bsc-leon-vatthauer/agda/bsc-thesis/Category.Construction.ElgotAlgebras.Exponentials.md

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<pre class="Agda"><a id="829" class="Keyword">module</a> <a id="836" href="Category.Construction.ElgotAlgebras.Exponentials.html" class="Module">Category.Construction.ElgotAlgebras.Exponentials</a> <a id="885" class="Symbol">{</a><a id="886" href="Category.Construction.ElgotAlgebras.Exponentials.html#886" class="Bound">o</a> <a id="888" href="Category.Construction.ElgotAlgebras.Exponentials.html#888" class="Bound">ℓ</a> <a id="890" href="Category.Construction.ElgotAlgebras.Exponentials.html#890" class="Bound">e</a><a id="891" class="Symbol">}</a> <a id="893" class="Symbol">{</a><a id="894" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a> <a id="896" class="Symbol">:</a> <a id="898" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="907" href="Category.Construction.ElgotAlgebras.Exponentials.html#886" class="Bound">o</a> <a id="909" href="Category.Construction.ElgotAlgebras.Exponentials.html#888" class="Bound">ℓ</a> <a id="911" href="Category.Construction.ElgotAlgebras.Exponentials.html#890" class="Bound">e</a><a id="912" class="Symbol">}</a> <a id="914" class="Symbol">(</a><a id="915" href="Category.Construction.ElgotAlgebras.Exponentials.html#915" class="Bound">distributive</a> <a id="928" class="Symbol">:</a> <a id="930" href="Categories.Category.Distributive.html#712" class="Record">Distributive</a> <a id="943" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a><a id="944" class="Symbol">)</a> <a id="946" class="Symbol">(</a><a id="947" href="Category.Construction.ElgotAlgebras.Exponentials.html#947" class="Bound">exp</a> <a id="951" class="Symbol">:</a> <a id="953" class="Symbol">∀</a> <a id="955" class="Symbol">{</a><a id="956" href="Category.Construction.ElgotAlgebras.Exponentials.html#956" class="Bound">A</a> <a id="958" href="Category.Construction.ElgotAlgebras.Exponentials.html#958" class="Bound">B</a><a id="959" class="Symbol">}</a> <a id="961" class="Symbol">→</a> <a id="963" href="Categories.Object.Exponential.html#583" class="Record">Exponential</a> <a id="975" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a> <a id="977" href="Category.Construction.ElgotAlgebras.Exponentials.html#956" class="Bound">A</a> <a id="979" href="Category.Construction.ElgotAlgebras.Exponentials.html#958" class="Bound">B</a><a id="980" class="Symbol">)</a> <a id="982" class="Keyword">where</a>
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  <a id="1028" class="Keyword">open</a> <a id="1033" href="Categories.Morphism.html" class="Module">M</a> <a id="1035" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a>
  <a id="1039" class="Keyword">open</a> <a id="1044" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="1047" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a>
  <a id="1051" class="Keyword">open</a> <a id="1056" href="Categories.Morphism.Properties.html" class="Module">MP</a> <a id="1059" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a>
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  <a id="ccc"></a><a id="1180" href="Category.Construction.ElgotAlgebras.Exponentials.html#1180" class="Function">ccc</a> <a id="1184" class="Symbol">:</a> <a id="1186" href="Categories.Category.CartesianClosed.html#1233" class="Record">CartesianClosed</a> <a id="1202" href="Category.Construction.ElgotAlgebras.Exponentials.html#894" class="Bound">C</a>
  <a id="1206" href="Category.Construction.ElgotAlgebras.Exponentials.html#1180" class="Function">ccc</a> <a id="1210" class="Symbol">=</a> <a id="1212" class="Keyword">record</a> <a id="1219" class="Symbol">{</a> <a id="1221" href="Categories.Category.CartesianClosed.html#1408" class="Field">cartesian</a> <a id="1231" class="Symbol">=</a> <a id="1233" href="Categories.Category.Distributive.html#765" class="Function">cartesian</a> <a id="1243" class="Symbol">;</a> <a id="1245" href="Categories.Category.CartesianClosed.html#1434" class="Field">exp</a> <a id="1249" class="Symbol">=</a> <a id="1251" href="Category.Construction.ElgotAlgebras.Exponentials.html#947" class="Bound">exp</a> <a id="1255" class="Symbol">}</a>
  <a id="1259" class="Keyword">open</a> <a id="1264" href="Categories.Category.CartesianClosed.html#1233" class="Module">CartesianClosed</a> <a id="1280" href="Category.Construction.ElgotAlgebras.Exponentials.html#1180" class="Function">ccc</a> <a id="1284" class="Keyword">hiding</a> <a id="1291" class="Symbol">(</a><a id="1292" href="Categories.Category.CartesianClosed.html#1408" class="Field">cartesian</a><a id="1301" class="Symbol">;</a> <a id="1303" href="Categories.Category.CartesianClosed.html#1434" class="Field">exp</a><a id="1306" class="Symbol">)</a>
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  <a id="1493" class="Keyword">open</a> <a id="1498" class="Keyword">import</a> <a id="1505" href="Category.Construction.ElgotAlgebras.html" class="Module">Category.Construction.ElgotAlgebras</a> <a id="1541" href="Categories.Category.Distributive.html#793" class="Function">cocartesian</a>
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    <a id="1766" class="Symbol">{</a> <a id="1768" href="Algebra.Elgot.html#16018" class="Field">A</a> <a id="1770" class="Symbol">=</a> <a id="1772" href="Algebra.Elgot.html#16018" class="Function">A</a> <a id="1774" href="Categories.Category.CartesianClosed.html#1513" class="Function Operator">^</a> <a id="1776" href="Category.Construction.ElgotAlgebras.Exponentials.html#1750" class="Bound">X</a>
    <a id="1782" class="Symbol">;</a> <a id="1784" href="Algebra.Elgot.html#16032" class="Field">algebra</a> <a id="1792" class="Symbol">=</a> <a id="1794" class="Keyword">record</a>
      <a id="1807" class="Symbol">{</a> <a id="1809" href="Algebra.Elgot.html#1938" class="Field Operator">_#</a> <a id="1812" class="Symbol">=</a> <a id="1814" class="Symbol">λ</a> <a id="1816" class="Symbol">{</a><a id="1817" href="Category.Construction.ElgotAlgebras.Exponentials.html#1817" class="Bound">Z</a><a id="1818" class="Symbol">}</a> <a id="1820" href="Category.Construction.ElgotAlgebras.Exponentials.html#1820" class="Bound">f</a> <a id="1822" class="Symbol">→</a> <a id="1824" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="1827" class="Symbol">(((</a><a id="1830" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="1836" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="1839" href="Categories.Category.Core.html#630" class="Function">id</a><a id="1841" class="Symbol">)</a> <a id="1843" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1845" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="1859" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1861" class="Symbol">(</a><a id="1862" href="Category.Construction.ElgotAlgebras.Exponentials.html#1820" class="Bound">f</a> <a id="1864" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="1866" href="Categories.Category.Core.html#630" class="Function">id</a><a id="1868" class="Symbol">))</a> <a id="1871" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="1873" class="Symbol">)</a>
