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Step * 5 1 of Lemma free-dist-lattice-adjunction


1. ∀Y:Type. (Point(free-dl(Y)) ~ free-dl-type(Y))
2. ∀Y:Type. ∀y:Y.  (free-dl-generator(y) ∈ Point(free-dl(Y)))
3. a1 : Type
4. a2 : Type
5. g : a1 ⟶ a2
6. x : a1
⊢ (fdl-hom(free-dl(a2);λx.free-dl-generator(g x)) free-dl-generator(x)) = free-dl-generator(g x) ∈ Point(free-dl(a2))
BY
{ (InstLemma `fdl-hom-agrees` [⌜a1⌝;⌜free-dl(a2)⌝;⌜λx.free-dl-generator(g x)⌝;⌜x⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  \mforall{}Y:Type.  (Point(free-dl(Y))  \msim{}  free-dl-type(Y))
2.  \mforall{}Y:Type.  \mforall{}y:Y.    (free-dl-generator(y)  \mmember{}  Point(free-dl(Y)))
3.  a1  :  Type
4.  a2  :  Type
5.  g  :  a1  {}\mrightarrow{}  a2
6.  x  :  a1
\mvdash{}  (fdl-hom(free-dl(a2);\mlambda{}x.free-dl-generator(g  x))  free-dl-generator(x))  =  free-dl-generator(g  x)


By

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Latex:
(InstLemma  `fdl-hom-agrees`  [\mkleeneopen{}a1\mkleeneclose{};\mkleeneopen{}free-dl(a2)\mkleeneclose{};\mkleeneopen{}\mlambda{}x.free-dl-generator(g  x)\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THEN  Auto)

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