bsc-leon-vatthauer/agda/bsc-thesis/Monad.Instance.Setoids.K.md

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</pre>-->

# The delay monad on the category of setoids is an instance of K

<pre class="Agda"><a id="1258" class="Keyword">module</a> <a id="1265" href="Monad.Instance.Setoids.K.html" class="Module">Monad.Instance.Setoids.K</a> <a id="1290" class="Symbol">{</a><a id="1291" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="1293" class="Symbol">:</a> <a id="1295" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="1300" class="Symbol">}</a> <a id="1302" class="Keyword">where</a>
  <a id="1310" class="Keyword">open</a> <a id="1315" href="Monad.Instance.Setoids.K.html#336" class="Module">_⟶_</a> <a id="1319" class="Keyword">using</a> <a id="1325" class="Symbol">(</a><a id="1326" href="Function.Bundles.html#2113" class="Field">cong</a><a id="1330" class="Symbol">)</a>
  <a id="1334" class="Keyword">open</a> <a id="1339" class="Keyword">import</a> <a id="1346" href="Category.Ambient.Setoids.html" class="Module">Category.Ambient.Setoids</a>
  <a id="1373" class="Keyword">open</a> <a id="1378" href="Category.Ambient.html#1681" class="Module">Ambient</a> <a id="1386" class="Symbol">(</a><a id="1387" href="Category.Ambient.Setoids.html#4545" class="Function">setoidAmbient</a> <a id="1401" class="Symbol">{</a><a id="1402" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1403" class="Symbol">})</a> <a id="1406" class="Keyword">using</a> <a id="1412" class="Symbol">(</a><a id="1413" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a><a id="1424" class="Symbol">;</a> <a id="1426" href="Category.Ambient.html#2762" class="Function">distributive</a><a id="1438" class="Symbol">)</a>
  <a id="1442" class="Keyword">open</a> <a id="1447" class="Keyword">import</a> <a id="1454" href="Monad.Instance.Setoids.Delay.html" class="Module">Monad.Instance.Setoids.Delay</a> <a id="1483" class="Symbol">{</a><a id="1484" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1485" class="Symbol">}</a> <a id="1487" class="Symbol">{</a><a id="1488" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1489" class="Symbol">}</a>
  <a id="1493" class="Keyword">open</a> <a id="1498" class="Keyword">import</a> <a id="1505" href="Monad.Instance.K.html" class="Module">Monad.Instance.K</a> <a id="1522" class="Symbol">(</a><a id="1523" href="Category.Ambient.Setoids.html#4545" class="Function">setoidAmbient</a> <a id="1537" class="Symbol">{</a><a id="1538" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1539" class="Symbol">})</a>
  <a id="1544" class="Keyword">open</a> <a id="1549" class="Keyword">import</a> <a id="1556" href="Algebra.Elgot.html" class="Module">Algebra.Elgot</a> <a id="1570" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a>
  <a id="1584" class="Keyword">open</a> <a id="1589" class="Keyword">import</a> <a id="1596" href="Algebra.Elgot.Free.html" class="Module">Algebra.Elgot.Free</a> <a id="1615" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a>
  <a id="1629" class="Keyword">open</a> <a id="1634" class="Keyword">import</a> <a id="1641" href="Algebra.Elgot.Stable.html" class="Module">Algebra.Elgot.Stable</a> <a id="1662" href="Category.Ambient.html#2762" class="Function">distributive</a>
  <a id="1677" class="Keyword">open</a> <a id="1682" class="Keyword">import</a> <a id="1689" href="Category.Construction.ElgotAlgebras.html" class="Module">Category.Construction.ElgotAlgebras</a> <a id="1725" class="Symbol">{</a><a id="1726" class="Argument">C</a> <a id="1728" class="Symbol">=</a> <a id="1730" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="1738" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="1740" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1741" class="Symbol">}</a> <a id="1743" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a>
  <a id="1757" class="Keyword">open</a> <a id="1762" class="Keyword">import</a> <a id="1769" href="Monad.PreElgot.html" class="Module">Monad.PreElgot</a> <a id="1784" class="Symbol">(</a><a id="1785" href="Category.Ambient.Setoids.html#4545" class="Function">setoidAmbient</a> <a id="1799" class="Symbol">{</a><a id="1800" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="1801" class="Symbol">})</a>
  <a id="1806" class="Keyword">open</a> <a id="1811" href="Monad.Instance.Setoids.Delay.html#1234" class="Module">Bisimilarity</a> <a id="1824" class="Keyword">renaming</a> <a id="1833" class="Symbol">(</a><a id="1834" href="Monad.Instance.Setoids.Delay.html#3314" class="Datatype Operator">_≈_</a> <a id="1838" class="Symbol">to</a> <a id="1841" class="Datatype Operator">[_][_≈_]</a><a id="1849" class="Symbol">;</a> <a id="1851" href="Monad.Instance.Setoids.Delay.html#3534" class="Record Operator">_≈′_</a> <a id="1856" class="Symbol">to</a> <a id="1859" class="Record Operator">[_][_≈′_]</a><a id="1868" class="Symbol">;</a> <a id="1870" href="Monad.Instance.Setoids.Delay.html#1653" class="Datatype Operator">_∼_</a> <a id="1874" class="Symbol">to</a> <a id="1877" class="Datatype Operator">[_][_∼_]</a><a id="1885" class="Symbol">;</a> <a id="1887" href="Monad.Instance.Setoids.Delay.html#1839" class="Record Operator">_∼′_</a> <a id="1892" class="Symbol">to</a> <a id="1895" class="Record Operator">[_][_∼′_]</a><a id="1904" class="Symbol">;</a> <a id="1906" href="Monad.Instance.Setoids.Delay.html#2932" class="Datatype Operator">_↓_</a> <a id="1910" class="Symbol">to</a> <a id="1913" class="Datatype Operator">[_][_↓_]</a><a id="1921" class="Symbol">)</a>
  <a id="1925" class="Keyword">open</a> <a id="1930" href="Monad.Instance.Setoids.Delay.html#5804" class="Module">DelayMonad</a>
  <a id="1943" class="Keyword">open</a> <a id="1948" href="Monad.Instance.Setoids.Delay.html#17842" class="Module">extra</a>
  <a id="1956" class="Keyword">open</a> <a id="1961" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="1968" class="Keyword">using</a> <a id="1974" class="Symbol">()</a> <a id="1977" class="Keyword">renaming</a> <a id="1986" class="Symbol">(</a><a id="1987" href="Relation.Binary.Bundles.html#1143" class="Field">Carrier</a> <a id="1995" class="Symbol">to</a> <a id="1998" class="Field">∣_∣</a><a id="2001" class="Symbol">;</a> <a id="2003" href="Relation.Binary.Bundles.html#1169" class="Field Operator">_≈_</a> <a id="2007" class="Symbol">to</a> <a id="2010" class="Field Operator">[_][_≡_]</a><a id="2018" class="Symbol">)</a>
  <a id="2022" class="Keyword">open</a> <a id="2027" href="Monad.Instance.Setoids.Delay.html#870" class="Module">eq</a> <a id="2030" class="Keyword">using</a> <a id="2036" class="Symbol">()</a> <a id="2039" class="Keyword">renaming</a> <a id="2048" class="Symbol">(</a><a id="2049" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="2054" class="Symbol">to</a> <a id="2057" class="Function">≡-refl</a><a id="2063" class="Symbol">;</a> <a id="2065" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="2069" class="Symbol">to</a> <a id="2072" class="Function">≡-sym</a><a id="2077" class="Symbol">;</a> <a id="2079" href="Relation.Binary.Structures.html#1648" class="Function">trans</a> <a id="2085" class="Symbol">to</a> <a id="2088" class="Function">≡-trans</a><a id="2095" class="Symbol">)</a>

  <a id="≡→≡"></a><a id="2100" href="Monad.Instance.Setoids.K.html#2100" class="Function">≡→≡</a> <a id="2104" class="Symbol">:</a> <a id="2106" class="Symbol">∀</a> <a id="2108" class="Symbol">{</a><a id="2109" href="Monad.Instance.Setoids.K.html#2109" class="Bound">A</a> <a id="2111" class="Symbol">:</a> <a id="2113" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2120" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="2122" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="2123" class="Symbol">}</a> <a id="2125" class="Symbol">{</a><a id="2126" href="Monad.Instance.Setoids.K.html#2126" class="Bound">x</a> <a id="2128" href="Monad.Instance.Setoids.K.html#2128" class="Bound">y</a> <a id="2130" class="Symbol">:</a> <a id="2132" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2134" href="Monad.Instance.Setoids.K.html#2109" class="Bound">A</a> <a id="2136" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="2137" class="Symbol">}</a> <a id="2139" class="Symbol">→</a> <a id="2141" href="Monad.Instance.Setoids.K.html#2126" class="Bound">x</a> <a id="2143" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="2145" href="Monad.Instance.Setoids.K.html#2128" class="Bound">y</a> <a id="2147" class="Symbol">→</a> <a id="2149" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="2151" href="Monad.Instance.Setoids.K.html#2109" class="Bound">A</a> <a id="2153" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="2156" href="Monad.Instance.Setoids.K.html#2126" class="Bound">x</a> <a id="2158" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="2160" href="Monad.Instance.Setoids.K.html#2128" class="Bound">y</a> <a id="2162" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
  <a id="2166" href="Monad.Instance.Setoids.K.html#2100" class="Function">≡→≡</a> <a id="2170" class="Symbol">{</a><a id="2171" href="Monad.Instance.Setoids.K.html#2171" class="Bound">A</a><a id="2172" class="Symbol">}</a> <a id="2174" class="Symbol">{</a><a id="2175" href="Monad.Instance.Setoids.K.html#2175" class="Bound">x</a><a id="2176" class="Symbol">}</a> <a id="2178" class="Symbol">{</a><a id="2179" href="Monad.Instance.Setoids.K.html#2179" class="Bound">y</a><a id="2180" class="Symbol">}</a> <a id="2182" href="Monad.Instance.Setoids.K.html#2182" class="Bound">eq</a> <a id="2185" class="Keyword">rewrite</a> <a id="2193" href="Monad.Instance.Setoids.K.html#2182" class="Bound">eq</a> <a id="2196" class="Symbol">=</a> <a id="2198" href="Monad.Instance.Setoids.K.html#2057" class="Function">≡-refl</a> <a id="2205" href="Monad.Instance.Setoids.K.html#2171" class="Bound">A</a>

