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12 | 12 | <a id="371" class="Keyword">open</a> <a id="376" class="Keyword">import</a> <a id="383" href="Data.Product.Base.html" class="Module">Data.Product.Base</a> <a id="401" class="Keyword">using</a> <a id="407" class="Symbol">(</a><a id="408" href="Data.Product.Base.html#1618" class="Function Operator">_×_</a><a id="411" class="Symbol">;</a> <a id="413" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="416" class="Symbol">)</a> |
13 | 13 | <a id="418" class="Keyword">open</a> <a id="423" class="Keyword">import</a> <a id="430" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a> <a id="451" class="Keyword">using</a> <a id="457" class="Symbol">(</a><a id="458" href="Relation.Binary.Core.html#896" class="Function">Rel</a><a id="461" class="Symbol">)</a> |
14 | 14 | <a id="463" class="Keyword">open</a> <a id="468" class="Keyword">import</a> <a id="475" href="Relation.Binary.Definitions.html" class="Module">Relation.Binary.Definitions</a> <a id="503" class="Keyword">using</a> <a id="509" class="Symbol">(</a><a id="510" href="Relation.Binary.Definitions.html#6907" class="Function">Decidable</a><a id="519" class="Symbol">)</a> |
15 | | -<a id="521" class="Keyword">open</a> <a id="526" class="Keyword">import</a> <a id="533" href="Relation.Nullary.Decidable.Core.html" class="Module">Relation.Nullary.Decidable.Core</a> <a id="565" class="Keyword">using</a> <a id="571" class="Symbol">(</a><a id="572" href="Relation.Nullary.Decidable.Core.html#2032" class="Field">does</a><a id="576" class="Symbol">;</a> <a id="578" href="Relation.Nullary.Decidable.Core.html#2099" class="InductiveConstructor">yes</a><a id="581" class="Symbol">;</a> <a id="583" href="Relation.Nullary.Decidable.Core.html#2136" class="InductiveConstructor">no</a><a id="585" class="Symbol">)</a> |
| 15 | +<a id="521" class="Keyword">open</a> <a id="526" class="Keyword">import</a> <a id="533" href="Relation.Nullary.Decidable.Core.html" class="Module">Relation.Nullary.Decidable.Core</a> <a id="565" class="Keyword">using</a> <a id="571" class="Symbol">(</a><a id="572" href="Relation.Nullary.Decidable.Core.html#2038" class="Field">does</a><a id="576" class="Symbol">;</a> <a id="578" href="Relation.Nullary.Decidable.Core.html#2105" class="InductiveConstructor">yes</a><a id="581" class="Symbol">;</a> <a id="583" href="Relation.Nullary.Decidable.Core.html#2142" class="InductiveConstructor">no</a><a id="585" class="Symbol">)</a> |
16 | 16 |
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17 | 17 | <a id="588" class="Keyword">module</a> <a id="595" href="Algebra.Construct.LexProduct.Base.html" class="Module">Algebra.Construct.LexProduct.Base</a> |
18 | 18 | <a id="631" class="Symbol">{</a><a id="632" href="Algebra.Construct.LexProduct.Base.html#632" class="Bound">a</a> <a id="634" href="Algebra.Construct.LexProduct.Base.html#634" class="Bound">b</a> <a id="636" href="Algebra.Construct.LexProduct.Base.html#636" class="Bound">ℓ</a><a id="637" class="Symbol">}</a> <a id="639" class="Symbol">{</a><a id="640" href="Algebra.Construct.LexProduct.Base.html#640" class="Bound">A</a> <a id="642" class="Symbol">:</a> <a id="644" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="648" href="Algebra.Construct.LexProduct.Base.html#632" class="Bound">a</a><a id="649" class="Symbol">}</a> <a id="651" class="Symbol">{</a><a id="652" href="Algebra.Construct.LexProduct.Base.html#652" class="Bound">B</a> <a id="654" class="Symbol">:</a> <a id="656" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="660" href="Algebra.Construct.LexProduct.Base.html#634" class="Bound">b</a><a id="661" class="Symbol">}</a> |
|
28 | 28 | <a id="973" class="Comment">-- operator that only calculates the second component of product.</a> |
29 | 29 |
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30 | 30 | <a id="innerLex"></a><a id="1040" href="Algebra.Construct.LexProduct.Base.html#1040" class="Function">innerLex</a> <a id="1049" class="Symbol">:</a> <a id="1051" href="Algebra.Construct.LexProduct.Base.html#640" class="Bound">A</a> <a id="1053" class="Symbol">→</a> <a id="1055" href="Algebra.Construct.LexProduct.Base.html#640" class="Bound">A</a> <a id="1057" class="Symbol">→</a> <a id="1059" href="Algebra.Construct.LexProduct.Base.html#652" class="Bound">B</a> <a id="1061" class="Symbol">→</a> <a id="1063" href="Algebra.Construct.LexProduct.Base.html#652" class="Bound">B</a> <a id="1065" class="Symbol">→</a> <a id="1067" href="Algebra.Construct.LexProduct.Base.html#652" class="Bound">B</a> |
