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<html><head><meta charset="utf-8"><title>Relation.Nullary</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">-- Operations on nullary relations (like negation and decidability)</a>
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<a id="174" class="Comment">------------------------------------------------------------------------</a>
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<a id="248" class="Comment">-- Some operations on/properties of nullary relations, i.e. sets.</a>
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<a id="315" class="Symbol">{-#</a> <a id="319" class="Keyword">OPTIONS</a> <a id="327" class="Pragma">--cubical-compatible</a> <a id="348" class="Pragma">--safe</a> <a id="355" class="Symbol">#-}</a>
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<a id="360" class="Keyword">module</a> <a id="367" href="Relation.Nullary.html" class="Module">Relation.Nullary</a> <a id="384" class="Keyword">where</a>
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<a id="391" class="Keyword">open</a> <a id="396" class="Keyword">import</a> <a id="403" href="Agda.Builtin.Equality.html" class="Module">Agda.Builtin.Equality</a>
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<a id="426" class="Comment">------------------------------------------------------------------------</a>
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<a id="499" class="Comment">-- Re-exports</a>
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<a id="514" class="Keyword">open</a> <a id="519" class="Keyword">import</a> <a id="526" href="Relation.Nullary.Negation.Core.html" class="Module">Relation.Nullary.Negation.Core</a> <a id="557" class="Keyword">public</a>
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<a id="564" class="Keyword">open</a> <a id="569" class="Keyword">import</a> <a id="576" href="Relation.Nullary.Reflects.html" class="Module">Relation.Nullary.Reflects</a> <a id="602" class="Keyword">public</a>
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<a id="609" class="Keyword">open</a> <a id="614" class="Keyword">import</a> <a id="621" href="Relation.Nullary.Decidable.Core.html" class="Module">Relation.Nullary.Decidable.Core</a> <a id="653" class="Keyword">public</a>
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<a id="661" class="Comment">------------------------------------------------------------------------</a>
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<a id="734" class="Comment">-- Irrelevant types</a>
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<a id="Irrelevant"></a><a id="755" href="Relation.Nullary.html#755" class="Function">Irrelevant</a> <a id="766" class="Symbol">:</a> <a id="768" class="Symbol">∀</a> <a id="770" class="Symbol">{</a><a id="771" href="Relation.Nullary.html#771" class="Bound">p</a><a id="772" class="Symbol">}</a> <a id="774" class="Symbol">→</a> <a id="776" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="780" href="Relation.Nullary.html#771" class="Bound">p</a> <a id="782" class="Symbol">→</a> <a id="784" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="788" href="Relation.Nullary.html#771" class="Bound">p</a>
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<a id="790" href="Relation.Nullary.html#755" class="Function">Irrelevant</a> <a id="801" href="Relation.Nullary.html#801" class="Bound">P</a> <a id="803" class="Symbol">=</a> <a id="805" class="Symbol">∀</a> <a id="807" class="Symbol">(</a><a id="808" href="Relation.Nullary.html#808" class="Bound">p₁</a> <a id="811" href="Relation.Nullary.html#811" class="Bound">p₂</a> <a id="814" class="Symbol">:</a> <a id="816" href="Relation.Nullary.html#801" class="Bound">P</a><a id="817" class="Symbol">)</a> <a id="819" class="Symbol">→</a> <a id="821" href="Relation.Nullary.html#808" class="Bound">p₁</a> <a id="824" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="826" href="Relation.Nullary.html#811" class="Bound">p₂</a>
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