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</pre>
<p>Stable free Elgot algebras have an additional universal iteration
preserving morphism.</p>
<pre class="Agda">
<a id="1431" class="Keyword">record</a> <a id="IsStableFreeElgotAlgebraˡ"></a><a id="1438" href="Algebra.Elgot.Stable.html#1438" class="Record">IsStableFreeElgotAlgebraˡ</a> <a id="1464" class="Symbol">{</a><a id="1465" href="Algebra.Elgot.Stable.html#1465" class="Bound">Y</a> <a id="1467" class="Symbol">:</a> <a id="1469" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="1472" class="Symbol">}</a> <a id="1474" class="Symbol">(</a><a id="1475" href="Algebra.Elgot.Stable.html#1475" class="Bound">freeElgot</a> <a id="1485" class="Symbol">:</a> <a id="1487" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a> <a id="1504" href="Algebra.Elgot.Stable.html#1465" class="Bound">Y</a><a id="1505" class="Symbol">)</a> <a id="1507" class="Symbol">:</a> <a id="1509" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1513" class="Symbol">(</a><a id="1514" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1518" href="Algebra.Elgot.Stable.html#788" class="Bound">o</a> <a id="1520" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1522" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1526" href="Algebra.Elgot.Stable.html#790" class="Bound">ℓ</a> <a id="1528" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1530" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1534" href="Algebra.Elgot.Stable.html#792" class="Bound">e</a><a id="1535" class="Symbol">)</a> <a id="1537" class="Keyword">where</a>
<a id="1548" class="Keyword">open</a> <a id="1553" href="Categories.FreeObjects.Free.html#485" class="Module">FreeObject</a> <a id="1564" href="Algebra.Elgot.Stable.html#1475" class="Bound">freeElgot</a> <a id="1574" class="Keyword">using</a> <a id="1580" class="Symbol">(</a><a id="1581" href="Categories.FreeObjects.Free.html#854" class="Field">η</a><a id="1582" class="Symbol">)</a> <a id="1584" class="Keyword">renaming</a> <a id="1593" class="Symbol">(</a><a id="1594" href="Categories.FreeObjects.Free.html#838" class="Field">FX</a> <a id="1597" class="Symbol">to</a> <a id="1600" class="Field">FY</a><a id="1602" class="Symbol">)</a>
<a id="1608" class="Keyword">open</a> <a id="1613" href="Algebra.Elgot.html#15964" class="Module">Elgot-Algebra</a> <a id="1627" href="Algebra.Elgot.Stable.html#1600" class="Function">FY</a> <a id="1630" class="Keyword">using</a> <a id="1636" class="Symbol">(</a><a id="1637" href="Algebra.Elgot.html#1938" class="Function Operator">_#</a><a id="1639" class="Symbol">)</a>
<a id="1646" class="Keyword">field</a>
<a id="IsStableFreeElgotAlgebraˡ.[_,_]♯ˡ"></a><a id="1658" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">[_,_]♯ˡ</a> <a id="1666" class="Symbol">:</a> <a id="1668" class="Symbol">∀</a> <a id="1670" class="Symbol">{</a><a id="1671" href="Algebra.Elgot.Stable.html#1671" class="Bound">X</a> <a id="1673" class="Symbol">:</a> <a id="1675" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="1678" class="Symbol">}</a> <a id="1680" class="Symbol">(</a><a id="1681" href="Algebra.Elgot.Stable.html#1681" class="Bound">A</a> <a id="1683" class="Symbol">:</a> <a id="1685" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="1698" class="Symbol">)</a> <a id="1700" class="Symbol">(</a><a id="1701" href="Algebra.Elgot.Stable.html#1701" class="Bound">f</a> <a id="1703" class="Symbol">:</a> <a id="1705" href="Algebra.Elgot.Stable.html#1465" class="Bound">Y</a> <a id="1707" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="1709" href="Algebra.Elgot.Stable.html#1671" class="Bound">X</a> <a id="1711" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1713" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="1729" href="Algebra.Elgot.Stable.html#1681" class="Bound">A</a><a id="1730" class="Symbol">)</a> <a id="1732" class="Symbol">→</a> <a id="1734" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="1750" href="Algebra.Elgot.Stable.html#1600" class="Function">FY</a> <a id="1753" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="1755" href="Algebra.Elgot.Stable.html#1671" class="Bound">X</a> <a id="1757" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1759" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="1775" href="Algebra.Elgot.Stable.html#1681" class="Bound">A</a>
