Symbol">=</a> <a id="2118" class="Keyword">record</a>
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<a id="2127" class="Symbol">{</a> <a id="2129" href="Relation.Binary.Structures.html#5575" class="Field">isPartialOrder</a> <a id="2144" class="Symbol">=</a> <a id="2146" href="Data.Unit.Polymorphic.Properties.html#1907" class="Function">≡-isPartialOrder</a> <a id="2163" href="Data.Unit.Polymorphic.Properties.html#2114" class="Bound">ℓ</a>
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<a id="2167" class="Symbol">;</a> <a id="2169" href="Relation.Binary.Structures.html#5615" class="Field">total</a> <a id="2184" class="Symbol">=</a> <a id="2186" href="Data.Unit.Polymorphic.Properties.html#1528" class="Function">≡-total</a>
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<a id="2196" class="Symbol">}</a>
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<a id="≡-isDecTotalOrder"></a><a id="2199" href="Data.Unit.Polymorphic.Properties.html#2199" class="Function">≡-isDecTotalOrder</a> <a id="2217" class="Symbol">:</a> <a id="2219" class="Symbol">∀</a> <a id="2221" href="Data.Unit.Polymorphic.Properties.html#2221" class="Bound">ℓ</a> <a id="2223" class="Symbol">→</a> <a id="2225" href="Relation.Binary.Structures.html#5825" class="Record">IsDecTotalOrder</a> <a id="2241" class="Symbol">{</a><a id="2242" href="Data.Unit.Polymorphic.Properties.html#2221" class="Bound">ℓ</a><a id="2243" class="Symbol">}</a> <a id="2245" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a> <a id="2249" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
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<a id="2253" href="Data.Unit.Polymorphic.Properties.html#2199" class="Function">≡-isDecTotalOrder</a> <a id="2271" href="Data.Unit.Polymorphic.Properties.html#2271" class="Bound">ℓ</a> <a id="2273" class="Symbol">=</a> <a id="2275" class="Keyword">record</a>
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<a id="2284" class="Symbol">{</a> <a id="2286" href="Relation.Binary.Structures.html#5914" class="Field">isTotalOrder</a> <a id="2299" class="Symbol">=</a> <a id="2301" href="Data.Unit.Polymorphic.Properties.html#2051" class="Function">≡-isTotalOrder</a> <a id="2316" href="Data.Unit.Polymorphic.Properties.html#2271" class="Bound">ℓ</a>
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<a id="2320" class="Symbol">;</a> <a id="2322" href="Relation.Binary.Structures.html#5950" class="Field Operator">_≟_</a> <a id="2335" class="Symbol">=</a> <a id="2337" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">_≟_</a>
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<a id="2343" class="Symbol">;</a> <a id="2345" href="Relation.Binary.Structures.html#5983" class="Field Operator">_≤?_</a> <a id="2358" class="Symbol">=</a> <a id="2360" href="Data.Unit.Polymorphic.Properties.html#1203" class="Function Operator">_≟_</a>
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<a id="2366" class="Symbol">}</a>
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<a id="2369" class="Comment">------------------------------------------------------------------------</a>
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<a id="2442" class="Comment">-- Bundles</a>
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<a id="≡-preorder"></a><a id="2454" href="Data.Unit.Polymorphic.Properties.html#2454" class="Function">≡-preorder</a> <a id="2465" class="Symbol">:</a> <a id="2467" class="Symbol">∀</a> <a id="2469" href="Data.Unit.Polymorphic.Properties.html#2469" class="Bound">ℓ</a> <a id="2471" class="Symbol">→</a> <a id="2473" href="Relation.Binary.Bundles.html#2121" class="Record">Preorder</a> <a id="2482" href="Data.Unit.Polymorphic.Properties.html#2469" class="Bound">ℓ</a> <a id="2484" href="Data.Unit.Polymorphic.Properties.html#2469" class="Bound">ℓ</a> <a id="2486" href="Data.Unit.Polymorphic.Properties.html#2469" class="Bound">ℓ</a>
|
||
<a id="2488" href="Data.Unit.Polymorphic.Properties.html#2454" class="Function">≡-preorder</a> <a id="2499" href="Data.Unit.Polymorphic.Properties.html#2499" class="Bound">ℓ</a> <a id="2501" class="Symbol">=</a> <a id="2503" class="Keyword">record</a>
|
||
<a id="2512" class="Symbol">{</a> <a id="2514" href="Relation.Binary.Bundles.html#2334" class="Field">isPreorder</a> <a id="2525" class="Symbol">=</a> <a id="2527" href="Data.Unit.Polymorphic.Properties.html#1738" class="Function">≡-isPreorder</a> <a id="2540" href="Data.Unit.Polymorphic.Properties.html#2499" class="Bound">ℓ</a>
|
||
<a id="2544" class="Symbol">}</a>
|
||
|
||
<a id="≡-poset"></a><a id="2547" href="Data.Unit.Polymorphic.Properties.html#2547" class="Function">≡-poset</a> <a id="2555" class="Symbol">:</a> <a id="2557" class="Symbol">∀</a> <a id="2559" href="Data.Unit.Polymorphic.Properties.html#2559" class="Bound">ℓ</a> <a id="2561" class="Symbol">→</a> <a id="2563" href="Relation.Binary.Bundles.html#3530" class="Record">Poset</a> <a id="2569" href="Data.Unit.Polymorphic.Properties.html#2559" class="Bound">ℓ</a> <a id="2571" href="Data.Unit.Polymorphic.Properties.html#2559" class="Bound">ℓ</a> <a id="2573" href="Data.Unit.Polymorphic.Properties.html#2559" class="Bound">ℓ</a>