  <a id="iter"></a><a id="2210" href="Monad.Instance.Setoids.K.html#2210" class="Function">iter</a> <a id="2215" class="Symbol">:</a> <a id="2217" class="Symbol">∀</a> <a id="2219" class="Symbol">{</a><a id="2220" href="Monad.Instance.Setoids.K.html#2220" class="Bound">A</a> <a id="2222" href="Monad.Instance.Setoids.K.html#2222" class="Bound">X</a> <a id="2224" class="Symbol">:</a> <a id="2226" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2233" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="2235" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="2236" class="Symbol">}</a> <a id="2238" class="Symbol">→</a> <a id="2240" class="Symbol">(</a><a id="2241" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2243" href="Monad.Instance.Setoids.K.html#2222" class="Bound">X</a> <a id="2245" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2247" class="Symbol">→</a> <a id="2249" class="Symbol">(</a><a id="2250" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="2256" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2258" href="Monad.Instance.Setoids.K.html#2220" class="Bound">A</a> <a id="2260" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2262" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="2264" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2266" href="Monad.Instance.Setoids.K.html#2222" class="Bound">X</a> <a id="2268" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="2269" class="Symbol">))</a> <a id="2272" class="Symbol">→</a> <a id="2274" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2276" href="Monad.Instance.Setoids.K.html#2222" class="Bound">X</a> <a id="2278" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2280" class="Symbol">→</a> <a id="2282" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="2288" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2290" href="Monad.Instance.Setoids.K.html#2220" class="Bound">A</a> <a id="2292" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a>
  <a id="iter′"></a><a id="2296" href="Monad.Instance.Setoids.K.html#2296" class="Function">iter′</a> <a id="2302" class="Symbol">:</a> <a id="2304" class="Symbol">∀</a> <a id="2306" class="Symbol">{</a><a id="2307" href="Monad.Instance.Setoids.K.html#2307" class="Bound">A</a> <a id="2309" href="Monad.Instance.Setoids.K.html#2309" class="Bound">X</a> <a id="2311" class="Symbol">:</a> <a id="2313" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2320" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="2322" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="2323" class="Symbol">}</a> <a id="2325" class="Symbol">→</a> <a id="2327" class="Symbol">(</a><a id="2328" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2330" href="Monad.Instance.Setoids.K.html#2309" class="Bound">X</a> <a id="2332" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2334" class="Symbol">→</a> <a id="2336" class="Symbol">(</a><a id="2337" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="2343" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2345" href="Monad.Instance.Setoids.K.html#2307" class="Bound">A</a> <a id="2347" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2349" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="2351" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2353" href="Monad.Instance.Setoids.K.html#2309" class="Bound">X</a> <a id="2355" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="2356" class="Symbol">))</a> <a id="2359" class="Symbol">→</a> <a id="2361" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2363" href="Monad.Instance.Setoids.K.html#2309" class="Bound">X</a> <a id="2365" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2367" class="Symbol">→</a> <a id="2369" href="Monad.Instance.Setoids.Delay.html#1125" class="Record">Delay′</a> <a id="2376" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2378" href="Monad.Instance.Setoids.K.html#2307" class="Bound">A</a> <a id="2380" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a>
  <a id="2384" href="Monad.Instance.Setoids.Delay.html#1190" class="Field">force</a> <a id="2390" class="Symbol">(</a><a id="2391" href="Monad.Instance.Setoids.K.html#2296" class="Function">iter′</a> <a id="2397" class="Symbol">{</a><a id="2398" href="Monad.Instance.Setoids.K.html#2398" class="Bound">A</a><a id="2399" class="Symbol">}</a> <a id="2401" class="Symbol">{</a><a id="2402" href="Monad.Instance.Setoids.K.html#2402" class="Bound">X</a><a id="2403" class="Symbol">}</a> <a id="2405" href="Monad.Instance.Setoids.K.html#2405" class="Bound">f</a> <a id="2407" href="Monad.Instance.Setoids.K.html#2407" class="Bound">x</a><a id="2408" class="Symbol">)</a> <a id="2410" class="Symbol">=</a> <a id="2412" href="Monad.Instance.Setoids.K.html#2210" class="Function">iter</a> <a id="2417" class="Symbol">{</a><a id="2418" href="Monad.Instance.Setoids.K.html#2398" class="Bound">A</a><a id="2419" class="Symbol">}</a> <a id="2421" class="Symbol">{</a><a id="2422" href="Monad.Instance.Setoids.K.html#2402" class="Bound">X</a><a id="2423" class="Symbol">}</a> <a id="2425" href="Monad.Instance.Setoids.K.html#2405" class="Bound">f</a> <a id="2427" href="Monad.Instance.Setoids.K.html#2407" class="Bound">x</a>
  <a id="2431" href="Monad.Instance.Setoids.K.html#2210" class="Function">iter</a> <a id="2436" class="Symbol">{</a><a id="2437" href="Monad.Instance.Setoids.K.html#2437" class="Bound">A</a><a id="2438" class="Symbol">}</a> <a id="2440" class="Symbol">{</a><a id="2441" href="Monad.Instance.Setoids.K.html#2441" class="Bound">X</a><a id="2442" class="Symbol">}</a> <a id="2444" href="Monad.Instance.Setoids.K.html#2444" class="Bound">f</a> <a id="2446" href="Monad.Instance.Setoids.K.html#2446" class="Bound">x</a> <a id="2448" class="Keyword">with</a> <a id="2453" href="Monad.Instance.Setoids.K.html#2444" class="Bound">f</a> <a id="2455" href="Monad.Instance.Setoids.K.html#2446" class="Bound">x</a> 
  <a id="2460" class="Symbol">...</a>              <a id="2477" class="Symbol">|</a> <a id="2479" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="2484" href="Monad.Instance.Setoids.K.html#2484" class="Bound">a</a> <a id="2486" class="Symbol">=</a> <a id="2488" href="Monad.Instance.Setoids.K.html#2484" class="Bound">a</a>
  <a id="2492" class="Symbol">...</a>              <a id="2509" class="Symbol">|</a> <a id="2511" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="2516" href="Monad.Instance.Setoids.K.html#2516" class="Bound">b</a> <a id="2518" class="Symbol">=</a> <a id="2520" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="2526" class="Symbol">(</a><a id="2527" href="Monad.Instance.Setoids.K.html#2296" class="Function">iter′</a> <a id="2533" class="Symbol">{</a><a id="2534" class="Bound">A</a><a id="2535" class="Symbol">}</a> <a id="2537" class="Symbol">{</a><a id="2538" class="Bound">X</a><a id="2539" class="Symbol">}</a> <a id="2541" class="Bound">f</a> <a id="2543" href="Monad.Instance.Setoids.K.html#2516" class="Bound">b</a><a id="2544" class="Symbol">)</a>

  <a id="conflict"></a><a id="2549" href="Monad.Instance.Setoids.K.html#2549" class="Function">conflict</a> <a id="2558" class="Symbol">:</a> <a id="2560" class="Symbol">∀</a> <a id="2562" class="Symbol">{</a><a id="2563" href="Monad.Instance.Setoids.K.html#2563" class="Bound">ℓ&#39;&#39;</a><a id="2566" class="Symbol">}</a> <a id="2568" class="Symbol">(</a><a id="2569" href="Monad.Instance.Setoids.K.html#2569" class="Bound">X</a> <a id="2571" href="Monad.Instance.Setoids.K.html#2571" class="Bound">Y</a> <a id="2573" class="Symbol">:</a> <a id="2575" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="2582" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="2584" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="2585" class="Symbol">)</a> <a id="2587" class="Symbol">{</a><a id="2588" href="Monad.Instance.Setoids.K.html#2588" class="Bound">Z</a> <a id="2590" class="Symbol">:</a> <a id="2592" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="2596" href="Monad.Instance.Setoids.K.html#2563" class="Bound">ℓ&#39;&#39;</a><a id="2599" class="Symbol">}</a>
    <a id="2605" class="Symbol">{</a><a id="2606" href="Monad.Instance.Setoids.K.html#2606" class="Bound">x</a> <a id="2608" class="Symbol">:</a> <a id="2610" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2612" href="Monad.Instance.Setoids.K.html#2569" class="Bound">X</a> <a id="2614" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="2615" class="Symbol">}</a> <a id="2617" class="Symbol">{</a><a id="2618" href="Monad.Instance.Setoids.K.html#2618" class="Bound">y</a> <a id="2620" class="Symbol">:</a> <a id="2622" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="2624" href="Monad.Instance.Setoids.K.html#2571" class="Bound">Y</a> <a id="2626" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="2627" class="Symbol">}</a> <a id="2629" class="Symbol">→</a> <a id="2631" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="2633" href="Monad.Instance.Setoids.K.html#2569" class="Bound">X</a> <a id="2635" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="2638" href="Monad.Instance.Setoids.K.html#2571" class="Bound">Y</a> <a id="2640" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="2643" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="2648" href="Monad.Instance.Setoids.K.html#2606" class="Bound">x</a> <a id="2650" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="2652" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="2657" href="Monad.Instance.Setoids.K.html#2618" class="Bound">y</a> <a id="2659" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a> <a id="2661" class="Symbol">→</a> <a id="2663" href="Monad.Instance.Setoids.K.html#2588" class="Bound">Z</a>
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  <a id="4530" class="Symbol">...</a>                             <a id="4562" class="Symbol">|</a> <a id="4564" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="4569" href="Monad.Instance.Setoids.K.html#4569" class="Bound">a</a>            <a id="4582" class="Symbol">|</a> <a id="4584" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="4589" href="Monad.Instance.Setoids.K.html#4589" class="Bound">b</a>        <a id="4598" class="Symbol">=</a> <a id="4600" href="Monad.Instance.Setoids.Delay.html#1768" class="InductiveConstructor">later∼</a> <a id="4607" class="Symbol">(</a><a id="4608" href="Monad.Instance.Setoids.K.html#3931" class="Function">iter-cong∼′</a> <a id="4620" class="Symbol">{</a><a id="4621" class="Bound">A</a><a id="4622" class="Symbol">}</a> <a id="4624" class="Symbol">{</a><a id="4625" class="Bound">X</a><a id="4626" class="Symbol">}</a> <a id="4628" class="Bound">f</a> <a id="4630" class="Symbol">(</a><a id="4631" href="Monad.Instance.Setoids.K.html#3045" class="Function">inj₂-helper</a> <a id="4643" class="Bound">f</a> <a id="4645" class="Bound">x≡y</a> <a id="4649" href="Monad.Instance.Setoids.K.html#4199" class="Bound">eqx</a> <a id="4653" href="Monad.Instance.Setoids.K.html#4216" class="Bound">eqy</a><a id="4656" class="Symbol">))</a>

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  <a id="5100" class="Symbol">...</a>                             <a id="5132" class="Symbol">|</a> <a id="5134" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="5139" href="Monad.Instance.Setoids.K.html#5139" class="Bound">a</a>            <a id="5152" class="Symbol">|</a> <a id="5154" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="5159" href="Monad.Instance.Setoids.K.html#5159" class="Bound">b</a>        <a id="5168" class="Symbol">=</a> <a id="5170" href="Monad.Instance.Setoids.K.html#2686" class="Function">inj₁-helper</a> <a id="5182" class="Bound">f</a> <a id="5184" class="Bound">x≡y</a> <a id="5188" href="Monad.Instance.Setoids.K.html#5076" class="Bound">eqx</a> <a id="5192" href="Monad.Instance.Setoids.K.html#5093" class="Bound">eqy</a>
  <a id="5198" class="Symbol">...</a>                             <a id="5230" class="Symbol">|</a> <a id="5232" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="5237" href="Monad.Instance.Setoids.K.html#5237" class="Bound">a</a>            <a id="5250" class="Symbol">|</a> <a id="5252" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="5257" href="Monad.Instance.Setoids.K.html#5257" class="Bound">b</a>        <a id="5266" class="Symbol">=</a> <a id="5268" href="Monad.Instance.Setoids.K.html#3404" class="Function">absurd-helper</a> <a id="5282" class="Bound">f</a> <a id="5284" class="Bound">x≡y</a> <a id="5288" href="Monad.Instance.Setoids.K.html#5076" class="Bound">eqx</a> <a id="5292" href="Monad.Instance.Setoids.K.html#5093" class="Bound">eqy</a>
  <a id="5298" class="Symbol">...</a>                             <a id="5330" class="Symbol">|</a> <a id="5332" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="5337" href="Monad.Instance.Setoids.K.html#5337" class="Bound">a</a>            <a id="5350" class="Symbol">|</a> <a id="5352" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="5357" href="Monad.Instance.Setoids.K.html#5357" class="Bound">b</a>        <a id="5366" class="Symbol">=</a> <a id="5368" href="Monad.Instance.Setoids.K.html#3404" class="Function">absurd-helper</a> <a id="5382" class="Bound">f</a> <a id="5384" class="Symbol">(</a><a id="5385" href="Monad.Instance.Setoids.K.html#2072" class="Function">≡-sym</a> <a id="5391" class="Bound">X</a> <a id="5393" class="Bound">x≡y</a><a id="5396" class="Symbol">)</a> <a id="5398" href="Monad.Instance.Setoids.K.html#5093" class="Bound">eqy</a> <a id="5402" href="Monad.Instance.Setoids.K.html#5076" class="Bound">eqx</a>
  <a id="5408" class="Symbol">...</a>                             <a id="5440" class="Symbol">|</a> <a id="5442" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="5447" href="Monad.Instance.Setoids.K.html#5447" class="Bound">a</a>            <a id="5460" class="Symbol">|</a> <a id="5462" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="5467" href="Monad.Instance.Setoids.K.html#5467" class="Bound">b</a>        <a id="5476" class="Symbol">=</a> <a id="5478" href="Monad.Instance.Setoids.Delay.html#3458" class="InductiveConstructor">later≈</a> <a id="5485" class="Symbol">(</a><a id="5486" href="Monad.Instance.Setoids.K.html#4813" class="Function">iter-cong′</a> <a id="5497" class="Symbol">{</a><a id="5498" class="Bound">A</a><a id="5499" class="Symbol">}</a> <a id="5501" class="Symbol">{</a><a id="5502" class="Bound">X</a><a id="5503" class="Symbol">}</a> <a id="5505" class="Bound">f</a> <a id="5507" class="Symbol">(</a><a id="5508" href="Monad.Instance.Setoids.K.html#3045" class="Function">inj₂-helper</a> <a id="5520" class="Bound">f</a> <a id="5522" class="Bound">x≡y</a> <a id="5526" href="Monad.Instance.Setoids.K.html#5076" class="Bound">eqx</a> <a id="5530" href="Monad.Instance.Setoids.K.html#5093" class="Bound">eqy</a><a id="5533" class="Symbol">))</a>