      <a id="1881" class="Symbol">;</a> <a id="1883" href="Algebra.Elgot.html#2011" class="Field">#-Fixpoint</a> <a id="1894" class="Symbol">=</a> <a id="1896" class="Symbol">λ</a> <a id="1898" class="Symbol">{</a><a id="1899" href="Category.Construction.ElgotAlgebras.Exponentials.html#1899" class="Bound">X</a><a id="1900" class="Symbol">}</a> <a id="1902" class="Symbol">{</a><a id="1903" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a><a id="1904" class="Symbol">}</a> <a id="1906" class="Symbol">→</a> <a id="1908" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
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        <a id="2007" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="2010" class="Symbol">(</a><a id="2011" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="2013" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2016" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="2018" class="Symbol">((</a><a id="2020" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2026" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2029" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2031" class="Symbol">)</a> <a id="2033" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2035" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2049" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2051" class="Symbol">(</a><a id="2052" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2054" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2056" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2058" class="Symbol">))</a> <a id="2061" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="2064" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="2066" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2068" class="Symbol">(</a><a id="2069" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2075" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2078" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2080" class="Symbol">)</a> <a id="2082" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2084" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2098" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2100" class="Symbol">(</a><a id="2101" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2103" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2105" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2107" class="Symbol">))</a> <a id="2110" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2113" href="Categories.Category.CartesianClosed.html#2186" class="Function">λ-cong</a> <a id="2120" class="Symbol">((</a><a id="2122" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="2128" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a><a id="2133" class="Symbol">)</a> <a id="2135" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="2137" class="Symbol">(</a><a id="2138" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="2147" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="2157" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="2166" class="Symbol">)</a> <a id="2168" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="2175" class="Symbol">)</a> <a id="2177" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
        <a id="2187" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="2190" class="Symbol">(</a><a id="2191" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="2193" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2199" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="2201" class="Symbol">((</a><a id="2203" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2209" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2212" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2214" class="Symbol">)</a> <a id="2216" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2218" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2232" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2234" class="Symbol">(</a><a id="2235" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2237" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2239" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2241" class="Symbol">))</a> <a id="2244" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="2247" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="2249" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2251" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2265" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2267" class="Symbol">(</a><a id="2268" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2270" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2272" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2274" class="Symbol">))</a> <a id="2277" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="2281" href="Categories.Category.CartesianClosed.html#3957" class="Function">λ-unique′</a> <a id="2291" class="Symbol">(</a><a id="2292" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
          <a id="2309" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2315" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2317" class="Symbol">((</a><a id="2319" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="2321" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2324" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="2326" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="2329" class="Symbol">(((</a><a id="2332" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2338" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2341" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2343" class="Symbol">)</a> <a id="2345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2347" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2361" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2363" class="Symbol">(</a><a id="2364" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2366" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2368" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2370" class="Symbol">))</a> <a