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

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[dm:DeMorganAlgebra]. ∀[eq2:EqDecider(Point(dm))].
  ∀f:T ⟶ Point(dm)
    ∀[g,h:dma-hom(free-DeMorgan-algebra(T;eq);dm)].
      g = h ∈ dma-hom(free-DeMorgan-algebra(T;eq);dm) supposing ∀i:T. ((g <i>) = (h <i>) ∈ Point(dm))
BY
{ (Auto THEN (InstLemma `free-dist-lattice-hom-unique2` [⌜T + T⌝;⌜union-deq(T;T;eq;eq)⌝;⌜dm⌝;⌜eq2⌝]⋅ THENA Auto)) }

1
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))
⊢ g = h ∈ dma-hom(free-DeMorgan-algebra(T;eq);dm)

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[dm:DeMorganAlgebra].  \mforall{}[eq2:EqDecider(Point(dm))].
    \mforall{}f:T  {}\mrightarrow{}  Point(dm)
        \mforall{}[g,h:dma-hom(free-DeMorgan-algebra(T;eq);dm)].    g  =  h  supposing  \mforall{}i:T.  ((g  <i>)  =  (h  <i>))


By

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Latex:
(Auto
  THEN  (InstLemma  `free-dist-lattice-hom-unique2`  [\mkleeneopen{}T  +  T\mkleeneclose{};\mkleeneopen{}union-deq(T;T;eq;eq)\mkleeneclose{};\mkleeneopen{}dm\mkleeneclose{};\mkleeneopen{}eq2\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  )

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