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  <a id="6124" class="Symbol">...</a>                                   <a id="6162" class="Symbol">|</a> <a id="6164" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="6169" href="Monad.Instance.Setoids.K.html#6169" class="Bound">a</a> <a id="6171" class="Symbol">=</a> <a id="6173" href="Monad.Instance.Setoids.Delay.html#4755" class="Function">≈-trans</a> <a id="6181" class="Bound">A</a> <a id="6183" class="Symbol">(</a><a id="6184" href="Monad.Instance.Setoids.Delay.html#4511" class="Function">≈-sym</a> <a id="6190" class="Bound">A</a> <a id="6192" href="Monad.Instance.Setoids.Delay.html#10235" class="Function">later-self</a><a id="6202" class="Symbol">)</a> <a id="6204" class="Symbol">(</a><a id="6205" href="Monad.Instance.Setoids.Delay.html#4293" class="Function">≈-refl</a> <a id="6212" class="Bound">A</a><a id="6213" class="Symbol">)</a>

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      <a id="7342" href="Monad.Instance.Setoids.K.html#7290" class="Function">helper</a> <a id="7349" class="Keyword">rewrite</a> <a id="7357" class="Symbol">(</a><a id="7358" href="Monad.Instance.Setoids.K.html#632" class="Function">≣-sym</a> <a id="7364" href="Monad.Instance.Setoids.K.html#6705" class="Bound">eqb</a><a id="7367" class="Symbol">)</a> <a id="7369" class="Symbol">|</a> <a id="7371" class="Symbol">(</a><a id="7372" href="Monad.Instance.Setoids.K.html#632" class="Function">≣-sym</a> <a id="7378" href="Monad.Instance.Setoids.K.html#6688" class="Bound">eqa</a><a id="7381" class="Symbol">)</a> <a id="7383" class="Symbol">=</a> <a id="7385" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="7393" class="Symbol">(</a><a id="7394" href="Monad.Instance.Setoids.Delay.html#5823" class="Function">Delayₛ</a> <a id="7401" class="Bound">A</a> <a id="7403" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="7406" class="Bound">X</a><a id="7407" class="Symbol">)</a> <a id="7409" class="Symbol">(</a><a id="7410" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="7415" class="Bound">f</a> <a id="7417" class="Bound">x≡y</a><a id="7420" class="Symbol">)</a> <a id="7422" class="Bound">f≋g</a>
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href="Monad.Instance.Setoids.K.html#9152" class="Bound">x</a> <a id="9244" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">≈</a> <a id="9246" href="Monad.Instance.Setoids.K.html#2210" class="Function">iter</a> <a id="9251" class="Symbol">{</a><a id="9252" href="Monad.Instance.Setoids.K.html#9086" class="Bound">A</a><a id="9253" class="Symbol">}</a> <a id="9255" class="Symbol">{</a><a id="9256" href="Monad.Instance.Setoids.K.html#9088" class="Bound">X</a> <a id="9258" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="9261" href="Monad.Instance.Setoids.K.html#9090" class="Bound">Y</a><a id="9262" class="Symbol">}</a> <a id="9264" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="9266" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="9268" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="9273" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a 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href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="9373" class="Symbol">(</a><a id="9374" href="Monad.Instance.Setoids.Delay.html#5823" class="Function">Delayₛ</a> <a id="9381" href="Monad.Instance.Setoids.K.html#9344" class="Bound">A</a> <a id="9383" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="9386" href="Monad.Instance.Setoids.K.html#9346" class="Bound">X</a><a id="9387" class="Symbol">)}</a> <a id="9390" class="Symbol">{</a><a id="9391" href="Monad.Instance.Setoids.K.html#9391" class="Bound">h</a> <a id="9393" class="Symbol">:</a> <a id="9395" href="Monad.Instance.Setoids.K.html#9348" class="Bound">Y</a> <a id="9397" href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="9399" class="Symbol">(</a><a id="9400" href="Monad.Instance.Setoids.K.html#9346" class="Bound">X</a> <a id="9402" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="9405" 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      <a id="10215" class="Symbol">...</a>               <a id="10233" class="Symbol">|</a> <a id="10235" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="10240" href="Monad.Instance.Setoids.K.html#10240" class="Bound">c</a> <a id="10242" class="Symbol">=</a> <a id="10244" href="Monad.Instance.Setoids.Delay.html#3458" class="InductiveConstructor">later≈</a> <a id="10251" class="Symbol">(</a><a id="10252" href="Monad.Instance.Setoids.K.html#10011" class="Function">helper′</a> <a id="10260" href="Monad.Instance.Setoids.K.html#10240" class="Bound">c</a><a id="10261" class="Symbol">)</a>
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    <a id="10764" class="Symbol">;</a> <a id="10766" href="Algebra.Elgot.html#2086" class="Field">#-Uniformity</a> <a id="10779" class="Symbol">=</a> <a id="10781" class="Symbol">λ</a> <a id="10783" class="Symbol">{</a><a id="10784" href="Monad.Instance.Setoids.K.html#10784" class="Bound">X</a><a id="10785" class="Symbol">}</a> <a id="10787" class="Symbol">{</a><a id="10788" href="Monad.Instance.Setoids.K.html#10788" class="Bound">Y</a><a id="10789" class="Symbol">}</a> <a id="10791" class="Symbol">{</a><a id="10792" href="Monad.Instance.Setoids.K.html#10792" class="Bound">f</a><a id="10793" class="Symbol">}</a> <a id="10795" class="Symbol">{</a><a id="10796" href="Monad.Instance.Setoids.K.html#10796" class="Bound">g</a><a id="10797" class="Symbol">}</a> <a id="10799" class="Symbol">{</a><a id="10800" href="Monad.Instance.Setoids.K.html#10800" class="Bound">h</a><a id="10801" class="Symbol">}</a> <a id="10803" href="Monad.Instance.Setoids.K.html#10803" class="Bound">eq</a> <a id="10806" class="Symbol">{</a><a id="10807" href="Monad.Instance.Setoids.K.html#10807" class="Bound">x</a><a id="10808" class="Symbol">}</a> <a id="10810" class="Symbol">→</a> <a id="10812" href="Monad.Instance.Setoids.K.html#7684" class="Function">iter-uni</a> <a id="10821" class="Symbol">{</a><a id="10822" href="Monad.Instance.Setoids.K.html#10670" class="Bound">A</a><a id="10823" class="Symbol">}</a> <a id="10825" class="Symbol">{</a><a id="10826" href="Monad.Instance.Setoids.K.html#10784" class="Bound">X</a><a id="10827" class="Symbol">}</a> <a id="10829" class="Symbol">{</a><a id="10830" href="Monad.Instance.Setoids.K.html#10788" class="Bound">Y</a><a id="10831" class="Symbol">}</a> <a id="10833" class="Symbol">{</a><a id="10834" href="Monad.Instance.Setoids.K.html#10792" class="Bound">f</a><a id="10835" class="Symbol">}</a> <a id="10837" class="Symbol">{</a><a id="10838" href="Monad.Instance.Setoids.K.html#10796" class="Bound">g</a><a id="10839" class="Symbol">}</a> <a id="10841" class="Symbol">{</a><a id="10842" href="Monad.Instance.Setoids.K.html#10800" class="Bound">h</a><a id="10843" class="Symbol">}</a> <a id="10845" href="Monad.Instance.Setoids.K.html#10803" class="Bound">eq</a> <a id="10848" class="Symbol">{</a><a id="10849" href="Monad.Instance.Setoids.K.html#10807" class="Bound">x</a><a id="10850" class="Symbol">}</a> <a id="10852" class="Symbol">{</a><a id="10853" href="Monad.Instance.Setoids.K.html#10800" class="Bound">h</a> <a id="10855" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="10859" href="Monad.Instance.Setoids.K.html#10807" class="Bound">x</a><a id="10860" class="Symbol">}</a> <a id="10862" class="Symbol">(</a><a id="10863" href="Monad.Instance.Setoids.K.html#2057" class="Function">≡-refl</a> <a id="10870" href="Monad.Instance.Setoids.K.html#10788" class="Bound">Y</a><a id="10871" class="Symbol">)</a>
    <a id="10877" class="Symbol">;</a> <a id="10879" href="Algebra.Elgot.html#2216" class="Field">#-Folding</a> <a id="10889" class="Symbol">=</a> <a id="10891" class="Symbol">λ</a> <a id="10893" class="Symbol">{</a><a id="10894" href="Monad.Instance.Setoids.K.html#10894" class="Bound">X</a><a id="10895" class="Symbol">}</a> <a id="10897" class="Symbol">{</a><a id="10898" href="Monad.Instance.Setoids.K.html#10898" class="Bound">Y</a><a id="10899" class="Symbol">}</a> <a id="10901" class="Symbol">{</a><a id="10902" href="Monad.Instance.Setoids.K.html#10902" class="Bound">f</a><a id="10903" class="Symbol">}</a> <a id="10905" class="Symbol">{</a><a id="10906" href="Monad.Instance.Setoids.K.html#10906" class="Bound">h</a><a id="10907" class="Symbol">}</a> <a id="10909" class="Symbol">{</a><a id="10910" href="Monad.Instance.Setoids.K.html#10910" class="Bound">x</a><a id="10911" class="Symbol">}</a> <a id="10913" class="Symbol">→</a> <a id="10915" href="Monad.Instance.Setoids.K.html#9068" class="Function">iter-folding</a> <a id="10928" class="Symbol">{</a><a id="10929" href="Monad.Instance.Setoids.K.html#10670" class="Bound">A</a><a id="10930" class="Symbol">}</a> <a id="10932" class="Symbol">{</a><a id="10933" href="Monad.Instance.Setoids.K.html#10894" class="Bound">X</a><a id="10934" class="Symbol">}</a> <a id="10936" class="Symbol">{</a><a id="10937" href="Monad.Instance.Setoids.K.html#10898" class="Bound">Y</a><a id="10938" class="Symbol">}</a> <a id="10940" class="Symbol">{</a><a id="10941" href="Monad.Instance.Setoids.K.html#10902" class="Bound">f</a><a id="10942" class="Symbol">}</a> <a id="10944" class="Symbol">{</a><a id="10945" href="Monad.Instance.Setoids.K.html#10906" class="Bound">h</a><a id="10946" class="Symbol">}</a> <a id="10948" class="Symbol">{</a><a id="10949" href="Monad.Instance.Setoids.K.html#10910" class="Bound">x</a><a id="10950" class="Symbol">}</a>
    <a id="10956" class="Symbol">;</a> <a id="10958" href="Algebra.Elgot.html#2331" class="Field">#-resp-≈</a> <a id="10967" class="Symbol">=</a> <a id="10969" class="Symbol">λ</a> <a id="10971" class="Symbol">{</a><a id="10972" href="Monad.Instance.Setoids.K.html#10972" class="Bound">X</a><a id="10973" class="Symbol">}</a> <a id="10975" class="Symbol">{</a><a id="10976" href="Monad.Instance.Setoids.K.html#10976" class="Bound">f</a><a id="10977" class="Symbol">}</a> <a id="10979" class="Symbol">{</a><a id="10980" href="Monad.Instance.Setoids.K.html#10980" class="Bound">g</a><a id="10981" class="Symbol">}</a> <a id="10983" href="Monad.Instance.Setoids.K.html#10983" class="Bound">f≋g</a> <a id="10987" class="Symbol">{</a><a id="10988" href="Monad.Instance.Setoids.K.html#10988" class="Bound">x</a><a id="10989" class="Symbol">}</a> <a id="10991" class="Symbol">→</a> <a id="10993" href="Monad.Instance.Setoids.K.html#6218" class="Function">iter-resp-≈</a> <a id="11005" class="Symbol">{</a><a id="11006" href="Monad.Instance.Setoids.K.html#10670" class="Bound">A</a><a id="11007" class="Symbol">}</a> <a id="11009" class="Symbol">{</a><a id="11010" href="Monad.Instance.Setoids.K.html#10972" class="Bound">X</a><a id="11011" class="Symbol">}</a> <a id="11013" href="Monad.Instance.Setoids.K.html#10976" class="Bound">f</a> <a id="11015" href="Monad.Instance.Setoids.K.html#10980" class="Bound">g</a> <a id="11017" href="Monad.Instance.Setoids.K.html#10983" class="Bound">f≋g</a> <a id="11021" class="Symbol">{</a><a id="11022" href="Monad.Instance.Setoids.K.html#10988" class="Bound">x</a><a id="11023" class="Symbol">}</a> <a id="11025" class="Symbol">{</a><a id="11026" href="Monad.Instance.Setoids.K.html#10988" class="Bound">x</a><a id="11027" class="Symbol">}</a> <a id="11029" class="Symbol">(</a><a id="11030" href="Monad.Instance.Setoids.K.html#2057" class="Function">≡-refl</a> <a id="11037" href="Monad.Instance.Setoids.K.html#10972" class="Bound">X</a><a id="11038" class="Symbol">)</a>
    <a id="11044" class="Symbol">}</a>