id="2373" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="2375" class="Symbol">)</a> <a id="2377" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="2379" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2381" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a><a id="2382" class="Symbol">)</a> <a id="2384" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2386" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2388" class="Symbol">)</a> <a id="2390" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="2394" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="2402" class="Symbol">(</a><a id="2403" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="2407" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="2409" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="2417" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="2422" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="2431" class="Symbol">)</a> <a id="2433" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
          <a id="2446" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2452" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2454" class="Symbol">(</a><a id="2455" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="2457" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2460" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="2462" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="2465" class="Symbol">(((</a><a id="2468" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2474" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2477" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2479" class="Symbol">)</a> <a id="2481" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2483" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2497" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2499" class="Symbol">(</a><a id="2500" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2502" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2504" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2506" class="Symbol">))</a> <a id="2509" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="2511" class="Symbol">)</a> <a id="2513" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="2515" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2517" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2519" class="Symbol">)</a> <a id="2521" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2523" class="Symbol">(</a><a id="2524" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2526" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2528" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2530" class="Symbol">)</a> <a id="2532" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2535" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="2543" class="Symbol">(</a><a id="2544" href="Category.Construction.ElgotAlgebras.Exponentials.html#1417" class="Function">⟨⟩-unique</a> <a id="2554" class="Symbol">(</a><a id="2555" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
            <a id="2574" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="2577" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2579" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="2581" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2584" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="2586" class="Symbol">(</a><a id="2587" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="2590" class="Symbol">(((</a><a id="2593" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="2599" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="2602" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2604" class="Symbol">)</a> <a id="2606" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2608" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2622" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2624" class="Symbol">(</a><a id="2625" href="Category.Construction.ElgotAlgebras.Exponentials.html#1903" class="Bound">f</a> <a id="2627" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2629" href="Categories.Category.Core.html#630" class="Function">id</a><a id="2631" class="Symbol">))</a> <a id="2634" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="2636" class="Symbol">))</a> <a id="2639" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2641" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2644" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="2646" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2648" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="2662" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2665" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="2671" class="Symbol">(</a><a id="2672" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a> <a id="2676" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="2678" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="2687" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="2695" href="Categories.Category.BinaryProducts.html#2391" class="Function">π₁∘⁂</a><a id="2699" class="Symbol">)</a> <a id="2701" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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      <a id="4967" href="Category.Construction.ElgotAlgebras.Exponentials.html#4836" class="Function">by-uni</a> <a id="4974" class="Symbol">=</a> <a id="4976" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
        <a id="4991" class="Symbol">(</a><a id="4992" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="4995" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4998" class="Symbol">(</a><a id="4999" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a> <a id="5001" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5003" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5005" class="Symbol">))</a> <a id="5008" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5010" class="Symbol">(</a><a id="5011" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5017" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5020" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5022" class="Symbol">)</a> <a id="5024" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5026" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5040" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5042" class="Symbol">(</a><a id="5043" href="Category.Construction.ElgotAlgebras.Exponentials.html#4408" class="Bound">f</a> <a id="5045" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5047" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5049" class="Symbol">)</a> <a id="5051" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5054" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5060" class="Symbol">(</a><a id="5061" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="5067" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5069" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="5078" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="5088" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="5097" class="Symbol">)</a> <a id="5099" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
