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Step * 1 1 of Lemma dma-lift-compose_wf


1. I : Type
2. J : Type
3. K : Type
4. eqi : EqDecider(I)
5. eqj : EqDecider(J)
6. f : J ⟶ Point(free-DeMorgan-algebra(I;eqi))
7. g : K ⟶ Point(free-DeMorgan-algebra(J;eqj))
⊢ free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f) o g ∈ K ⟶ Point(free-DeMorgan-algebra(I;eqi))
BY
{ Assert ⌜free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f) ∈ Point(free-DeMorgan-algebra(J;eqj))
          ⟶ Point(free-DeMorgan-algebra(I;eqi))⌝⋅ }

1
.....assertion..... 
1. I : Type
2. J : Type
3. K : Type
4. eqi : EqDecider(I)
5. eqj : EqDecider(J)
6. f : J ⟶ Point(free-DeMorgan-algebra(I;eqi))
7. g : K ⟶ Point(free-DeMorgan-algebra(J;eqj))
⊢ free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f) ∈ Point(free-DeMorgan-algebra(J;eqj))
  ⟶ Point(free-DeMorgan-algebra(I;eqi))

2
1. I : Type
2. J : Type
3. K : Type
4. eqi : EqDecider(I)
5. eqj : EqDecider(J)
6. f : J ⟶ Point(free-DeMorgan-algebra(I;eqi))
7. g : K ⟶ Point(free-DeMorgan-algebra(J;eqj))
8. free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f) ∈ Point(free-DeMorgan-algebra(J;eqj))
   ⟶ Point(free-DeMorgan-algebra(I;eqi))
⊢ free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f) o g ∈ K ⟶ Point(free-DeMorgan-algebra(I;eqi))

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Latex:

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Latex:

1.  I  :  Type
2.  J  :  Type
3.  K  :  Type
4.  eqi  :  EqDecider(I)
5.  eqj  :  EqDecider(J)
6.  f  :  J  {}\mrightarrow{}  Point(free-DeMorgan-algebra(I;eqi))
7.  g  :  K  {}\mrightarrow{}  Point(free-DeMorgan-algebra(J;eqj))
\mvdash{}  free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f)  o  g  \mmember{}  K
    {}\mrightarrow{}  Point(free-DeMorgan-algebra(I;eqi))


By

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Latex:
Assert  \mkleeneopen{}free-dma-lift(J;eqj;free-DeMorgan-algebra(I;eqi);free-dml-deq(I;eqi);f)
                \mmember{}  Point(free-DeMorgan-algebra(J;eqj))  {}\mrightarrow{}  Point(free-DeMorgan-algebra(I;eqi))\mkleeneclose{}\mcdot{}

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