  <a id="delay-algebras"></a><a id="11049" href="Monad.Instance.Setoids.K.html#11049" class="Function">delay-algebras</a> <a id="11064" class="Symbol">:</a> <a id="11066" class="Symbol">∀</a> <a id="11068" class="Symbol">(</a><a id="11069" href="Monad.Instance.Setoids.K.html#11069" class="Bound">A</a> <a id="11071" class="Symbol">:</a> <a id="11073" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="11080" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="11082" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="11083" class="Symbol">)</a> <a id="11085" class="Symbol">→</a> <a id="11087" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a>
  <a id="11103" href="Monad.Instance.Setoids.K.html#11049" class="Function">delay-algebras</a> <a id="11118" href="Monad.Instance.Setoids.K.html#11118" class="Bound">A</a> <a id="11120" class="Symbol">=</a> <a id="11122" class="Keyword">record</a> <a id="11129" class="Symbol">{</a> <a id="11131" href="Algebra.Elgot.html#16018" class="Field">A</a> <a id="11133" class="Symbol">=</a> <a id="11135" href="Monad.Instance.Setoids.Delay.html#5823" class="Function">Delayₛ</a> <a id="11142" href="Monad.Instance.Setoids.K.html#11118" class="Bound">A</a> <a id="11144" class="Symbol">;</a> <a id="11146" href="Algebra.Elgot.html#16032" class="Field">algebra</a> <a id="11154" class="Symbol">=</a> <a id="11156" href="Monad.Instance.Setoids.K.html#10580" class="Function">delay-algebras-on</a> <a id="11174" class="Symbol">{</a><a id="11175" href="Monad.Instance.Setoids.K.html#11118" class="Bound">A</a><a id="11176" class="Symbol">}}</a>

  <a id="11182" class="Keyword">open</a> <a id="11187" href="Algebra.Elgot.html#15964" class="Module">Elgot-Algebra</a> <a id="11201" class="Keyword">using</a> <a id="11207" class="Symbol">(</a><a id="11208" href="Algebra.Elgot.html#2011" class="Function">#-Fixpoint</a><a id="11218" class="Symbol">;</a> <a id="11220" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a><a id="11232" class="Symbol">;</a> <a id="11234" href="Algebra.Elgot.html#2470" class="Function">#-Compositionality</a><a id="11252" class="Symbol">;</a> <a id="11254" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a><a id="11262" class="Symbol">;</a> <a id="11264" href="Algebra.Elgot.html#8386" class="Function">#-Diamond</a><a id="11273" class="Symbol">)</a> <a id="11275" class="Keyword">renaming</a> <a id="11284" class="Symbol">(</a><a id="11285" href="Algebra.Elgot.html#16018" class="Field">A</a> <a id="11287" class="Symbol">to</a> <a id="11290" class="Field">⟦_⟧</a><a id="11293" class="Symbol">)</a>


  <a id="delay-lift"></a><a id="11299" href="Monad.Instance.Setoids.K.html#11299" class="Function">delay-lift</a> <a id="11310" class="Symbol">:</a> <a id="11312" class="Symbol">∀</a> <a id="11314" class="Symbol">{</a><a id="11315" href="Monad.Instance.Setoids.K.html#11315" class="Bound">A</a> <a id="11317" class="Symbol">:</a> <a id="11319" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="11326" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="11328" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="11329" class="Symbol">}</a> <a id="11331" class="Symbol">{</a><a id="11332" href="Monad.Instance.Setoids.K.html#11332" class="Bound">B</a> <a id="11334" class="Symbol">:</a> <a id="11336" href="Algebra.Elgot.html#15964" class="Record">Elgot-Algebra</a><a id="11349" class="Symbol">}</a> <a id="11351" class="Symbol">→</a> <a id="11353" href="Monad.Instance.Setoids.K.html#11315" class="Bound">A</a> <a id="11355" href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="11357" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="11359" href="Monad.Instance.Setoids.K.html#11332" class="Bound">B</a> <a id="11361" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="11363" class="Symbol">→</a> <a id="11365" href="Category.Construction.ElgotAlgebras.html#727" class="Record">Elgot-Algebra-Morphism</a> <a id="11388" class="Symbol">(</a><a id="11389" href="Monad.Instance.Setoids.K.html#11049" class="Function">delay-algebras</a> <a id="11404" href="Monad.Instance.Setoids.K.html#11315" class="Bound">A</a><a id="11405" class="Symbol">)</a> <a id="11407" href="Monad.Instance.Setoids.K.html#11332" class="Bound">B</a>
  <a id="11411" href="Monad.Instance.Setoids.K.html#11299" class="Function">delay-lift</a> <a id="11422" class="Symbol">{</a><a id="11423" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="11424" class="Symbol">}</a> <a id="11426" class="Symbol">{</a><a id="11427" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a><a id="11428" class="Symbol">}</a> <a id="11430" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="11432" class="Symbol">=</a> <a id="11434" class="Keyword">record</a> <a id="11441" class="Symbol">{</a> <a id="11443" href="Category.Construction.ElgotAlgebras.html#794" class="Field">h</a> <a id="11445" class="Symbol">=</a> <a id="11447" href="Monad.Instance.Setoids.K.html#18889" class="Function">delay-lift&#39;</a> <a id="11459" class="Symbol">;</a> <a id="11461" href="Category.Construction.ElgotAlgebras.html#812" class="Field">preserves</a> <a id="11471" class="Symbol">=</a> <a id="11473" class="Symbol">λ</a> <a id="11475" class="Symbol">{</a><a id="11476" href="Monad.Instance.Setoids.K.html#11476" class="Bound">X</a><a id="11477" class="Symbol">}</a> <a id="11479" class="Symbol">{</a><a id="11480" href="Monad.Instance.Setoids.K.html#11480" class="Bound">g</a><a id="11481" class="Symbol">}</a> <a id="11483" class="Symbol">{</a><a id="11484" href="Monad.Instance.Setoids.K.html#11484" class="Bound">x</a><a id="11485" class="Symbol">}</a> <a id="11487" class="Symbol">→</a> <a id="11489" href="Monad.Instance.Setoids.K.html#19960" class="Function">preserves&#39;</a> <a id="11500" class="Symbol">{</a><a id="11501" href="Monad.Instance.Setoids.K.html#11476" class="Bound">X</a><a id="11502" class="Symbol">}</a> <a id="11504" class="Symbol">{</a><a id="11505" href="Monad.Instance.Setoids.K.html#11480" class="Bound">g</a><a id="11506" class="Symbol">}</a> <a id="11508" class="Symbol">{</a><a id="11509" href="Monad.Instance.Setoids.K.html#11484" class="Bound">x</a><a id="11510" class="Symbol">}</a> <a id="11512" class="Symbol">}</a>
    <a id="11518" class="Keyword">where</a>
    <a id="11528" class="Keyword">open</a> <a id="11533" href="Algebra.Elgot.html#15964" class="Module">Elgot-Algebra</a> <a id="11547" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="11549" class="Keyword">using</a> <a id="11555" class="Symbol">(</a><a id="11556" href="Algebra.Elgot.html#1938" class="Function Operator">_#</a><a id="11558" class="Symbol">)</a>
    <a id="11564" class="Comment">-- (f + id) ∘ out</a>
    <a id="11586" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="11594" class="Symbol">:</a> <a id="11596" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="11602" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11604" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="11606" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11608" class="Symbol">→</a> <a id="11610" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11612" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="11614" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="11616" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="11618" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11620" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="11622" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="11628" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11630" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="11632" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a>
    <a id="11638" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="11646" class="Symbol">(</a><a id="11647" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="11651" href="Monad.Instance.Setoids.K.html#11651" class="Bound">x</a><a id="11652" class="Symbol">)</a>   <a id="11656" class="Symbol">=</a> <a id="11658" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="11663" class="Symbol">(</a><a id="11664" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&lt;</a> <a id="11666" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="11668" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&gt;</a> <a id="11670" href="Monad.Instance.Setoids.K.html#11651" class="Bound">x</a><a id="11671" class="Symbol">)</a>
    <a id="11677" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="11685" class="Symbol">(</a><a id="11686" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="11692" href="Monad.Instance.Setoids.K.html#11692" class="Bound">x</a><a id="11693" class="Symbol">)</a> <a id="11695" class="Symbol">=</a> <a id="11697" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="11702" class="Symbol">(</a><a id="11703" href="Monad.Instance.Setoids.Delay.html#1190" class="Field">force</a> <a id="11709" href="Monad.Instance.Setoids.K.html#11692" class="Bound">x</a><a id="11710" class="Symbol">)</a>

    <a id="11717" href="Monad.Instance.Setoids.K.html#11717" class="Function">helper₁-cong</a> <a id="11730" class="Symbol">:</a> <a id="11732" class="Symbol">{</a><a id="11733" href="Monad.Instance.Setoids.K.html#11733" class="Bound">x</a> <a id="11735" href="Monad.Instance.Setoids.K.html#11735" class="Bound">y</a> <a id="11737" class="Symbol">:</a> <a id="11739" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="11745" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="11747" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="11749" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="11750" class="Symbol">}</a> <a id="11752" class="Symbol">→</a> <a id="11754" class="Symbol">(</a><a id="11755" href="Monad.Instance.Setoids.K.html#11755" class="Bound">x∼y</a> <a id="11759" class="Symbol">:</a> <a id="11761" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">[</a> <a id="11763" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="11765" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">][</a> <a id="11768" href="Monad.Instance.Setoids.K.html#11733" class="Bound">x</a> <a id="11770" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">∼</a> <a id="11772" href="Monad.Instance.Setoids.K.html#11735" class="Bound">y</a> <a id="11774" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">]</a><a id="11775" class="Symbol">)</a> <a id="11777" class="Symbol">→</a> <a id="11779" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="11781" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="11783" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="11785" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="11787" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="11790" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="11798" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="11800" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="11803" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="11811" href="Monad.Instance.Setoids.K.html#11733" class="Bound">x</a> <a id="11813" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="11815" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="11823" href="Monad.Instance.Setoids.K.html#11735" class="Bound">y</a> <a id="11825" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
    <a id="11831" href="Monad.Instance.Setoids.K.html#11717" class="Function">helper₁-cong</a> <a id="11844" class="Symbol">(</a><a id="11845" href="Monad.Instance.Setoids.Delay.html#1711" class="InductiveConstructor">now∼</a> <a id="11850" href="Monad.Instance.Setoids.K.html#11850" class="Bound">x≡y</a><a id="11853" class="Symbol">)</a>   <a id="11857" class="Symbol">=</a> <a id="11859" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a> <a id="11864" class="Symbol">(</a><a id="11865" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="11870" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="11872" href="Monad.Instance.Setoids.K.html#11850" class="Bound">x≡y</a><a id="11875" class="Symbol">)</a>
    <a id="11881" href="Monad.Instance.Setoids.K.html#11717" class="Function">helper₁-cong</a> <a id="11894" class="Symbol">(</a><a id="11895" href="Monad.Instance.Setoids.Delay.html#1768" class="InductiveConstructor">later∼</a> <a id="11902" href="Monad.Instance.Setoids.K.html#11902" class="Bound">x≡y</a><a id="11905" class="Symbol">)</a> <a id="11907" class="Symbol">=</a> <a id="11909" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a> <a id="11914" class="Symbol">(</a><a id="11915" href="Monad.Instance.Setoids.Delay.html#1929" class="Field">force∼</a> <a id="11922" href="Monad.Instance.Setoids.K.html#11902" class="Bound">x≡y</a><a id="11925" class="Symbol">)</a>
  
