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<html><head><meta charset="utf-8"><title>Algebra.Lattice.Bundles.Raw</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">-- Definitions of 'raw' bundles</a>
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<a id="138" class="Comment">------------------------------------------------------------------------</a>
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<a id="212" class="Symbol">{-#</a> <a id="216" class="Keyword">OPTIONS</a> <a id="224" class="Pragma">--cubical-compatible</a> <a id="245" class="Pragma">--safe</a> <a id="252" class="Symbol">#-}</a>
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<a id="257" class="Keyword">module</a> <a id="264" href="Algebra.Lattice.Bundles.Raw.html" class="Module">Algebra.Lattice.Bundles.Raw</a> <a id="292" class="Keyword">where</a>
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<a id="299" class="Keyword">open</a> <a id="304" class="Keyword">import</a> <a id="311" href="Algebra.Core.html" class="Module">Algebra.Core</a>
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<a id="324" class="Keyword">open</a> <a id="329" class="Keyword">import</a> <a id="336" href="Algebra.Bundles.Raw.html" class="Module">Algebra.Bundles.Raw</a> <a id="356" class="Keyword">using</a> <a id="362" class="Symbol">(</a><a id="363" href="Algebra.Bundles.Raw.html#644" class="Record">RawMagma</a><a id="371" class="Symbol">)</a>
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<a id="373" class="Keyword">open</a> <a id="378" class="Keyword">import</a> <a id="385" href="Level.html" class="Module">Level</a> <a id="391" class="Keyword">using</a> <a id="397" class="Symbol">(</a><a id="398" href="Agda.Primitive.html#931" class="Primitive">suc</a><a id="401" class="Symbol">;</a> <a id="403" href="Agda.Primitive.html#961" class="Primitive Operator">_⊔_</a><a id="406" class="Symbol">)</a>
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<a id="408" class="Keyword">open</a> <a id="413" class="Keyword">import</a> <a id="420" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a> <a id="441" class="Keyword">using</a> <a id="447" class="Symbol">(</a><a id="448" href="Relation.Binary.Core.html#896" class="Function">Rel</a><a id="451" class="Symbol">)</a>
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<a id="454" class="Keyword">record</a> <a id="RawLattice"></a><a id="461" href="Algebra.Lattice.Bundles.Raw.html#461" class="Record">RawLattice</a> <a id="472" href="Algebra.Lattice.Bundles.Raw.html#472" class="Bound">c</a> <a id="474" href="Algebra.Lattice.Bundles.Raw.html#474" class="Bound">ℓ</a> <a id="476" class="Symbol">:</a> <a id="478" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="482" class="Symbol">(</a><a id="483" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="487" class="Symbol">(</a><a id="488" href="Algebra.Lattice.Bundles.Raw.html#472" class="Bound">c</a> <a id="490" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="492" href="Algebra.Lattice.Bundles.Raw.html#474" class="Bound">ℓ</a><a id="493" class="Symbol">))</a> <a id="496" class="Keyword">where</a>
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<a id="504" class="Keyword">infixr</a> <a id="511" class="Number">7</a> <a id="513" href="Algebra.Lattice.Bundles.Raw.html#607" class="Field Operator">_∧_</a>
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<a id="519" class="Keyword">infixr</a> <a id="526" class="Number">6</a> <a id="528" href="Algebra.Lattice.Bundles.Raw.html#633" class="Field Operator">_∨_</a>
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<a id="534" class="Keyword">infix</a> <a id="541" class="Number">4</a> <a id="543" href="Algebra.Lattice.Bundles.Raw.html#579" class="Field Operator">_≈_</a>
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<a id="549" class="Keyword">field</a>
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<a id="RawLattice.Carrier"></a><a id="559" href="Algebra.Lattice.Bundles.Raw.html#559" class="Field">Carrier</a> <a id="567" class="Symbol">:</a> <a id="569" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="573" href="Algebra.Lattice.Bundles.Raw.html#472" class="Bound">c</a>
