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24 lines
4.9 KiB
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<html><head><meta charset="utf-8"><title>Algebra.Consequences.Base</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">-- Lemmas relating algebraic definitions (such as associativity and</a>
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<a id="174" class="Comment">-- commutativity) that don't the equality relation to be a setoid.</a>
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<a id="241" class="Comment">------------------------------------------------------------------------</a>
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<a id="315" class="Symbol">{-#</a> <a id="319" class="Keyword">OPTIONS</a> <a id="327" class="Pragma">--without-K</a> <a id="339" class="Pragma">--safe</a> <a id="346" class="Symbol">#-}</a>
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<a id="351" class="Keyword">module</a> <a id="358" href="Algebra.Consequences.Base.html" class="Module">Algebra.Consequences.Base</a>
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<a id="386" class="Symbol">{</a><a id="387" href="Algebra.Consequences.Base.html#387" class="Bound">a</a><a id="388" class="Symbol">}</a> <a id="390" class="Symbol">{</a><a id="391" href="Algebra.Consequences.Base.html#391" class="Bound">A</a> <a id="393" class="Symbol">:</a> <a id="395" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="399" href="Algebra.Consequences.Base.html#387" class="Bound">a</a><a id="400" class="Symbol">}</a> <a id="402" class="Keyword">where</a>
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<a id="409" class="Keyword">open</a> <a id="414" class="Keyword">import</a> <a id="421" href="Algebra.Core.html" class="Module">Algebra.Core</a>
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<a id="434" class="Keyword">open</a> <a id="439" class="Keyword">import</a> <a id="446" href="Algebra.Definitions.html" class="Module">Algebra.Definitions</a>
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<a id="466" class="Keyword">open</a> <a id="471" class="Keyword">import</a> <a id="478" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a>
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<a id="492" class="Keyword">open</a> <a id="497" class="Keyword">import</a> <a id="504" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a>
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<a id="sel⇒idem"></a><a id="526" href="Algebra.Consequences.Base.html#526" class="Function">sel⇒idem</a> <a id="535" class="Symbol">:</a> <a id="537" class="Symbol">∀</a> <a id="539" class="Symbol">{</a><a id="540" href="Algebra.Consequences.Base.html#540" class="Bound">ℓ</a><a id="541" class="Symbol">}</a> <a id="543" class="Symbol">{</a><a id="544" href="Algebra.Consequences.Base.html#544" class="Bound Operator">_•_</a> <a id="548" class="Symbol">:</a> <a id="550" href="Algebra.Core.html#518" class="Function">Op₂</a> <a id="554" href="Algebra.Consequences.Base.html#391" class="Bound">A</a><a id="555" class="Symbol">}</a> <a id="557" class="Symbol">(</a><a id="558" href="Algebra.Consequences.Base.html#558" class="Bound Operator">_≈_</a> <a id="562" class="Symbol">:</a> <a id="564" href="Relation.Binary.Core.html#882" class="Function">Rel</a> <a id="568" href="Algebra.Consequences.Base.html#391" class="Bound">A</a> <a id="570" href="Algebra.Consequences.Base.html#540" class="Bound">ℓ</a><a id="571" class="Symbol">)</a> <a id="573" class="Symbol">→</a>
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<a id="586" href="Algebra.Definitions.html#2782" class="Function">Selective</a> <a id="596" href="Algebra.Consequences.Base.html#558" class="Bound Operator">_≈_</a> <a id="600" href="Algebra.Consequences.Base.html#544" class="Bound Operator">_•_</a> <a id="604" class="Symbol">→</a> <a id="606" href="Algebra.Definitions.html#2647" class="Function">Idempotent</a> <a id="617" href="Algebra.Consequences.Base.html#558" class="Bound Operator">_≈_</a> <a id="621" href="Algebra.Consequences.Base.html#544" class="Bound Operator">_•_</a>
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<a id="625" href="Algebra.Consequences.Base.html#526" class="Function">sel⇒idem</a> <a id="634" class="Symbol">_</a> <a id="636" href="Algebra.Consequences.Base.html#636" class="Bound">sel</a> <a id="640" href="Algebra.Consequences.Base.html#640" class="Bound">x</a> <a id="642" class="Keyword">with</a> <a id="647" href="Algebra.Consequences.Base.html#636" class="Bound">sel</a> <a id="651" href="Algebra.Consequences.Base.html#640" class="Bound">x</a> <a id="653" href="Algebra.Consequences.Base.html#640" class="Bound">x</a>
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<a id="655" class="Symbol">...</a> <a id="659" class="Symbol">|</a> <a id="661" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="666" href="Algebra.Consequences.Base.html#666" class="Bound">x•x≈x</a> <a id="672" class="Symbol">=</a> <a id="674" href="Algebra.Consequences.Base.html#666" class="Bound">x•x≈x</a>
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<a id="680" class="Symbol">...</a> <a id="684" class="Symbol">|</a> <a id="686" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="691" href="Algebra.Consequences.Base.html#691" class="Bound">x•x≈x</a> <a id="697" class="Symbol">=</a> <a id="699" href="Algebra.Consequences.Base.html#691" class="Bound">x•x≈x</a>
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</pre></body></html> |