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Step * 3 1 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. d : Type
4. x : d
⊢ ((fdl-hom(free-dl(d);λg.g) o fdl-hom(free-dl(Point(free-dl(d)));λx.free-dl-generator(free-dl-generator(x)))) 
   free-dl-generator(x))
= ((λx.x) free-dl-generator(x))
∈ Point(free-dl(d))
BY
{ RepUR ``compose`` 0 }

1
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. d : Type
4. x : d
⊢ (fdl-hom(free-dl(d);λg.g) 
   (fdl-hom(free-dl(Point(free-dl(d)));λx.free-dl-generator(free-dl-generator(x))) free-dl-generator(x)))
= free-dl-generator(x)
∈ Point(free-dl(d))

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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.  d  :  Type
4.  x  :  d
\mvdash{}  ((fdl-hom(free-dl(d);\mlambda{}g.g)
        o  fdl-hom(free-dl(Point(free-dl(d)));\mlambda{}x.free-dl-generator(free-dl-generator(x)))) 
      free-dl-generator(x))
=  ((\mlambda{}x.x)  free-dl-generator(x))


By

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Latex:
RepUR  ``compose``  0

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