<a id="IsStableFreeElgotAlgebraˡ.♯ˡ-law"></a><a id="1783" href="Algebra.Elgot.Stable.html#1783" class="Field">♯ˡ-law</a> <a id="1790" class="Symbol">:</a> <a id="1792" class="Symbol">∀</a> <a id="1794" class="Symbol">{</a><a id="1795" href="Algebra.Elgot.Stable.html#1795" class="Bound">X</a> <a id="1797" class="Symbol">:</a> <a id="1799" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="1802" class="Symbol">}</a> <a id="1804" class="Symbol">{</a><a id="1805" href="Algebra.Elgot.Stable.html#1805" class="Bound">A</a> <a id="1807" class="Symbol">:</a> <a id="1809" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="1822" class="Symbol">}</a> <a id="1824" class="Symbol">(</a><a id="1825" href="Algebra.Elgot.Stable.html#1825" class="Bound">f</a> <a id="1827" class="Symbol">:</a> <a id="1829" href="Algebra.Elgot.Stable.html#1465" class="Bound">Y</a> <a id="1831" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="1833" href="Algebra.Elgot.Stable.html#1795" class="Bound">X</a> <a id="1835" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1837" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="1853" href="Algebra.Elgot.Stable.html#1805" class="Bound">A</a><a id="1854" class="Symbol">)</a> <a id="1856" class="Symbol">→</a> <a id="1858" href="Algebra.Elgot.Stable.html#1825" class="Bound">f</a> <a id="1860" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1862" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">[</a> <a id="1864" href="Algebra.Elgot.Stable.html#1805" class="Bound">A</a> <a id="1866" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">,</a> <a id="1868" href="Algebra.Elgot.Stable.html#1825" class="Bound">f</a> <a id="1870" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">]♯ˡ</a> <a id="1874" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1876" class="Symbol">(</a><a id="1877" href="Categories.FreeObjects.Free.html#854" class="Function">η</a> <a id="1879" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="1881" href="Categories.Category.Core.html#630" class="Function">id</a><a id="1883" class="Symbol">)</a>
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<a id="2644" class="Keyword">field</a>
<a id="IsStableFreeElgotAlgebra.[_,_]♯"></a><a id="2658" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">[_,_]♯</a> <a id="2665" class="Symbol">:</a> <a id="2667" class="Symbol">∀</a> <a id="2669" class="Symbol">{</a><a id="2670" href="Algebra.Elgot.Stable.html#2670" class="Bound">X</a> <a id="2672" class="Symbol">:</a> <a id="2674" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="2677" class="Symbol">}</a> <a id="2679" class="Symbol">(</a><a id="2680" href="Algebra.Elgot.Stable.html#2680" class="Bound">A</a> <a id="2682" class="Symbol">:</a> <a id="2684" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="2697" class="Symbol">)</a> <a id="2699" class="Symbol">(</a><a id="2700" href="Algebra.Elgot.Stable.html#2700" class="Bound">f</a> <a id="2702" class="Symbol">:</a> <a id="2704" href="Algebra.Elgot.Stable.html#2670" class="Bound">X</a> <a id="2706" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="2708" href="Algebra.Elgot.Stable.html#2463" class="Bound">Y</a> <a id="2710" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2712" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="2728" href="Algebra.Elgot.Stable.html#2680" class="Bound">A</a><a id="2729" class="Symbol">)</a> <a id="2731" class="Symbol">→</a> <a id="2733" href="Algebra.Elgot.Stable.html#2670" class="Bound">X</a> <a id="2735" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="2737" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="2753" href="Algebra.Elgot.Stable.html#2598" class="Function">FY</a> <a id="2756" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2758" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="2774" href="Algebra.Elgot.Stable.html#2680" class="Bound">A</a>