        <a id="5110" class="Symbol">(</a><a id="5111" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5117" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5120" class="Symbol">(</a><a id="5121" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a> <a id="5123" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5125" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5127" class="Symbol">))</a> <a id="5130" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5132" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5146" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5148" class="Symbol">(</a><a id="5149" href="Category.Construction.ElgotAlgebras.Exponentials.html#4408" class="Bound">f</a> <a id="5151" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5153" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5155" class="Symbol">)</a> <a id="5157" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="5161" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5167" class="Symbol">(</a><a id="5168" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="5174" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5176" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="5185" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="5195" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="5204" class="Symbol">)</a> <a id="5206" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
        <a id="5217" class="Symbol">(</a><a id="5218" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5224" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5227" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5229" class="Symbol">)</a> <a id="5231" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5233" class="Symbol">(</a><a id="5234" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5237" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5240" class="Symbol">(</a><a id="5241" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a> <a id="5243" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5245" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5247" class="Symbol">))</a> <a id="5250" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5252" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5266" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5268" class="Symbol">(</a><a id="5269" href="Category.Construction.ElgotAlgebras.Exponentials.html#4408" class="Bound">f</a> <a id="5271" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5273" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5275" class="Symbol">)</a> <a id="5277" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5280" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5288" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5294" class="Symbol">((</a><a id="5296" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="5305" class="Symbol">(</a><a id="5306" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="5310" class="Symbol">(</a><a id="5311" href="Category.Construction.ElgotAlgebras.Exponentials.html#1417" class="Function">⟨⟩-unique</a> <a id="5321" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="5329" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="5336" class="Symbol">))</a> <a id="5339" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="5343" class="Symbol">)</a> <a id="5345" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="5353" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5355" href="Categories.Category.Distributive.Properties.html#4502" class="Function">distributeʳ⁻¹-natural</a> <a id="5377" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5380" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5383" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a><a id="5384" class="Symbol">)</a> <a id="5386" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
        <a id="5396" class="Symbol">(</a><a id="5397" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5403" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5406" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5408" class="Symbol">)</a> <a id="5410" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5412" class="Symbol">(</a><a id="5413" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5427" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5429" class="Symbol">((</a><a id="5431" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="5434" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5437" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a><a id="5438" class="Symbol">)</a> <a id="5440" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5442" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5444" class="Symbol">))</a> <a id="5447" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5449" class="Symbol">(</a><a id="5450" href="Category.Construction.ElgotAlgebras.Exponentials.html#4408" class="Bound">f</a> <a id="5452" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5454" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5456" class="Symbol">)</a> <a id="5458" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5461" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5469" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="5475" class="Symbol">(</a><a id="5476" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="5480" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5482" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="5490" href="Category.Construction.ElgotAlgebras.Exponentials.html#4419" class="Bound">eq</a> <a id="5493" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="5502" class="Symbol">)</a> <a id="5504" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