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<a id="RawLattice._≈_"></a><a id="579" href="Algebra.Lattice.Bundles.Raw.html#579" class="Field Operator">_≈_</a> <a id="587" class="Symbol">:</a> <a id="589" href="Relation.Binary.Core.html#896" class="Function">Rel</a> <a id="593" href="Algebra.Lattice.Bundles.Raw.html#559" class="Field">Carrier</a> <a id="601" href="Algebra.Lattice.Bundles.Raw.html#474" class="Bound">ℓ</a>
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<a id="RawLattice._∧_"></a><a id="607" href="Algebra.Lattice.Bundles.Raw.html#607" class="Field Operator">_∧_</a> <a id="615" class="Symbol">:</a> <a id="617" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="621" href="Algebra.Lattice.Bundles.Raw.html#559" class="Field">Carrier</a>
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<a id="RawLattice._∨_"></a><a id="633" href="Algebra.Lattice.Bundles.Raw.html#633" class="Field Operator">_∨_</a> <a id="641" class="Symbol">:</a> <a id="643" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="647" href="Algebra.Lattice.Bundles.Raw.html#559" class="Field">Carrier</a>
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<a id="RawLattice.∨-rawMagma"></a><a id="658" href="Algebra.Lattice.Bundles.Raw.html#658" class="Function">∨-rawMagma</a> <a id="669" class="Symbol">:</a> <a id="671" href="Algebra.Bundles.Raw.html#644" class="Record">RawMagma</a> <a id="680" href="Algebra.Lattice.Bundles.Raw.html#472" class="Bound">c</a> <a id="682" href="Algebra.Lattice.Bundles.Raw.html#474" class="Bound">ℓ</a>
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<a id="686" href="Algebra.Lattice.Bundles.Raw.html#658" class="Function">∨-rawMagma</a> <a id="697" class="Symbol">=</a> <a id="699" class="Keyword">record</a> <a id="706" class="Symbol">{</a> <a id="708" href="Algebra.Bundles.Raw.html#745" class="Field Operator">_≈_</a> <a id="712" class="Symbol">=</a> <a id="714" href="Algebra.Lattice.Bundles.Raw.html#579" class="Field Operator">_≈_</a><a id="717" class="Symbol">;</a> <a id="719" href="Algebra.Bundles.Raw.html#773" class="Field Operator">_∙_</a> <a id="723" class="Symbol">=</a> <a id="725" href="Algebra.Lattice.Bundles.Raw.html#633" class="Field Operator">_∨_</a> <a id="729" class="Symbol">}</a>
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<a id="RawLattice.∧-rawMagma"></a><a id="734" href="Algebra.Lattice.Bundles.Raw.html#734" class="Function">∧-rawMagma</a> <a id="745" class="Symbol">:</a> <a id="747" href="Algebra.Bundles.Raw.html#644" class="Record">RawMagma</a> <a id="756" href="Algebra.Lattice.Bundles.Raw.html#472" class="Bound">c</a> <a id="758" href="Algebra.Lattice.Bundles.Raw.html#474" class="Bound">ℓ</a>
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<a id="762" href="Algebra.Lattice.Bundles.Raw.html#734" class="Function">∧-rawMagma</a> <a id="773" class="Symbol">=</a> <a id="775" class="Keyword">record</a> <a id="782" class="Symbol">{</a> <a id="784" href="Algebra.Bundles.Raw.html#745" class="Field Operator">_≈_</a> <a id="788" class="Symbol">=</a> <a id="790" href="Algebra.Lattice.Bundles.Raw.html#579" class="Field Operator">_≈_</a><a id="793" class="Symbol">;</a> <a id="795" href="Algebra.Bundles.Raw.html#773" class="Field Operator">_∙_</a> <a id="799" class="Symbol">=</a> <a id="801" href="Algebra.Lattice.Bundles.Raw.html#607" class="Field Operator">_∧_</a> <a id="805" class="Symbol">}</a>
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<a id="810" class="Keyword">open</a> <a id="815" href="Algebra.Bundles.Raw.html#644" class="Module">RawMagma</a> <a id="824" href="Algebra.Lattice.Bundles.Raw.html#658" class="Function">∨-rawMagma</a> <a id="835" class="Keyword">public</a>
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<a id="846" class="Keyword">using</a> <a id="852" class="Symbol">(</a><a id="853" href="Algebra.Bundles.Raw.html#812" class="Function Operator">_≉_</a><a id="856" class="Symbol">)</a>
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