<a id="IsStableFreeElgotAlgebra.♯-law"></a><a id="2784" href="Algebra.Elgot.Stable.html#2784" class="Field">♯-law</a> <a id="2790" class="Symbol">:</a> <a id="2792" class="Symbol">∀</a> <a id="2794" class="Symbol">{</a><a id="2795" href="Algebra.Elgot.Stable.html#2795" class="Bound">X</a> <a id="2797" class="Symbol">:</a> <a id="2799" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="2802" class="Symbol">}</a> <a id="2804" class="Symbol">{</a><a id="2805" href="Algebra.Elgot.Stable.html#2805" class="Bound">A</a> <a id="2807" class="Symbol">:</a> <a id="2809" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="2822" class="Symbol">}</a> <a id="2824" class="Symbol">(</a><a id="2825" href="Algebra.Elgot.Stable.html#2825" class="Bound">f</a> <a id="2827" class="Symbol">:</a> <a id="2829" href="Algebra.Elgot.Stable.html#2795" class="Bound">X</a> <a id="2831" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="2833" href="Algebra.Elgot.Stable.html#2463" class="Bound">Y</a> <a id="2835" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2837" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="2853" href="Algebra.Elgot.Stable.html#2805" class="Bound">A</a><a id="2854" class="Symbol">)</a> <a id="2856" class="Symbol">→</a> <a id="2858" href="Algebra.Elgot.Stable.html#2825" class="Bound">f</a> <a id="2860" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="2862" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">[</a> <a id="2864" href="Algebra.Elgot.Stable.html#2805" class="Bound">A</a> <a id="2866" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">,</a> <a id="2868" href="Algebra.Elgot.Stable.html#2825" class="Bound">f</a> <a id="2870" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">]♯</a> <a id="2873" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2875" class="Symbol">(</a><a id="2876" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="2879" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="2881" href="Categories.FreeObjects.Free.html#854" class="Function">η</a><a id="2882" class="Symbol">)</a>
<a id="IsStableFreeElgotAlgebra.♯-preserving"></a><a id="2892" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a> <a id="2905" class="Symbol">:</a> <a id="2907" class="Symbol">∀</a> <a id="2909" class="Symbol">{</a><a id="2910" href="Algebra.Elgot.Stable.html#2910" class="Bound">X</a> <a id="2912" class="Symbol">:</a> <a id="2914" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="2917" class="Symbol">}</a> <a id="2919" class="Symbol">{</a><a id="2920" href="Algebra.Elgot.Stable.html#2920" class="Bound">B</a> <a id="2922" class="Symbol">:</a> <a id="2924" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="2937" class="Symbol">}</a> <a id="2939" class="Symbol">(</a><a id="2940" href="Algebra.Elgot.Stable.html#2940" class="Bound">f</a> <a id="2942" class="Symbol">:</a> <a id="2944" href="Algebra.Elgot.Stable.html#2910" class="Bound">X</a> <a id="2946" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="2948" href="Algebra.Elgot.Stable.html#2463" class="Bound">Y</a> <a id="2950" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2952" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="2968" href="Algebra.Elgot.Stable.html#2920" class="Bound">B</a><a id="2969" class="Symbol">)</a> <a id="2971" class="Symbol">{</a><a id="2972" href="Algebra.Elgot.Stable.html#2972" class="Bound">Z</a> <a id="2974" class="Symbol">:</a> <a id="2976" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="2979" class="Symbol">}</a> <a id="2981" class="Symbol">(</a><a id="2982" href="Algebra.Elgot.Stable.html#2982" class="Bound">h</a> <a