        <a id="5515" class="Symbol">(</a><a id="5516" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5522" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5525" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5527" class="Symbol">)</a> <a id="5529" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5531" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5545" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5547" class="Symbol">(</a><a id="5548" href="Category.Construction.ElgotAlgebras.Exponentials.html#4412" class="Bound">g</a> <a id="5550" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5552" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a> <a id="5554" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5556" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5558" class="Symbol">)</a> <a id="5560" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="5564" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="5570" class="Symbol">(</a><a id="5571" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="5577" class="Symbol">(</a><a id="5578" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="5582" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5584" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="5592" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="5597" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="5606" class="Symbol">))</a> <a id="5609" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
        <a id="5620" class="Symbol">((</a><a id="5622" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5628" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5631" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5633" class="Symbol">)</a> <a id="5635" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5637" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5651" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5653" class="Symbol">(</a><a id="5654" href="Category.Construction.ElgotAlgebras.Exponentials.html#4412" class="Bound">g</a> <a id="5656" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5658" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5660" class="Symbol">))</a> <a id="5663" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5665" class="Symbol">(</a><a id="5666" href="Category.Construction.ElgotAlgebras.Exponentials.html#4416" class="Bound">h</a> <a id="5668" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5670" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5672" class="Symbol">)</a> <a id="5674" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
    <a id="5680" href="Category.Construction.ElgotAlgebras.Exponentials.html#5680" class="Function">#-Folding</a> <a id="5690" class="Symbol">:</a> <a id="5692" class="Symbol">∀</a> <a id="5694" class="Symbol">{</a><a id="5695" href="Category.Construction.ElgotAlgebras.Exponentials.html#5695" class="Bound">D</a> <a id="5697" href="Category.Construction.ElgotAlgebras.Exponentials.html#5697" class="Bound">E</a><a id="5698" class="Symbol">}</a> <a id="5700" class="Symbol">{</a><a id="5701" href="Category.Construction.ElgotAlgebras.Exponentials.html#5701" class="Bound">f</a> <a id="5703" class="Symbol">:</a> <a id="5705" href="Category.Construction.ElgotAlgebras.Exponentials.html#5695" class="Bound">D</a> <a id="5707" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5709" href="Algebra.Elgot.html#16018" class="Function">A</a> <a id="5711" href="Categories.Category.CartesianClosed.html#1513" class="Function Operator">^</a> <a id="5713" href="Category.Construction.ElgotAlgebras.Exponentials.html#1750" class="Bound">X</a> <a id="5715" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="5717" href="Category.Construction.ElgotAlgebras.Exponentials.html#5695" class="Bound">D</a><a id="5718" class="Symbol">}</a> <a id="5720" class="Symbol">{</a><a id="5721" href="Category.Construction.ElgotAlgebras.Exponentials.html#5721" class="Bound">h</a> <a id="5723" class="Symbol">:</a> <a id="5725" href="Category.Construction.ElgotAlgebras.Exponentials.html#5697" class="Bound">E</a> <a id="5727" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5729" href="Category.Construction.ElgotAlgebras.Exponentials.html#5695" class="Bound">D</a> <a id="5731" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="5733" href="Category.Construction.ElgotAlgebras.Exponentials.html#5697" class="Bound">E</a><a id="5734" class="Symbol">}</a> <a id="5736" class="Symbol">→</a> <a id="5738" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="5741" class="Symbol">(((</a><a id="5744" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5750" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5753" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5755" class="Symbol">)</a> <a id="5757" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5759" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5773" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5775" class="Symbol">((</a><a id="5777" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="5780" class="Symbol">(((</a><a id="5783" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5789" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5792" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5794" class="Symbol">)</a> <a id="5796" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5798" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5812" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5814" class="Symbol">(</a><a id="5815" href="Category.Construction.ElgotAlgebras.Exponentials.html#5701" class="Bound">f</a> <a id="5817" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5819" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5821" class="Symbol">))</a> <a id="5824" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="5826" class="Symbol">)</a> <a id="5828" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5831" href="Category.Construction.ElgotAlgebras