31 | | -<a id="1069" href="Algebra.Construct.LexProduct.Base.html#1040" class="Function">innerLex</a> <a id="1078" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1080" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a> <a id="1082" href="Algebra.Construct.LexProduct.Base.html#1082" class="Bound">x</a> <a id="1084" href="Algebra.Construct.LexProduct.Base.html#1084" class="Bound">y</a> <a id="1086" class="Keyword">with</a> <a id="1091" href="Relation.Nullary.Decidable.Core.html#2032" class="Field">does</a> <a id="1096" class="Symbol">((</a><a id="1098" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1100" href="Algebra.Construct.LexProduct.Base.html#666" class="Bound Operator">∙</a> <a id="1102" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1103" class="Symbol">)</a> <a id="1105" href="Algebra.Construct.LexProduct.Base.html#713" class="Bound Operator">≟₁</a> <a id="1108" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a><a id="1109" class="Symbol">)</a> <a id="1111" class="Symbol">|</a> <a id="1113" href="Relation.Nullary.Decidable.Core.html#2032" class="Field">does</a> <a id="1118" class="Symbol">((</a><a id="1120" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1122" href="Algebra.Construct.LexProduct.Base.html#666" class="Bound Operator">∙</a> <a id="1124" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1125" class="Symbol">)</a> <a id="1127" href="Algebra.Construct.LexProduct.Base.html#713" class="Bound Operator">≟₁</a> <a id="1130" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1131" class="Symbol">)</a> |
| 31 | +<a id="1069" href="Algebra.Construct.LexProduct.Base.html#1040" class="Function">innerLex</a> <a id="1078" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1080" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a> <a id="1082" href="Algebra.Construct.LexProduct.Base.html#1082" class="Bound">x</a> <a id="1084" href="Algebra.Construct.LexProduct.Base.html#1084" class="Bound">y</a> <a id="1086" class="Keyword">with</a> <a id="1091" href="Relation.Nullary.Decidable.Core.html#2038" class="Field">does</a> <a id="1096" class="Symbol">((</a><a id="1098" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1100" href="Algebra.Construct.LexProduct.Base.html#666" class="Bound Operator">∙</a> <a id="1102" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1103" class="Symbol">)</a> <a id="1105" href="Algebra.Construct.LexProduct.Base.html#713" class="Bound Operator">≟₁</a> <a id="1108" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a><a id="1109" class="Symbol">)</a> <a id="1111" class="Symbol">|</a> <a id="1113" href="Relation.Nullary.Decidable.Core.html#2038" class="Field">does</a> <a id="1118" class="Symbol">((</a><a id="1120" href="Algebra.Construct.LexProduct.Base.html#1078" class="Bound">a</a> <a id="1122" href="Algebra.Construct.LexProduct.Base.html#666" class="Bound Operator">∙</a> <a id="1124" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1125" class="Symbol">)</a> <a id="1127" href="Algebra.Construct.LexProduct.Base.html#713" class="Bound Operator">≟₁</a> <a id="1130" href="Algebra.Construct.LexProduct.Base.html#1080" class="Bound">b</a><a id="1131" class="Symbol">)</a> |
32 | 32 | <a id="1133" class="Symbol">...</a> <a id="1137" class="Symbol">|</a> <a id="1139" href="Agda.Builtin.Bool.html#198" class="InductiveConstructor">true</a> <a id="1145" class="Symbol">|</a> <a id="1147" href="Agda.Builtin.Bool.html#192" class="InductiveConstructor">false</a> <a id="1153" class="Symbol">=</a> <a id="1155" class="Bound">x</a> |
33 | 33 | <a id="1157" class="Symbol">...</a> <a id="1161" class="Symbol">|</a> <a id="1163" href="Agda.Builtin.Bool.html#192" class="InductiveConstructor">false</a> <a id="1169" class="Symbol">|</a> <a id="1171" href="Agda.Builtin.Bool.html#198" class="InductiveConstructor">true</a> <a id="1177" class="Symbol">=</a> <a id="1179" class="Bound">y</a> |
34 | 34 | <a id="1181" class="CatchallClause Symbol">...</a><a id="1184" class="CatchallClause"> </a><a id="1185" class="CatchallClause Symbol">|</a><a id="1186" class="CatchallClause"> </a><a id="1191" class="CatchallClause Symbol">_</a><a id="1192" class="CatchallClause"> </a><a id="1193" class="CatchallClause Symbol">|</a><a id="1194" class="CatchallClause"> </a><a id="1199" class="CatchallClause Symbol">_</a> <a id="1201" class="Symbol">=</a> <a id="1203" class="Bound">x</a> <a id="1205" href="Algebra.Construct.LexProduct.Base.html#680" class="Bound Operator">◦</a> <a id="1207" class="Bound">y</a> |
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