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Step * 1 2 of Lemma free-DeMorgan-algebra-hom-unique

.....wf..... 
1. T : Type
2. eq : EqDecider(T)
3. dm : DeMorganAlgebra
4. eq2 : EqDecider(Point(dm))
5. f : T ⟶ Point(dm)
6. g : dma-hom(free-DeMorgan-algebra(T;eq);dm)
7. h : dma-hom(free-DeMorgan-algebra(T;eq);dm)
8. ∀i:T. ((g <i>) = (h <i>) ∈ Point(dm))
9. ∀[g,h:Hom(free-dist-lattice(T + T; union-deq(T;T;eq;eq));dm)].
     g = h ∈ Hom(free-dist-lattice(T + T; union-deq(T;T;eq;eq));dm) 
     supposing ∀x:T + T. ((g free-dl-inc(x)) = (h free-dl-inc(x)) ∈ Point(dm))
⊢ h ∈ Hom(free-dist-lattice(T + T; union-deq(T;T;eq;eq));dm)
BY
{ (Fold `free-DeMorgan-lattice` 0 THEN DVar `h' THEN InferEqualType THEN Auto) }

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Latex:

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Latex:
.....wf..... 
1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  dm  :  DeMorganAlgebra
4.  eq2  :  EqDecider(Point(dm))
5.  f  :  T  {}\mrightarrow{}  Point(dm)
6.  g  :  dma-hom(free-DeMorgan-algebra(T;eq);dm)
7.  h  :  dma-hom(free-DeMorgan-algebra(T;eq);dm)
8.  \mforall{}i:T.  ((g  <i>)  =  (h  <i>))
9.  \mforall{}[g,h:Hom(free-dist-lattice(T  +  T;  union-deq(T;T;eq;eq));dm)].
          g  =  h  supposing  \mforall{}x:T  +  T.  ((g  free-dl-inc(x))  =  (h  free-dl-inc(x)))
\mvdash{}  h  \mmember{}  Hom(free-dist-lattice(T  +  T;  union-deq(T;T;eq;eq));dm)


By

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Latex:
(Fold  `free-DeMorgan-lattice`  0  THEN  DVar  `h'  THEN  InferEqualType  THEN  Auto)

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