id="2984" class="Symbol">:</a> <a id="2986" href="Algebra.Elgot.Stable.html#2972" class="Bound">Z</a> <a id="2988" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="2990" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="3006" href="Algebra.Elgot.Stable.html#2598" class="Function">FY</a> <a id="3009" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="3011" href="Algebra.Elgot.Stable.html#2972" class="Bound">Z</a><a id="3012" class="Symbol">)</a> <a id="3014" class="Symbol">→</a> <a id="3016" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">[</a> <a id="3018" href="Algebra.Elgot.Stable.html#2920" class="Bound">B</a> <a id="3020" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">,</a> <a id="3022" href="Algebra.Elgot.Stable.html#2940" class="Bound">f</a> <a id="3024" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">]♯</a> <a id="3027" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3029" class="Symbol">(</a><a id="3030" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3033" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3035" href="Algebra.Elgot.Stable.html#2982" class="Bound">h</a> <a id="3037" href="Algebra.Elgot.html#1938" class="Function Operator">#</a><a id="3038" class="Symbol">)</a> <a id="3040" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3042" href="Algebra.Elgot.html#1938" class="Function Operator">Elgot-Algebra._#</a> <a id="3059" href="Algebra.Elgot.Stable.html#2920" class="Bound">B</a> <a id="3061" class="Symbol">((</a><a id="3063" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">[</a> <a id="3065" href="Algebra.Elgot.Stable.html#2920" class="Bound">B</a> <a id="3067" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">,</a> <a id="3069" href="Algebra.Elgot.Stable.html#2940" class="Bound">f</a> <a id="3071" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">]♯</a> <a id="3074" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="3077" href="Categories.Category.Core.html#630" class="Function">id</a><a id="3079" class="Symbol">)</a> <a id="3081" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3083" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="3097" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3099" class="Symbol">(</a><a id="3100" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3103" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3105" href="Algebra.Elgot.Stable.html#2982" class="Bound">h</a><a id="3106" class="Symbol">))</a>
<a id="IsStableFreeElgotAlgebra.♯-unique"></a><a id="3117" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a> <a id="3126" class="Symbol">:</a> <a id="3128" class="Symbol">∀</a> <a id="3130" class="Symbol">{</a><a id="3131" href="Algebra.Elgot.Stable.html#3131" class="Bound">X</a> <a id="3133" class="Symbol">:</a> <a id="3135" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="3138" class="Symbol">}</a> <a id="3140" class="Symbol">{</a><a id="3141" href="Algebra.Elgot.Stable.html#3141" class="Bound">B</a> <a id="3143" class="Symbol">:</a> <a id="3145" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="3158" class="Symbol">}</a> <a id="3160" class="Symbol">(</a><a id="3161" href="Algebra.Elgot.Stable.html#3161" class="Bound">f</a> <a id="3163" class="Symbol">:</a> <a id="3165" href="Algebra.Elgot.Stable.html#3131" class="Bound">X</a> <a id="3167" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3169" href="Algebra.Elgot.Stable.html#2463" class="Bound">Y</a> <a id="3171" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3173" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="3189" href="Algebra.Elgot.Stable.html#3141" class="Bound">B</a><a id="3190" class="Symbol">)</a> <a id="3192" class="Symbol">(</a><a id="3193" href="Algebra.Elgot.Stable.html#3193" class="Bound">g</a> <a id="3195" class="Symbol">:</a> <a id="3197" href="Algebra.Elgot.Stable.html#3131" class="Bound">X</a> <a id="3199" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3201" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="3217" href="Algebra.Elgot.Stable.html#2598" class="Function">FY</a> <a id="3220" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3222" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="3238" href="Algebra.Elgot.Stable.html#3141" class="Bound">B</a><a id="3239" class="Symbol">)</a>