    <a id="11934" class="Comment">-- -- setoid-morphism that preserves strong-bisimilarity</a>
    <a id="11995" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12002" class="Symbol">:</a> <a id="12004" class="Symbol">(</a><a id="12005" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="12013" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="12014" class="Symbol">)</a> <a id="12016" href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="12018" class="Symbol">(</a><a id="12019" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12021" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12023" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="12025" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="12028" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="12036" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="12037" class="Symbol">)</a>
    <a id="12043" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12050" class="Symbol">=</a> <a id="12052" class="Keyword">record</a> <a id="12059" class="Symbol">{</a> <a id="12061" href="Function.Bundles.html#2094" class="Field">to</a> <a id="12064" class="Symbol">=</a> <a id="12066" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="12074" class="Symbol">;</a> <a id="12076" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="12081" class="Symbol">=</a> <a id="12083" href="Monad.Instance.Setoids.K.html#11717" class="Function">helper₁-cong</a><a id="12095" class="Symbol">}</a>

    <a id="12102" href="Monad.Instance.Setoids.K.html#12102" class="Function">helper#∼-cong</a> <a id="12116" class="Symbol">:</a> <a id="12118" class="Symbol">{</a><a id="12119" href="Monad.Instance.Setoids.K.html#12119" class="Bound">x</a> <a id="12121" href="Monad.Instance.Setoids.K.html#12121" class="Bound">y</a> <a id="12123" class="Symbol">:</a> <a id="12125" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="12131" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="12133" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12135" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="12136" class="Symbol">}</a> <a id="12138" class="Symbol">→</a> <a id="12140" class="Symbol">(</a><a id="12141" href="Monad.Instance.Setoids.K.html#12141" class="Bound">x∼y</a> <a id="12145" class="Symbol">:</a> <a id="12147" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">[</a> <a id="12149" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12151" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">][</a> <a id="12154" href="Monad.Instance.Setoids.K.html#12119" class="Bound">x</a> <a id="12156" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">∼</a> <a id="12158" href="Monad.Instance.Setoids.K.html#12121" class="Bound">y</a> <a id="12160" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">]</a><a id="12161" class="Symbol">)</a> <a id="12163" class="Symbol">→</a> <a id="12165" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="12167" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12169" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12171" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="12173" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="12176" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12183" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12185" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12189" href="Monad.Instance.Setoids.K.html#12119" class="Bound">x</a> <a id="12191" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="12193" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12200" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12202" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12206" href="Monad.Instance.Setoids.K.html#12121" class="Bound">y</a> <a id="12208" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
    <a id="12214" href="Monad.Instance.Setoids.K.html#12102" class="Function">helper#∼-cong</a> <a id="12228" class="Symbol">{</a><a id="12229" href="Monad.Instance.Setoids.K.html#12229" class="Bound">x</a><a id="12230" class="Symbol">}</a> <a id="12232" class="Symbol">{</a><a id="12233" href="Monad.Instance.Setoids.K.html#12233" class="Bound">y</a><a id="12234" class="Symbol">}</a> <a id="12236" href="Monad.Instance.Setoids.K.html#12236" class="Bound">x∼y</a> <a id="12240" class="Symbol">=</a> <a id="12242" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="12247" class="Symbol">(</a><a id="12248" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12255" href="Algebra.Elgot.html#1938" class="Function Operator">#</a><a id="12256" class="Symbol">)</a> <a id="12258" href="Monad.Instance.Setoids.K.html#12236" class="Bound">x∼y</a>

    <a id="12267" href="Monad.Instance.Setoids.K.html#12267" class="Function">helper#≈-cong</a> <a id="12281" class="Symbol">:</a> <a id="12283" class="Symbol">{</a><a id="12284" href="Monad.Instance.Setoids.K.html#12284" class="Bound">x</a> <a id="12286" href="Monad.Instance.Setoids.K.html#12286" class="Bound">y</a> <a id="12288" class="Symbol">:</a> <a id="12290" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="12296" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="12298" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12300" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a><a id="12301" class="Symbol">}</a> <a id="12303" class="Symbol">→</a> <a id="12305" class="Symbol">(</a><a id="12306" href="Monad.Instance.Setoids.K.html#12306" class="Bound">x≈y</a> <a id="12310" class="Symbol">:</a> <a id="12312" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">[</a> <a id="12314" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12316" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">][</a> <a id="12319" href="Monad.Instance.Setoids.K.html#12284" class="Bound">x</a> <a id="12321" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">≈</a> <a id="12323" href="Monad.Instance.Setoids.K.html#12286" class="Bound">y</a> <a id="12325" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">]</a><a id="12326" class="Symbol">)</a> <a id="12328" class="Symbol">→</a> <a id="12330" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="12332" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12334" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12336" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="12338" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="12341" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12348" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12350" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12354" href="Monad.Instance.Setoids.K.html#12284" class="Bound">x</a> <a id="12356" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="12358" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12365" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12367" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12371" href="Monad.Instance.Setoids.K.html#12286" class="Bound">y</a> <a id="12373" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
    <a id="12379" class="Comment">-- key special case</a>
    <a id="12403" href="Monad.Instance.Setoids.K.html#12403" class="Function">helper#≈-cong&#39;</a> <a id="12418" class="Symbol">:</a> <a id="12420" class="Symbol">{</a><a id="12421" href="Monad.Instance.Setoids.K.html#12421" class="Bound">z</a> <a id="12423" class="Symbol">:</a> <a id="12425" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="12431" class="Symbol">(</a><a id="12432" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="12434" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12436" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="12438" href="Data.Product.Base.html#1618" class="Function Operator">×</a> <a id="12440" href="Category.Ambient.Setoids.html#1884" class="Datatype">ℕ</a><a id="12441" class="Symbol">)}</a> <a id="12444" class="Symbol">→</a> <a id="12446" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="12448" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12450" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12452" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="12454" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="12457" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12464" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12466" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12470" href="Monad.Instance.Setoids.Delay.html#7297" class="Function">liftF</a> <a id="12476" href="Data.Product.Base.html#636" class="Field">proj₁</a> <a id="12482" href="Monad.Instance.Setoids.K.html#12421" class="Bound">z</a> <a id="12484" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="12486" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="12493" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="12495" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="12499" href="Monad.Instance.Setoids.Delay.html#12391" class="Function">μ</a> <a id="12501" class="Symbol">{</a><a id="12502" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="12503" class="Symbol">}</a> <a id="12505" class="Symbol">(</a><a id="12506" href="Monad.Instance.Setoids.Delay.html#7297" class="Function">liftF</a> <a id="12512" class="Symbol">(</a><a id="12513" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a> <a id="12515" class="Symbol">{</a><a id="12516" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="12517" class="Symbol">})</a> <a id="12520" href="Monad.Instance.Setoids.K.html#12421" class="Bound">z</a><a id="12521" class="Symbol">)</a> <a id="12523" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>

    <a id="12530" href="Monad.Instance.Setoids.K.html#12267" class="Function">helper#≈-cong</a> <a id="12544" href="Monad.Instance.Setoids.K.html#12544" class="Bound">x≈y</a> <a id="12548" class="Symbol">=</a>
      <a id="12556" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="12564" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12566" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12568" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a>
         <a id="12579" class="Symbol">(</a><a id="12580" href="Monad.Instance.Setoids.K.html#12102" class="Function">helper#∼-cong</a> <a id="12594" class="Symbol">(</a><a id="12595" href="Monad.Instance.Setoids.Delay.html#2377" class="Function">∼-sym</a> <a id="12601" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="12603" class="Symbol">(</a><a id="12604" href="Monad.Instance.Setoids.Delay.html#21437" class="Function">delta-prop₂</a> <a id="12616" class="Symbol">{</a><a id="12617" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="12618" class="Symbol">}</a> <a id="12620" href="Monad.Instance.Setoids.K.html#12993" class="Function">ineq₂</a><a id="12625" class="Symbol">)))</a>
         <a id="12638" class="Symbol">(</a><a id="12639" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="12647" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12649" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12651" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a>
           <a id="12664" class="Symbol">(</a><a id="12665" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="12673" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="12675" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="12677" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a>
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        <a id="14397" href="Monad.Instance.Setoids.K.html#14269" class="Function">helper₁&#39;&#39;</a> <a id="14407" class="Symbol">(</a><a id="14408" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="14414" href="Monad.Instance.Setoids.K.html#14414" class="Bound">y</a><a id="14415" class="Symbol">)</a>      <a id="14422" class="Symbol">=</a> <a id="14424" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="14429" class="Symbol">(</a><a id="14430" href="Monad.Instance.Setoids.Delay.html#1190" class="Field">force</a> <a id="14436" href="Monad.Instance.Setoids.K.html#14414" class="Bound">y</a><a id="14437" class="Symbol">)</a>

        <a id="14448" href="Monad.Instance.Setoids.K.html#14448" class="Function">helper₁-cong&#39;&#39;</a> <a id="14463" class="Symbol">:</a> <a id="14465" class="Symbol">{</a><a id="14466" href="Monad.Instance.Setoids.K.html#14466" class="Bound">x</a> <a id="14468" href="Monad.Instance.Setoids.K.html#14468" class="Bound">y</a> <a id="14470" class="Symbol">:</a> <a id="14472" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="14478" class="Symbol">(</a><a id="14479" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="14481" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="14483" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="14485" href="Data.Product.Base.html#1618" class="Function Operator">×</a> <a id="14487" href="Category.Ambient.Setoids.html#1884" class="Datatype">ℕ</a> <a id="14489" class="Symbol">{</a><a id="14490" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="14491" class="Symbol">})}</a> <a id="14495" class="Symbol">→</a> <a id="14497" class="Symbol">(</a><a id="14498" href="Monad.Instance.Setoids.K.html#14498" class="Bound">x∼y</a> <a id="14502" class="Symbol">:</a> <a id="14504" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">[</a> <a id="14506" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="14508" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="14511" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a> <a id="14520" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">][</a> <a id="14523" href="Monad.Instance.Setoids.K.html#14466" class="Bound">x</a> <a id="14525" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">∼</a> <a id="14527" href="Monad.Instance.Setoids.K.html#14468" class="Bound">y</a> <a id="14529" href="Monad.Instance.Setoids.K.html#1877" class="Datatype Operator">]</a><a id="14530" class="Symbol">)</a> <a id="14532" class="Symbol">→</a> <a id="14534" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="14536" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="14538" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="14540" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="14542" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="14545" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="14553" class="Symbol">(</a><a id="14554" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="14556" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="14559" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="14567" class="Symbol">)</a> <a id="14569" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="14572" href="Monad.Instance.Setoids.K.html#14269" class="Function">helper₁&#39;&#39;</a> <a id="14582" href="Monad.Instance.Setoids.K.html#14466" class="Bound">x</a> <a id="14584" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="14586" href="Monad.Instance.Setoids.K.html#14269" class="Function">helper₁&#39;&#39;</a> <a id="14596" href="Monad.Instance.Setoids.K.html#14468" class="Bound">y</a> <a id="14598" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
        <a id="14608" href="Monad.Instance.Setoids.K.html#14448" class="Function">helper₁-cong&#39;&#39;</a> <a id="14623" class="Symbol">{</a><a id="14624" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="14628" class="Symbol">(</a><a id="14629" href="Monad.Instance.Setoids.K.html#14629" class="Bound">x</a> <a id="14631" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="14633" class="Symbol">_)}</a>  <a id="14638" class="Symbol">(</a><a id="14639" href="Monad.Instance.Setoids.Delay.html#1711" class="InductiveConstructor">now∼</a> <a id="14644" class="Symbol">(</a><a id="14645" href="Monad.Instance.Setoids.K.html#14645" class="Bound">x≡y</a> <a id="14649" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="14651" href="Monad.Instance.Setoids.K.html#647" class="InductiveConstructor">≣-refl</a><a id="14657" class="Symbol">))</a> <a id="14660" class="Symbol">=</a> <a id="14662" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a> <a id="14667" class="Symbol">(</a><a id="14668" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="14673" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="14675" href="Monad.Instance.Setoids.K.html#14645" class="Bound">x≡y</a><a id="14678" class="Symbol">)</a>
        <a id="14688" href="Monad.Instance.Setoids.K.html#14448" class="Function">helper₁-cong&#39;&#39;</a> <a id="14703" class="Symbol">(</a><a id="14704" href="Monad.Instance.Setoids.Delay.html#1768" class="InductiveConstructor">later∼</a> <a id="14711" href="Monad.Instance.Setoids.K.html#14711" class="Bound">x∼y</a><a id="14714" class="Symbol">)</a> <a id="14716" class="Symbol">=</a> <a id="14718" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a> <a id="14723" class="Symbol">(</a><a id="14724" href="Monad.Instance.Setoids.Delay.html#1929" class="Field">force∼</a> <a id="14731" href="Monad.Instance.Setoids.K.html#14711" class="Bound">x∼y</a><a id="14734" class="Symbol">)</a>