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      <a id="5977" class="Symbol">((</a><a id="5979" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="5985" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5988" href="Categories.Category.Core.html#630" class="Function">id</a><a id="5990" class="Symbol">)</a> <a id="5992" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5994" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6008" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6010" class="Symbol">((</a><a id="6012" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="6015" class="Symbol">(((</a><a id="6018" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6024" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6027" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6029" class="Symbol">)</a> <a id="6031" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6033" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6047" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6049" class="Symbol">(</a><a id="6050" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6052" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6054" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6056" class="Symbol">))</a> <a id="6059" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="6061" class="Symbol">)</a> <a id="6063" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6066" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a><a id="6067" class="Symbol">)</a> <a id="6069" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6071" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6073" class="Symbol">))</a> <a id="6076" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6079" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6082" href="Category.Construction.ElgotAlgebras.Exponentials.html#4158" class="Function">#ᵃ-resp-≈</a> <a id="6092" class="Symbol">(</a><a id="6093" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6101" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="6105" class="Symbol">(</a><a id="6106" href="Categories.Category.Distributive.Properties.html#4502" class="Function">distributeʳ⁻¹-natural</a> <a id="6128" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6131" class="Symbol">(</a><a id="6132" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="6135" class="Symbol">(((</a><a id="6138" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6144" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6147" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6149" class="Symbol">)</a> <a id="6151" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6153" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6167" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6169" class="Symbol">(</a><a id="6170" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6172" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6174" href="Categories.Category.Core.html#630" class="Functi
      <a id="6197" class="Symbol">((</a><a id="6199" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6205" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6208" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6210" class="Symbol">)</a> <a id="6212" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6214" class="Symbol">((</a><a id="6216" href="Categories.Category.CartesianClosed.html#2130" class="Function">λg</a> <a id="6219" class="Symbol">(((</a><a id="6222" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6228" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6231" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6233" class="Symbol">)</a> <a id="6235" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6237" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6251" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6253" class="Symbol">(</a><a id="6254" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6256" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6258" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6260" class="Symbol">))</a> <a id="6263" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a><a id="6265" class="Symbol">)</a> <a id="6267" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6269" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6271" class="Symbol">)</a> <a id="6273" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6276" class="Symbol">(</a><a id="6277" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="6279" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6281" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6283" class="Symbol">))</a> <a id="6286" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6288" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="6301" class="Symbol">)</a> <a id="6303" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6306" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6309" href="Category.Construction.ElgotAlgebras.Exponentials.html#4158" class="Function">#ᵃ-resp-≈</a> <a id="6319" class="Symbol">(</a><a id="6320" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="6326" class="Symbol">(</a><a id="6327" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="6333" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="6335" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="6344" href="Categories.Category.CartesianClosed.html#4217" class="Function">β′</a> <a id="6347" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="6356" class="Symbol">))</a> <a id="6359" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
      <a id="6368" class="Symbol">((((</a><a id="6372" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6378" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6381" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6383" class="Symbol">)</a> <a id="6385" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6387" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6401" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6403" class="Symbol">(</a><a id="6404" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6406" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6408" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6410" class="Symbol">))</a> <a id="6413" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6416" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6419" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="6421" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6423" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6425" class="Symbol">)</a> <a id="6427" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6429" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="6442" class="Symbol">)</a> <a id="6444" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6447" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6450" href="Category.Construction.ElgotAlgebras.Exponentials.html#4106" class="Function">#ᵃ-Uniformity</a> <a id="6464" href="Category.Construction.ElgotAlgebras.Exponentials.html#6848" class="Function">by-uni₁</a> <a id="6472" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