<a id="3251" class="Symbol">→</a> <a id="3253" href="Algebra.Elgot.Stable.html#3161" class="Bound">f</a> <a id="3255" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3257" href="Algebra.Elgot.Stable.html#3193" class="Bound">g</a> <a id="3259" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3261" class="Symbol">(</a><a id="3262" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3265" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3267" href="Categories.FreeObjects.Free.html#854" class="Function">η</a><a id="3268" class="Symbol">)</a>
<a id="3280" class="Symbol">→</a> <a id="3282" class="Symbol">(∀</a> <a id="3285" class="Symbol">{</a><a id="3286" href="Algebra.Elgot.Stable.html#3286" class="Bound">Z</a> <a id="3288" class="Symbol">:</a> <a id="3290" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="3293" class="Symbol">}</a> <a id="3295" class="Symbol">(</a><a id="3296" href="Algebra.Elgot.Stable.html#3296" class="Bound">h</a> <a id="3298" class="Symbol">:</a> <a id="3300" href="Algebra.Elgot.Stable.html#3286" class="Bound">Z</a> <a id="3302" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3304" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="3320" href="Algebra.Elgot.Stable.html#2598" class="Function">FY</a> <a id="3323" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="3325" href="Algebra.Elgot.Stable.html#3286" class="Bound">Z</a><a id="3326" class="Symbol">)</a> <a id="3328" class="Symbol">→</a> <a id="3330" href="Algebra.Elgot.Stable.html#3193" class="Bound">g</a> <a id="3332" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3334" class="Symbol">(</a><a id="3335" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3338" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3340" href="Algebra.Elgot.Stable.html#3296" class="Bound">h</a> <a id="3342" href="Algebra.Elgot.html#1938" class="Function Operator">#</a><a id="3343" class="Symbol">)</a> <a id="3345" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3347" href="Algebra.Elgot.html#1938" class="Function Operator">Elgot-Algebra._#</a> <a id="3364" href="Algebra.Elgot.Stable.html#3141" class="Bound">B</a> <a id="3366" class="Symbol">((</a><a id="3368" href="Algebra.Elgot.Stable.html#3193" class="Bound">g</a> <a id="3370" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="3373" href="Categories.Category.Core.html#630" class="Function">id</a><a id="3375" class="Symbol">)</a> <a id="3377" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3379" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="3393" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3395" class="Symbol">(</a><a id="3396" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="3399" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3401" href="Algebra.Elgot.Stable.html#3296" class="Bound">h</a><a id="3402" class="Symbol">)))</a>
<a id="3416" class="Symbol">→</a> <a id="3418" href="Algebra.Elgot.Stable.html#3193" class="Bound">g</a> <a id="3420" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3422" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">[</a> <a id="3424" href="Algebra.Elgot.Stable.html#3141" class="Bound">B</a> <a id="3426" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">,</a> <a id="3428" href="Algebra.Elgot.Stable.html#3161" class="Bound">f</a> <a id="3430" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">]♯</a>