        <a id="14745" href="Monad.Instance.Setoids.K.html#14745" class="Function">helper&#39;&#39;</a> <a id="14754" class="Symbol">:</a> <a id="14756" class="Symbol">(</a><a id="14757" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="14765" class="Symbol">(</a><a id="14766" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="14768" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="14771" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="14779" class="Symbol">))</a> <a id="14782" href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="14784" class="Symbol">(</a><a id="14785" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="14787" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="14789" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="14791" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="14794" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="14802" class="Symbol">(</a><a id="14803" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="14805" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="14808" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="14816" class="Symbol">))</a>
        <a id="14827" href="Monad.Instance.Setoids.K.html#14745" class="Function">helper&#39;&#39;</a> <a id="14836" class="Symbol">=</a> <a id="14838" class="Keyword">record</a> <a id="14845" class="Symbol">{</a> <a id="14847" href="Function.Bundles.html#2094" class="Field">to</a> <a id="14850" class="Symbol">=</a> <a id="14852" href="Monad.Instance.Setoids.K.html#14269" class="Function">helper₁&#39;&#39;</a> <a id="14862" class="Symbol">;</a> <a id="14864" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="14869" class="Symbol">=</a> <a id="14871" href="Monad.Instance.Setoids.K.html#14448" class="Function">helper₁-cong&#39;&#39;</a><a id="14885" class="Symbol">}</a>

        <a id="14896" class="Comment">-- Needs #-Diamond</a>
        <a id="14923" href="Monad.Instance.Setoids.K.html#14923" class="Function">eq₀</a> <a id="14927" class="Symbol">:</a> <a id="14929" class="Symbol">∀</a> <a id="14931" class="Symbol">{</a><a id="14932" href="Monad.Instance.Setoids.K.html#14932" class="Bound">z</a><a id="14933" class="Symbol">}</a> <a id="14935" class="Symbol">→</a> <a id="14937" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="14939" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="14941" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="14943" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="14945" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="14948" href="Monad.Instance.Setoids.K.html#14122" class="Function">helper&#39;</a> <a id="14956" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="14958" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="14962" href="Monad.Instance.Setoids.K.html#14932" class="Bound">z</a> <a id="14964" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="14966" href="Monad.Instance.Setoids.K.html#14745" class="Function">helper&#39;&#39;</a> <a id="14975" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="14977" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="14981" href="Monad.Instance.Setoids.K.html#14932" class="Bound">z</a> <a id="14983" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
        <a id="14993" href="Monad.Instance.Setoids.K.html#14923" class="Function">eq₀</a> <a id="14997" class="Symbol">{</a><a id="14998" href="Monad.Instance.Setoids.K.html#14998" class="Bound">z</a><a id="14999" class="Symbol">}</a> <a id="15001" class="Symbol">=</a> <a id="15003" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="15011" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="15013" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15015" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> 
                    <a id="15038" class="Symbol">(</a><a id="15039" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="15048" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15050" class="Symbol">{</a><a id="15051" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="15059" class="Symbol">(</a><a id="15060" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="15062" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="15065" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="15073" class="Symbol">)}</a> <a id="15076" class="Symbol">{</a><a id="15077" href="Monad.Instance.Setoids.K.html#14122" class="Function">helper&#39;</a><a id="15084" class="Symbol">}</a> <a id="15086" href="Monad.Instance.Setoids.K.html#16318" class="Function">step₁</a><a id="15091" class="Symbol">)</a>
                    <a id="15113" class="Symbol">(</a><a id="15114" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="15122" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="15124" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15126" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a>
                      <a id="15150" class="Symbol">(</a><a id="15151" href="Algebra.Elgot.html#8386" class="Function">#-Diamond</a> <a id="15161" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15163" class="Symbol">{</a><a id="15164" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="15172" class="Symbol">(</a><a id="15173" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="15175" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="15178" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="15186" class="Symbol">)}</a> <a id="15189" href="Monad.Instance.Setoids.K.html#16125" class="Function">helper&#39;&#39;&#39;</a><a id="15198" class="Symbol">)</a> 
                      <a id="15223" class="Symbol">(</a><a id="15224" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="15233" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15235" class="Symbol">(λ</a> <a id="15238" class="Symbol">{</a><a id="15239" href="Monad.Instance.Setoids.K.html#15239" class="Bound">x</a><a id="15240" class="Symbol">}</a> <a id="15242" class="Symbol">→</a> <a id="15244" class="Symbol">(</a><a id="15245" href="Monad.Instance.Setoids.K.html#16683" class="Function">step₂</a> <a id="15251" class="Symbol">{</a><a id="15252" href="Monad.Instance.Setoids.K.html#15239" class="Bound">x</a><a id="15253" class="Symbol">}))))</a>
          <a id="15269" class="Keyword">where</a>
            <a id="15287" href="Monad.Instance.Setoids.K.html#15287" class="Function">helper₁&#39;&#39;&#39;</a> <a id="15298" class="Symbol">:</a> <a id="15300" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="15306" class="Symbol">(</a><a id="15307" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15309" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="15311" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15313" href="Data.Product.Base.html#1618" class="Function Operator">×</a> <a id="15315" href="Category.Ambient.Setoids.html#1884" class="Datatype">ℕ</a> <a id="15317" class="Symbol">{</a><a id="15318" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="15319" class="Symbol">})</a> <a id="15322" class="Symbol">→</a> <a id="15324" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15326" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="15328" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="15330" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="15332" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15334" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="15336" class="Symbol">(</a><a id="15337" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="15343" class="Symbol">(</a><a id="15344" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15346" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="15348" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15350" href="Data.Product.Base.html#1618" class="Function Operator">×</a> <a id="15352" href="Category.Ambient.Setoids.html#1884" class="Datatype">ℕ</a> <a id="15354" class="Symbol">{</a><a id="15355" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="15356" class="Symbol">})</a> <a id="15359" href="Data.Sum.Base.html#625" class="Datatype Operator">⊎</a> <a id="15361" href="Monad.Instance.Setoids.Delay.html#1021" class="Datatype">Delay</a> <a id="15367" class="Symbol">(</a><a id="15368" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15370" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="15372" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="15374" href="Data.Product.Base.html#1618" class="Function Operator">×</a> <a id="15376" href="Category.Ambient.Setoids.html#1884" class="Datatype">ℕ</a> <a id="15378" class="Symbol">{</a><a id="15379" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="15380" class="Symbol">}))</a>
            <a id="15396" href="Monad.Instance.Setoids.K.html#15287" class="Function">helper₁&#39;&#39;&#39;</a> <a id="15407" class="Symbol">(</a><a id="15408" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="15412" class="Symbol">(</a><a id="15413" href="Monad.Instance.Setoids.K.html#15413" class="Bound">x</a> <a id="15415" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="15417" href="Category.Ambient.Setoids.html#1904" class="InductiveConstructor">zero</a><a id="15421" class="Symbol">))</a>  <a id="15425" class="Symbol">=</a> <a id="15427" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="15432" class="Symbol">(</a><a id="15433" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&lt;</a> <a id="15435" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="15437" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&gt;</a> <a id="15439" href="Monad.Instance.Setoids.K.html#15413" class="Bound">x</a><a id="15440" class="Symbol">)</a>
            <a id="15454" href="Monad.Instance.Setoids.K.html#15287" class="Function">helper₁&#39;&#39;&#39;</a> <a id="15465" class="Symbol">(</a><a id="15466" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="15470" class="Symbol">(</a><a id="15471" href="Monad.Instance.Setoids.K.html#15471" class="Bound">x</a> <a id="15473" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="15475" href="Category.Ambient.Setoids.html#1917" class="InductiveConstructor">suc</a> <a id="15479" href="Monad.Instance.Setoids.K.html#15479" class="Bound">n</a><a id="15480" class="Symbol">))</a> <a id="15483" class="Symbol">=</a> <a id="15485" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="15490" class="Symbol">(</a><a id="15491" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="15496" class="Symbol">(</a><a id="15497" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&lt;</a> <a id="15499" href="Monad.Instance.Setoids.Delay.html#8881" class="Function">liftFₛ∼</a> <a id="15507" href="Monad.Instance.Setoids.K.html#13203" class="Function">outer</a> <a id="15513" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&gt;</a> <a id="15515" class="Symbol">(</a><a id="15516" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a> <a id="15518" class="Symbol">{</a><a id="15519" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="15520" class="Symbol">}</a> <a id="15522" class="Symbol">(</a><a id="15523" href="Monad.Instance.Setoids.K.html#15471" class="Bound">x</a> <a id="15525" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="15527" href="Monad.Instance.Setoids.K.html#15479" class="Bound">n</a><a id="15528" class="Symbol">))))</a>
            <a id="15545" href="Monad.Instance.Setoids.K.html#15287" class="Function">helper₁&#39;&#39;&#39;</a> <a id="15556" class="Symbol">(</a><a id="15557" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="15563" href="Monad.Instance.Setoids.K.html#15563" class="Bound">y</a><a id="15564" class="Symbol">)</a>         <a id="15574" class="Symbol">=</a> <a id="15576" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="15581" class="Symbol">(</a><a id="15582" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="15587" class="Symbol">(</a><a id="15588" href="Monad.Instance.Setoids.Delay.html#1190" class="Field">force</a> <a id="15594" href="Monad.Instance.Setoids.K.html#15563" class="Bound">y</a><a id="15595" class="Symbol">))</a>

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            <a id="16610" href="Monad.Instance.Setoids.K.html#16318" class="Function">step₁</a> <a id="16616" class="Symbol">{</a><a id="16617" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="16623" href="Monad.Instance.Setoids.K.html#16623" class="Bound">x</a><a id="16624" class="Symbol">}</a> <a id="16626" class="Symbol">=</a> <a id="16628" href="Monad.Instance.Setoids.K.html#2057" class="Function">≡-refl</a> <a id="16635" class="Symbol">(</a><a id="16636" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="16638" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="16640" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="16642" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="16645" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="16653" class="Symbol">(</a><a id="16654" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="16656" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="16659" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="16667" class="Symbol">))</a>