|
||
<a id="2575" href="Data.Unit.Polymorphic.Properties.html#2547" class="Function">≡-poset</a> <a id="2583" href="Data.Unit.Polymorphic.Properties.html#2583" class="Bound">ℓ</a> <a id="2585" class="Symbol">=</a> <a id="2587" class="Keyword">record</a>
|
||
<a id="2596" class="Symbol">{</a> <a id="2598" href="Relation.Binary.Bundles.html#3705" class="Field">isPartialOrder</a> <a id="2613" class="Symbol">=</a> <a id="2615" href="Data.Unit.Polymorphic.Properties.html#1907" class="Function">≡-isPartialOrder</a> <a id="2632" href="Data.Unit.Polymorphic.Properties.html#2583" class="Bound">ℓ</a>
|
||
<a id="2636" class="Symbol">}</a>
|
||
|
||
<a id="≡-totalOrder"></a><a id="2639" href="Data.Unit.Polymorphic.Properties.html#2639" class="Function">≡-totalOrder</a> <a id="2652" class="Symbol">:</a> <a id="2654" class="Symbol">∀</a> <a id="2656" href="Data.Unit.Polymorphic.Properties.html#2656" class="Bound">ℓ</a> <a id="2658" class="Symbol">→</a> <a id="2660" href="Relation.Binary.Bundles.html#6458" class="Record">TotalOrder</a> <a id="2671" href="Data.Unit.Polymorphic.Properties.html#2656" class="Bound">ℓ</a> <a id="2673" href="Data.Unit.Polymorphic.Properties.html#2656" class="Bound">ℓ</a> <a id="2675" href="Data.Unit.Polymorphic.Properties.html#2656" class="Bound">ℓ</a>
|
||
<a id="2677" href="Data.Unit.Polymorphic.Properties.html#2639" class="Function">≡-totalOrder</a> <a id="2690" href="Data.Unit.Polymorphic.Properties.html#2690" class="Bound">ℓ</a> <a id="2692" class="Symbol">=</a> <a id="2694" class="Keyword">record</a>
|
||
<a id="2703" class="Symbol">{</a> <a id="2705" href="Relation.Binary.Bundles.html#6632" class="Field">isTotalOrder</a> <a id="2718" class="Symbol">=</a> <a id="2720" href="Data.Unit.Polymorphic.Properties.html#2051" class="Function">≡-isTotalOrder</a> <a id="2735" href="Data.Unit.Polymorphic.Properties.html#2690" class="Bound">ℓ</a>
|
||
<a id="2739" class="Symbol">}</a>
|
||
|
||
<a id="≡-decTotalOrder"></a><a id="2742" href="Data.Unit.Polymorphic.Properties.html#2742" class="Function">≡-decTotalOrder</a> <a id="2758" class="Symbol">:</a> <a id="2760" class="Symbol">∀</a> <a id="2762" href="Data.Unit.Polymorphic.Properties.html#2762" class="Bound">ℓ</a> <a id="2764" class="Symbol">→</a> <a id="2766" href="Relation.Binary.Bundles.html#7041" class="Record">DecTotalOrder</a> <a id="2780" href="Data.Unit.Polymorphic.Properties.html#2762" class="Bound">ℓ</a> <a id="2782" href="Data.Unit.Polymorphic.Properties.html#2762" class="Bound">ℓ</a> <a id="2784" href="Data.Unit.Polymorphic.Properties.html#2762" class="Bound">ℓ</a>
|
||
<a id="2786" href="Data.Unit.Polymorphic.Properties.html#2742" class="Function">≡-decTotalOrder</a> <a id="2802" href="Data.Unit.Polymorphic.Properties.html#2802" class="Bound">ℓ</a> <a id="2804" class="Symbol">=</a> <a id="2806" class="Keyword">record</a>
|
||
<a id="2815" class="Symbol">{</a> <a id="2817" href="Relation.Binary.Bundles.html#7227" class="Field">isDecTotalOrder</a> <a id="2833" class="Symbol">=</a> <a id="2835" href="Data.Unit.Polymorphic.Properties.html#2199" class="Function">≡-isDecTotalOrder</a> <a id="2853" href="Data.Unit.Polymorphic.Properties.html#2802" class="Bound">ℓ</a>
|
||
<a id="2857" class="Symbol">}</a>
|
||
|
||
<a id="⊤↔⊤*"></a><a id="2860" href="Data.Unit.Polymorphic.Properties.html#2860" class="Function">⊤↔⊤*</a> <a id="2865" class="Symbol">:</a> <a id="2867" href="Data.Unit.Polymorphic.Base.html#489" class="Function">⊤</a> <a id="2869" class="Symbol">{</a><a id="2870" href="Data.Unit.Polymorphic.Properties.html#1020" class="Generalizable">ℓ</a><a id="2871" class="Symbol">}</a> <a id="2873" href="Function.Bundles.html#12340" class="Function Operator">↔</a> <a id="2875" href="Data.Unit.Polymorphic.Properties.html#563" class="Record">⊤*</a>
|
||
<a id="2878" href="Data.Unit.Polymorphic.Properties.html#2860" class="Function">⊤↔⊤*</a> <a id="2883" class="Symbol">=</a> <a id="2885" href="Function.Bundles.html#14187" class="Function">mk↔</a> <a id="2889" class="Symbol">((λ</a> <a id="2893" href="Data.Unit.Polymorphic.Properties.html#2893" class="Bound">_</a> <a id="2895" class="Symbol">→</a> <a id="2897" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a><a id="2901" class="Symbol">)</a> <a id="2903" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="2905" class="Symbol">(λ</a> <a id="2908" href="Data.Unit.Polymorphic.Properties.html#2908" class="Bound">_</a> <a id="2910" class="Symbol">→</a> <a id="2912" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a><a id="2916" class="Symbol">))</a>
|
||
</pre></body></html> |