      <a id="6481" class="Symbol">(((</a><a id="6484" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6490" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6493" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6495" class="Symbol">)</a> <a id="6497" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6499" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6513" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6515" class="Symbol">(</a><a id="6516" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6518" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6520" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6522" class="Symbol">))</a> <a id="6525" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6528" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6531" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6545" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6547" class="Symbol">(</a><a id="6548" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="6550" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6552" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6554" class="Symbol">))</a> <a id="6557" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6560" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6562" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6576" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6579" href="Category.Construction.ElgotAlgebras.Exponentials.html#4134" class="Function">#ᵃ-Folding</a> <a id="6590" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="6598" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
      <a id="6607" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="6609" class="Symbol">((</a><a id="6611" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6614" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6617" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="6619" class="Symbol">)</a> <a id="6621" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6623" class="Symbol">(</a><a id="6624" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6630" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6633" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6635" class="Symbol">)</a> <a id="6637" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6639" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6653" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6655" class="Symbol">(</a><a id="6656" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6658" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6660" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6662" class="Symbol">))</a> <a id="6665" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="6667" class="Symbol">(</a><a id="6668" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a> <a id="6671" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6673" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6687" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6689" class="Symbol">(</a><a id="6690" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="6692" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6694" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6696" class="Symbol">))</a> <a id="6699" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="6701" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6704" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6706" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6720" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="6724" href="Category.Construction.ElgotAlgebras.Exponentials.html#4106" class="Function">#ᵃ-Uniformity</a> <a id="6738" href="Category.Construction.ElgotAlgebras.Exponentials.html#7337" class="Function">by-uni₂</a> <a id="6746" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
      <a id="6755" class="Symbol">((</a><a id="6757" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="6763" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6766" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6768" class="Symbol">)</a> <a id="6770" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6772" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="6786" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6788" class="Symbol">(</a><a id="6789" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="6791" class="Symbol">(</a><a id="6792" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="6795" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="6798" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="6800" class="Symbol">)</a> <a id="6802" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6804" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="6806" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="6808" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a> <a id="6811" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6813" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="6815" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="6817" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6819" href="Categories.Category.Core.html#630" class="Function">id</a><a id="6821" class="Symbol">))</a> <a id="6824" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="6827" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="6828" class="Symbol">)</a>
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        <a id="7235" class="Symbol">((((</a><a id="7239" href="Categories.Category.CartesianClosed.html#3883" class="Function">eval′</a> <a id="7245" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="7248" href="Categories.Category.Core.html#630" class="Function">id</a><a id="7250" class="Symbol">)</a> <a id="7252" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7254" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="7268" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7270" class="Symbol">(</a><a id="7271" href="Category.Construction.ElgotAlgebras.Exponentials.html#5947" class="Bound">f</a> <a id="7273" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7275" href="Categories.Category.Core.html#630" class="Function">id</a><a id="7277" class="Symbol">))</a> <a id="7280" href="Category.Construction.ElgotAlgebras.Exponentials.html#4058" class="Function Operator">#ᵃ</a> <a id="7283" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="7286" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="7300" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7302" class="Symbol">(</a><a id="7303" href="Category.Construction.ElgotAlgebras.Exponentials.html#5951" class="Bound">h</a> <a id="7305" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7307" href="Categories.Category.Core.html#630" class="Function">id</a><a id="7309" class="Symbol">)))</a> <a id="7313" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7315" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="7329" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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</pre>