            <a id="16683" href="Monad.Instance.Setoids.K.html#16683" class="Function">step₂</a> <a id="16689" class="Symbol">:</a> <a id="16691" class="Symbol">∀</a> <a id="16693" class="Symbol">{</a><a id="16694" href="Monad.Instance.Setoids.K.html#16694" class="Bound">x</a><a id="16695" class="Symbol">}</a> <a id="16697" class="Symbol">→</a> <a id="16699" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="16701" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="16703" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="16705" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="16707" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="16710" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="16718" class="Symbol">(</a><a id="16719" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="16721" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="16724" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="16732" class="Symbol">)</a> <a id="16734" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="16737" class="Symbol">(</a><a id="16738" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="16740" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="16745" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a id="16747" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="16749" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="16754" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="16757" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&lt;</a> <a id="16759" class="Symbol">(</a><a id="16760" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[</a> <a id="16762" href="Data.Sum.Function.Setoid.html#868" class="Function">inj₁ₛ</a> <a id="16768" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">,</a> <a id="16770" href="Data.Sum.Function.Setoid.html#936" class="Function">inj₂ₛ</a> <a id="16776" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="16778" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[</a> <a id="16780" href="Monad.Instance.Setoids.K.html#403" class="Function">idₛ</a> <a id="16784" class="Symbol">(</a><a id="16785" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="16793" class="Symbol">(</a><a id="16794" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="16796" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="16799" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="16807" class="Symbol">))</a> <a id="16810" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">,</a> <a id="16812" href="Monad.Instance.Setoids.K.html#403" class="Function">idₛ</a> <a id="16816" class="Symbol">(</a><a id="16817" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="16825" class="Symbol">(</a><a id="16826" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="16828" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="16831" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="16839" class="Symbol">))</a> <a id="16842" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">]ₛ</a> <a id="16845" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">]ₛ</a> <a id="16848" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="16850" href="Monad.Instance.Setoids.K.html#16125" class="Function">helper&#39;&#39;&#39;</a><a id="16859" class="Symbol">)</a> <a id="16861" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="16863" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&gt;</a> <a id="16865" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a id="16867" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="16872" href="Data.Sum.Base.html#811" class="Function Operator">]</a> <a id="16874" href="Data.Sum.Base.html#811" class="Function Operator">]</a> <a id="16876" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="16879" href="Monad.Instance.Setoids.K.html#15287" class="Function">helper₁&#39;&#39;&#39;</a><a id="16889" class="Symbol">)</a> <a id="16891" href="Monad.Instance.Setoids.K.html#16694" class="Bound">x</a> <a id="16893" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="16895" href="Monad.Instance.Setoids.K.html#14745" class="Function">helper&#39;&#39;</a> <a id="16904" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="16908" href="Monad.Instance.Setoids.K.html#16694" class="Bound">x</a> <a id="16910" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
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            <a id="17003" href="Monad.Instance.Setoids.K.html#16683" class="Function">step₂</a> <a id="17009" class="Symbol">{</a><a id="17010" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="17014" class="Symbol">(</a><a id="17015" href="Monad.Instance.Setoids.K.html#17015" class="Bound">x</a> <a id="17017" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="17019" href="Category.Ambient.Setoids.html#1917" class="InductiveConstructor">suc</a> <a id="17023" href="Monad.Instance.Setoids.K.html#17023" class="Bound">n</a><a id="17024" class="Symbol">)}</a> <a id="17027" class="Symbol">=</a> <a id="17029" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a> <a id="17034" class="Symbol">(</a><a id="17035" href="Monad.Instance.Setoids.K.html#17087" class="Function">by-induction</a> <a id="17048" href="Monad.Instance.Setoids.K.html#17023" class="Bound">n</a><a id="17049" class="Symbol">)</a>
              <a id="17065" class="Keyword">where</a>
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                <a id="17336" href="Monad.Instance.Setoids.K.html#17087" class="Function">by-induction</a> <a id="17349" class="Symbol">(</a><a id="17350" href="Category.Ambient.Setoids.html#1917" class="InductiveConstructor">suc</a> <a id="17354" href="Monad.Instance.Setoids.K.html#17354" class="Bound">n</a><a id="17355" class="Symbol">)</a> <a id="17357" class="Symbol">=</a> <a id="17359" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="17367" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="17369" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="17371" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="17373" class="Symbol">(</a><a id="17374" href="Algebra.Elgot.html#2011" class="Function">#-Fixpoint</a> <a id="17385" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a><a id="17386" class="Symbol">)</a> <a id="17388" class="Symbol">(</a><a id="17389" href="Monad.Instance.Setoids.K.html#17087" class="Function">by-induction</a> <a id="17402" href="Monad.Instance.Setoids.K.html#17354" class="Bound">n</a><a id="17403" class="Symbol">)</a>
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            <a id="18178" href="Monad.Instance.Setoids.K.html#18178" class="Function">eq&#39;</a> <a id="18182" class="Symbol">:</a> <a id="18184" class="Symbol">∀</a> <a id="18186" class="Symbol">{</a><a id="18187" href="Monad.Instance.Setoids.K.html#18187" class="Bound">n</a><a id="18188" class="Symbol">}</a> <a id="18190" class="Symbol">→</a> <a id="18192" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="18194" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="18196" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="18198" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="18200" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="18203" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="18211" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18213" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="18216" href="Data.Sum.Base.html#811" class="Function Operator">[</a> <a id="18218" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="18223" href="Data.Sum.Base.html#811" class="Function Operator">,</a> <a id="18225" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="18230" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="18233" href="Monad.Instance.Setoids.Delay.html#12391" class="Function">μ</a> <a id="18235" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="18238" href="Monad.Instance.Setoids.Delay.html#7297" class="Function">liftF</a> <a id="18244" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a> <a id="18246" href="Data.Sum.Base.html#811" class="Function Operator">]</a> <a id="18248" class="Symbol">(</a><a id="18249" href="Monad.Instance.Setoids.K.html#13431" class="Function">helper₁&#39;</a> <a id="18258" class="Symbol">(</a><a id="18259" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="18263" class="Symbol">(</a><a id="18264" href="Monad.Instance.Setoids.K.html#18095" class="Bound">x</a> <a id="18266" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18268" href="Monad.Instance.Setoids.K.html#18187" class="Bound">n</a><a id="18269" class="Symbol">)))</a> <a id="18273" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="18275" class="Symbol">(</a><a id="18276" href="Monad.Instance.Setoids.K.html#11586" class="Function">helper₁</a> <a id="18284" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="18287" href="Monad.Instance.Setoids.Delay.html#12391" class="Function">μ</a> <a id="18289" class="Symbol">{</a><a id="18290" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18291" class="Symbol">}</a> <a id="18293" href="Function.Base.html#3626" class="Function Operator">∘′</a> <a id="18296" href="Monad.Instance.Setoids.Delay.html#7297" class="Function">liftF</a> <a id="18302" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a><a id="18303" class="Symbol">)</a> <a id="18305" class="Symbol">(</a><a id="18306" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="18310" class="Symbol">(</a><a id="18311" href="Monad.Instance.Setoids.K.html#18109" class="Bound">y</a> <a id="18313" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18315" href="Monad.Instance.Setoids.K.html#18187" class="Bound">n</a><a id="18316" class="Symbol">))</a> <a id="18319" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
            <a id="18333" href="Monad.Instance.Setoids.K.html#18178" class="Function">eq&#39;</a> <a id="18337" class="Symbol">{</a><a id="18338" href="Category.Ambient.Setoids.html#1904" class="InductiveConstructor">zero</a><a id="18342" class="Symbol">}</a>  <a id="18345" class="Symbol">=</a> <a id="18347" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a> <a id="18352" class="Symbol">(</a><a id="18353" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18358" href="Monad.Instance.Setoids.K.html#11430" class="Bound">f</a> <a id="18360" href="Monad.Instance.Setoids.K.html#18125" class="Bound">x∼y</a><a id="18363" class="Symbol">)</a>
            <a id="18377" href="Monad.Instance.Setoids.K.html#18178" class="Function">eq&#39;</a> <a id="18381" class="Symbol">{</a><a id="18382" href="Category.Ambient.Setoids.html#1917" class="InductiveConstructor">suc</a> <a id="18386" href="Monad.Instance.Setoids.K.html#18386" class="Bound">n</a><a id="18387" class="Symbol">}</a> <a id="18389" class="Symbol">=</a> <a id="18391" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a> <a id="18396" class="Symbol">(</a><a id="18397" href="Monad.Instance.Setoids.Delay.html#2612" class="Function">∼-trans</a> <a id="18405" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18407" class="Symbol">(</a><a id="18408" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18413" class="Symbol">(</a><a id="18414" href="Monad.Instance.Setoids.Delay.html#14628" class="Function">μₛ∼</a> <a id="18418" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18419" class="Symbol">)</a> <a id="18421" class="Symbol">(</a><a id="18422" href="Monad.Instance.Setoids.Delay.html#2377" class="Function">∼-sym</a> <a id="18428" class="Symbol">(</a><a id="18429" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="18437" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18438" class="Symbol">)</a> <a id="18440" class="Symbol">(</a><a id="18441" href="Monad.Instance.Setoids.Delay.html#9397" class="Function">lift-comp∼</a> <a id="18452" class="Symbol">{</a><a id="18453" class="Argument">f</a> <a id="18455" class="Symbol">=</a> <a id="18457" href="Monad.Instance.Setoids.K.html#13203" class="Function">outer</a><a id="18462" class="Symbol">}</a> <a id="18464" class="Symbol">{</a><a id="18465" class="Argument">g</a> <a id="18467" class="Symbol">=</a> <a id="18469" href="Monad.Instance.Setoids.Delay.html#20586" class="Function">ιₛ&#39;</a><a id="18472" class="Symbol">}</a> <a id="18474" class="Symbol">{</a><a id="18475" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a> <a id="18477" class="Symbol">(</a><a id="18478" href="Monad.Instance.Setoids.K.html#18095" class="Bound">x</a> <a id="18480" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18482" href="Monad.Instance.Setoids.K.html#18386" class="Bound">n</a><a id="18483" class="Symbol">)}</a> <a id="18486" class="Symbol">(</a><a id="18487" href="Monad.Instance.Setoids.Delay.html#2126" class="Function">∼-refl</a> <a id="18494" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18495" class="Symbol">))))</a> <a id="18500" class="Symbol">(</a><a id="18501" href="Monad.Instance.Setoids.Delay.html#2612" class="Function">∼-trans</a> <a id="18509" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18511" href="Monad.Instance.Setoids.Delay.html#16441" class="Function">identityˡ∼</a> <a id="18522" class="Symbol">(</a><a id="18523" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18528" href="Monad.Instance.Setoids.Delay.html#20586" class="Function">ιₛ&#39;</a> <a id="18532" class="Symbol">(</a><a id="18533" href="Monad.Instance.Setoids.K.html#18125" class="Bound">x∼y</a> <a id="18537" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18539" href="Monad.Instance.Setoids.K.html#647" class="InductiveConstructor">≣-refl</a><a id="18545" class="Symbol">))))</a>
        <a id="18558" href="Monad.Instance.Setoids.K.html#17929" class="Function">eq</a> <a id="18561" class="Symbol">(</a><a id="18562" href="Monad.Instance.Setoids.Delay.html#1768" class="InductiveConstructor">later∼</a> <a id="18569" href="Monad.Instance.Setoids.K.html#18569" class="Bound">x∼y</a><a id="18572" class="Symbol">)</a> <a id="18574" class="Symbol">=</a> <a id="18576" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a> <a id="18581" class="Symbol">(</a><a id="18582" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18587" class="Symbol">(</a><a id="18588" href="Monad.Instance.Setoids.Delay.html#14628" class="Function">μₛ∼</a> <a id="18592" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18593" class="Symbol">)</a> <a id="18595" class="Symbol">(</a><a id="18596" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18601" class="Symbol">(</a><a id="18602" href="Monad.Instance.Setoids.Delay.html#8881" class="Function">liftFₛ∼</a> <a id="18610" href="Monad.Instance.Setoids.Delay.html#20586" class="Function">ιₛ&#39;</a><a id="18613" class="Symbol">)</a> <a id="18615" class="Symbol">(</a><a id="18616" href="Monad.Instance.Setoids.Delay.html#1929" class="Field">force∼</a> <a id="18623" href="Monad.Instance.Setoids.K.html#18569" class="Bound">x∼y</a><a id="18626" class="Symbol">)))</a>

        <a id="18639" href="Monad.Instance.Setoids.K.html#18639" class="Function">eq₂</a> <a id="18643" class="Symbol">:</a> <a id="18645" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[</a> <a id="18647" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="18649" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="18651" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="18653" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">][</a> <a id="18656" href="Monad.Instance.Setoids.K.html#14122" class="Function">helper&#39;</a> <a id="18664" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="18666" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="18670" href="Monad.Instance.Setoids.K.html#13108" class="Bound">z</a> <a id="18672" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">≡</a> <a id="18674" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="18681" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="18683" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="18687" href="Monad.Instance.Setoids.Delay.html#12391" class="Function">μ</a> <a id="18689" class="Symbol">{</a><a id="18690" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18691" class="Symbol">}</a> <a id="18693" class="Symbol">(</a><a id="18694" href="Monad.Instance.Setoids.Delay.html#7297" class="Function">liftF</a> <a id="18700" class="Symbol">(</a><a id="18701" href="Monad.Instance.Setoids.Delay.html#20433" class="Function">ι</a> <a id="18703" class="Symbol">{</a><a id="18704" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18705" class="Symbol">})</a> <a id="18708" href="Monad.Instance.Setoids.K.html#13108" class="Bound">z</a><a id="18709" class="Symbol">)</a><a id="18710" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">]</a>
        <a id="18720" href="Monad.Instance.Setoids.K.html#18639" class="Function">eq₂</a> <a id="18724" class="Symbol">=</a> <a id="18726" href="Algebra.Elgot.html#2086" class="Function">Elgot-Algebra.#-Uniformity</a> <a id="18753" href="Monad.Instance.Setoids.K.html#11427" class="Bound">B</a> <a id="18755" class="Symbol">{</a><a id="18756" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="18764" class="Symbol">(</a><a id="18765" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18767" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="18770" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a> <a id="18779" class="Symbol">{</a><a id="18780" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="18781" class="Symbol">})}</a> <a id="18785" class="Symbol">{</a><a id="18786" href="Monad.Instance.Setoids.Delay.html#6016" class="Function">Delayₛ∼</a> <a id="18794" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a><a id="18795" class="Symbol">}</a> <a id="18797" class="Symbol">{</a><a id="18798" href="Monad.Instance.Setoids.K.html#14122" class="Function">helper&#39;</a><a id="18805" class="Symbol">}</a> <a id="18807" class="Symbol">{</a><a id="18808" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a><a id="18814" class="Symbol">}</a> <a id="18816" class="Symbol">{</a><a id="18817" href="Monad.Instance.Setoids.Delay.html#14628" class="Function">μₛ∼</a> <a id="18821" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18823" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="18825" href="Monad.Instance.Setoids.Delay.html#8881" class="Function">liftFₛ∼</a> <a id="18833" href="Monad.Instance.Setoids.Delay.html#20586" class="Function">ιₛ&#39;</a><a id="18836" class="Symbol">}</a> <a id="18838" class="Symbol">(λ</a> <a id="18841" class="Symbol">{</a><a id="18842" href="Monad.Instance.Setoids.K.html#18842" class="Bound">x</a><a id="18843" class="Symbol">}</a> <a id="18845" class="Symbol">→</a> <a id="18847" href="Monad.Instance.Setoids.K.html#17929" class="Function">eq</a> <a id="18850" class="Symbol">{</a><a id="18851" href="Monad.Instance.Setoids.K.html#18842" class="Bound">x</a><a id="18852" class="Symbol">}</a> <a id="18854" class="Symbol">{</a><a id="18855" href="Monad.Instance.Setoids.K.html#18842" class="Bound">x</a><a id="18856" class="Symbol">}</a> <a id="18858" class="Symbol">(</a><a id="18859" href="Monad.Instance.Setoids.Delay.html#2126" class="Function">∼-refl</a> <a id="18866" class="Symbol">(</a><a id="18867" href="Monad.Instance.Setoids.K.html#11423" class="Bound">A</a> <a id="18869" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="18872" href="Category.Ambient.Setoids.html#2317" class="Function">ℕ-setoid</a><a id="18880" class="Symbol">)))</a>