<a id="isStable⇒isStableˡ"></a><a id="3436" href="Algebra.Elgot.Stable.html#3436" class="Function">isStable⇒isStableˡ</a> <a id="3455" class="Symbol">:</a> <a id="3457" class="Symbol">∀</a> <a id="3459" class="Symbol">{</a><a id="3460" href="Algebra.Elgot.Stable.html#3460" class="Bound">Y</a><a id="3461" class="Symbol">}</a> <a id="3463" class="Symbol">(</a><a id="3464" href="Algebra.Elgot.Stable.html#3464" class="Bound">freeElgot</a> <a id="3474" class="Symbol">:</a> <a id="3476" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a> <a id="3493" href="Algebra.Elgot.Stable.html#3460" class="Bound">Y</a><a id="3494" class="Symbol">)</a> <a id="3496" class="Symbol">→</a> <a id="3498" href="Algebra.Elgot.Stable.html#2437" class="Record">IsStableFreeElgotAlgebra</a> <a id="3523" class="Symbol">{</a><a id="3524" href="Algebra.Elgot.Stable.html#3460" class="Bound">Y</a><a id="3525" class="Symbol">}</a> <a id="3527" href="Algebra.Elgot.Stable.html#3464" class="Bound">freeElgot</a> <a id="3537" class="Symbol">→</a> <a id="3539" href="Algebra.Elgot.Stable.html#1438" class="Record">IsStableFreeElgotAlgebraˡ</a> <a id="3565" class="Symbol">{</a><a id="3566" href="Algebra.Elgot.Stable.html#3460" class="Bound">Y</a><a id="3567" class="Symbol">}</a> <a id="3569" href="Algebra.Elgot.Stable.html#3464" class="Bound">freeElgot</a>
<a id="3582" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">IsStableFreeElgotAlgebraˡ.[_,_]♯ˡ</a> <a id="3616" class="Symbol">(</a><a id="3617" href="Algebra.Elgot.Stable.html#3436" class="Function">isStable⇒isStableˡ</a> <a id="3636" class="Symbol">{</a><a id="3637" href="Algebra.Elgot.Stable.html#3637" class="Bound">Y</a><a id="3638" class="Symbol">}</a> <a id="3640" href="Algebra.Elgot.Stable.html#3640" class="Bound">fe</a> <a id="3643" href="Algebra.Elgot.Stable.html#3643" class="Bound">isStable</a><a id="3651" class="Symbol">)</a> <a id="3653" class="Symbol">{</a><a id="3654" href="Algebra.Elgot.Stable.html#3654" class="Bound">X</a><a id="3655" class="Symbol">}</a> <a id="3657" href="Algebra.Elgot.Stable.html#3657" class="Bound">A</a> <a id="3659" href="Algebra.Elgot.Stable.html#3659" class="Bound">f</a> <a id="3661" class="Symbol">=</a> <a id="3663" href="Algebra.Elgot.Stable.html#2658" class="Function Operator">[</a> <a id="3665" href="Algebra.Elgot.Stable.html#3657" class="Bound">A</a> <a id="3667" href="Algebra.Elgot.Stable.html#2658" class="Function Operator">,</a> <a id="3669" class="Symbol">(</a><a id="3670" href="Algebra.Elgot.Stable.html#3659" class="Bound">f</a> <a id="3672" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3674" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="3678" class="Symbol">)</a> <a id="3680" href="Algebra.Elgot.Stable.html#2658" class="Function Operator">]♯</a> <a id="3683" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3685" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a>
<a id="3695" class="Keyword">where</a> <a id="3701" class="Keyword">open</a> <a id="3706" href="Algebra.Elgot.Stable.html#2437" class="Module">IsStableFreeElgotAlgebra</a> <a id="3731" href="Algebra.Elgot.Stable.html#3643" class="Bound">isStable</a>
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<a id="StableFreeElgotAlgebra.freeElgot"></a><a id="11106" href="Algebra.Elgot.Stable.html#11106" class="Field">freeElgot</a> <a id="11116" class="Symbol">:</a> <a id="11118" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a> <a id="11135" href="Algebra.Elgot.Stable.html#11092" class="Field">Y</a>
<a id="StableFreeElgotAlgebra.isStableFreeElgotAlgebra"></a><a id="11143" href="Algebra.Elgot.Stable.html#11143" class="Field">isStableFreeElgotAlgebra</a> <a id="11168" class="Symbol">:</a> <a id="11170" href="Algebra.Elgot.Stable.html#2437" class="Record">IsStableFreeElgotAlgebra</a> <a id="11195" href="Algebra.Elgot.Stable.html#11106" class="Field">freeElgot</a>
<a id="11214" class="Keyword">open</a> <a id="11219" href="Algebra.Elgot.Stable.html#2437" class="Module">IsStableFreeElgotAlgebra</a> <a id="11244" href="Algebra.Elgot.Stable.html#11143" class="Field">isStableFreeElgotAlgebra</a> <a id="11269" class="Keyword">public</a>
</pre>
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