    <a id="18889" href="Monad.Instance.Setoids.K.html#18889" class="Function">delay-lift&#39;</a> <a id="18901" class="Symbol">=</a> <a id="18903" class="Keyword">record</a> <a id="18910" class="Symbol">{</a> <a id="18912" href="Function.Bundles.html#2094" class="Field">to</a> <a id="18915" class="Symbol">=</a> <a id="18917" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&lt;</a> <a id="18919" href="Monad.Instance.Setoids.K.html#11995" class="Function">helper</a> <a id="18926" href="Algebra.Elgot.html#1938" class="Function Operator">#</a> <a id="18928" href="Monad.Instance.Setoids.Delay.html#6211" class="Function Operator">&gt;</a> <a id="18930" class="Symbol">;</a> <a id="18932" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="18937" class="Symbol">=</a> <a id="18939" href="Monad.Instance.Setoids.K.html#12267" class="Function">helper#≈-cong</a> <a id="18953" class="Symbol">}</a>

    <a id="18960" class="Comment">-- discretize a setoid</a>
    <a id="18987" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖_‖</a> <a id="18991" class="Symbol">:</a> <a id="18993" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="19000" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="19002" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="19004" class="Symbol">→</a> <a id="19006" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="19013" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="19015" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a>
    <a id="19021" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣_∣</a> <a id="19025" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19027" href="Monad.Instance.Setoids.K.html#19027" class="Bound">X</a> <a id="19029" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a>      <a id="19036" class="Symbol">=</a> <a id="19038" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a> <a id="19040" href="Monad.Instance.Setoids.K.html#19027" class="Bound">X</a> <a id="19042" href="Monad.Instance.Setoids.K.html#1998" class="Field Operator">∣</a>
    <a id="19048" href="Monad.Instance.Setoids.K.html#2010" class="Field Operator">[_][_≡_]</a> <a id="19057" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19059" href="Monad.Instance.Setoids.K.html#19059" class="Bound">X</a> <a id="19061" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19063" class="Symbol">=</a> <a id="19065" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a>
    <a id="19073" href="Relation.Binary.Bundles.html#1203" class="Field">Setoid.isEquivalence</a> <a id="19094" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19096" href="Monad.Instance.Setoids.K.html#19096" class="Bound">X</a> <a id="19098" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19100" class="Symbol">=</a> <a id="19102" href="Relation.Binary.PropositionalEquality.Properties.html#5422" class="Function">Eq.isEquivalence</a>

    <a id="19124" href="Monad.Instance.Setoids.K.html#19124" class="Function">‖‖-quote</a> <a id="19133" class="Symbol">:</a> <a id="19135" class="Symbol">∀</a> <a id="19137" class="Symbol">{</a><a id="19138" href="Monad.Instance.Setoids.K.html#19138" class="Bound">X</a> <a id="19140" class="Symbol">:</a> <a id="19142" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a> <a id="19149" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a> <a id="19151" href="Monad.Instance.Setoids.K.html#1291" class="Bound">ℓ</a><a id="19152" class="Symbol">}</a> <a id="19154" class="Symbol">→</a> <a id="19156" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19158" href="Monad.Instance.Setoids.K.html#19138" class="Bound">X</a> <a id="19160" href="Monad.Instance.Setoids.K.html#18987" class="Function Operator">‖</a> <a id="19162" href="Monad.Instance.Setoids.K.html#336" class="Record Operator">⟶</a> <a id="19164" href="Monad.Instance.Setoids.K.html#19138" class="Bound">X</a>
    <a id="19170" href="Function.Bundles.html#2094" class="Field">_⟶_.to</a> <a id="19177" href="Monad.Instance.Setoids.K.html#19124" class="Function">‖‖-quote</a> <a id="19186" href="Monad.Instance.Setoids.K.html#19186" class="Bound">x</a>          <a id="19197" class="Symbol">=</a> <a id="19199" href="Monad.Instance.Setoids.K.html#19186" class="Bound">x</a>
    <a id="19205" href="Function.Bundles.html#2113" class="Field">cong</a> <a id="19210" class="Symbol">(</a><a id="19211" href="Monad.Instance.Setoids.K.html#19124" class="Function">‖‖-quote</a> <a id="19220" class="Symbol">{</a><a id="19221" href="Monad.Instance.Setoids.K.html#19221" class="Bound">X</a><a id="19222" class="Symbol">})</a> <a id="19225" href="Monad.Instance.Setoids.K.html#647" class="InductiveConstructor">≣-refl</a> <a id="19232" class="Symbol">=</a> <a id="19234" href="Monad.Instance.Setoids.K.html#2057" class="Function">≡-refl</a> <a id="19241" href="Monad.Instance.Setoids.K.html#19221" class="Bound">X</a>

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        <a id="24036" href="Monad.Instance.Setoids.K.html#23769" class="Function">helper-eq&#39;</a> <a id="24047" class="Symbol">{</a><a id="24048" href="Monad.Instance.Setoids.Delay.html#1057" class="InductiveConstructor">now</a> <a id="24052" href="Monad.Instance.Setoids.K.html#24052" class="Bound">x</a><a id="24053" class="Symbol">}</a> <a id="24055" class="Symbol">=</a> <a id="24057" href="Data.Sum.Relation.Binary.Pointwise.html#1176" class="InductiveConstructor">inj₁</a> <a id="24062" class="Symbol">(</a><a id="24063" href="Monad.Instance.Setoids.K.html#2088" class="Function">≡-trans</a> <a id="24071" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="24073" href="Monad.Instance.Setoids.K.html#22655" class="Bound">B</a> <a id="24075" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="24077" href="Monad.Instance.Setoids.K.html#22664" class="Bound">eqᵍ</a> <a id="24081" class="Symbol">(</a><a id="24082" href="Monad.Instance.Setoids.K.html#2072" class="Function">≡-sym</a> <a id="24088" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟦</a> <a id="24090" href="Monad.Instance.Setoids.K.html#22655" class="Bound">B</a> <a id="24092" href="Monad.Instance.Setoids.K.html#11290" class="Field Operator">⟧</a> <a id="24094" href="Monad.Instance.Setoids.K.html#22668" class="Bound">eqʰ</a><a id="24097" class="Symbol">))</a>
        <a id="24108" href="Monad.Instance.Setoids.K.html#23769" class="Function">helper-eq&#39;</a> <a id="24119" class="Symbol">{</a><a id="24120" href="Monad.Instance.Setoids.Delay.html#1088" class="InductiveConstructor">later</a> <a id="24126" href="Monad.Instance.Setoids.K.html#24126" class="Bound">x</a><a id="24127" class="Symbol">}</a> <a id="24129" class="Symbol">=</a> <a id="24131" href="Data.Sum.Relation.Binary.Pointwise.html#1235" class="InductiveConstructor">inj₂</a> <a id="24136" class="Symbol">(</a><a id="24137" href="Monad.Instance.Setoids.Delay.html#2126" class="Function">∼-refl</a> <a id="24144" href="Monad.Instance.Setoids.K.html#22202" class="Bound">A</a><a id="24145" class="Symbol">)</a>

        <a id="24156" href="Monad.Instance.Setoids.K.html#24156" class="Function">iter-id</a> <a id="24164" class="Symbol">:</a>  <a id="24167" class="Symbol">∀</a> <a id="24169" class="Symbol">{</a><a id="24170" href="Monad.Instance.Setoids.K.html#24170" class="Bound">x</a><a id="24171" class="Symbol">}</a> <a id="24173" class="Symbol">→</a> <a id="24175" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">[</a> <a id="24177" href="Monad.Instance.Setoids.K.html#22202" class="Bound">A</a> <a id="24179" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">][</a> <a id="24182" href="Monad.Instance.Setoids.K.html#24170" class="Bound">x</a> <a id="24184" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">≈</a>  <a id="24187" href="Monad.Instance.Setoids.K.html#5699" class="Function">iterₛ</a> <a id="24193" class="Symbol">(</a><a id="24194" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[</a> <a id="24196" href="Data.Sum.Function.Setoid.html#868" class="Function">inj₁ₛ</a> <a id="24202" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="24204" href="Monad.Instance.Setoids.K.html#23237" class="Function">D∼⇒D≈</a> <a id="24210" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">,</a> <a id="24212" href="Data.Sum.Function.Setoid.html#936" class="Function">inj₂ₛ</a> <a id="24218" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">]ₛ</a> <a id="24221" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="24223" href="Monad.Instance.Setoids.K.html#23521" class="Function">helper-now</a><a id="24233" class="Symbol">)</a> <a id="24235" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="24239" href="Monad.Instance.Setoids.K.html#24170" class="Bound">x</a> <a id="24241" href="Monad.Instance.Setoids.K.html#1841" class="Datatype Operator">]</a>
        <a id="24251" href="Monad.Instance.Setoids.K.html#24251" class="Function">iter-id′</a> <a id="24260" class="Symbol">:</a> <a id="24262" class="Symbol">∀</a> <a id="24264" class="Symbol">{</a><a id="24265" href="Monad.Instance.Setoids.K.html#24265" class="Bound">x</a><a id="24266" class="Symbol">}</a> <a id="24268" class="Symbol">→</a> <a id="24270" href="Monad.Instance.Setoids.K.html#1859" class="Record Operator">[</a> <a id="24272" href="Monad.Instance.Setoids.K.html#22202" class="Bound">A</a> <a id="24274" href="Monad.Instance.Setoids.K.html#1859" class="Record Operator">][</a> <a id="24277" href="Monad.Instance.Setoids.K.html#24265" class="Bound">x</a> <a id="24279" href="Monad.Instance.Setoids.K.html#1859" class="Record Operator">≈′</a> <a id="24282" href="Monad.Instance.Setoids.K.html#5699" class="Function">iterₛ</a> <a id="24288" class="Symbol">(</a><a id="24289" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[</a> <a id="24291" href="Data.Sum.Function.Setoid.html#868" class="Function">inj₁ₛ</a> <a id="24297" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="24299" href="Monad.Instance.Setoids.K.html#23237" class="Function">D∼⇒D≈</a> <a id="24305" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">,</a> <a id="24307" href="Data.Sum.Function.Setoid.html#936" class="Function">inj₂ₛ</a> <a id="24313" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">]ₛ</a> <a id="24316" href="Monad.Instance.Setoids.K.html#478" class="Function Operator">∘</a> <a id="24318" href="Monad.Instance.Setoids.K.html#23521" class="Function">helper-now</a><a id="24328" class="Symbol">)</a> <a id="24330" href="Function.Bundles.html#15133" class="Function Operator">⟨$⟩</a> <a id="24334" href="Monad.Instance.Setoids.K.html#24265" class="Bound">x</a> <a id="24336" href="Monad.Instance.Setoids.K.html#1859" class="Record Operator">]</a>
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</pre>