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Step * of Lemma dma-lift-compose-assoc

∀[I,J,K,H:Type]. ∀[eqi:EqDecider(I)]. ∀[eqj:EqDecider(J)]. ∀[eqk:EqDecider(K)].
∀[f:J ⟶ Point(free-DeMorgan-algebra(I;eqi))]. ∀[g:K ⟶ Point(free-DeMorgan-algebra(J;eqj))].
∀[h:H ⟶ Point(free-DeMorgan-algebra(K;eqk))].
  (dma-lift-compose(I;K;eqi;eqk;dma-lift-compose(I;J;eqi;eqj;f;g);h)
  = dma-lift-compose(I;J;eqi;eqj;f;dma-lift-compose(J;K;eqj;eqk;g;h))
  ∈ (H ⟶ Point(free-DeMorgan-algebra(I;eqi))))
BY
{ (Auto THEN (FunExt THENA Auto) THEN RepUR ``dma-lift-compose`` 0) }

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

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Latex:

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Latex:
\mforall{}[I,J,K,H:Type].  \mforall{}[eqi:EqDecider(I)].  \mforall{}[eqj:EqDecider(J)].  \mforall{}[eqk:EqDecider(K)].
\mforall{}[f:J  {}\mrightarrow{}  Point(free-DeMorgan-algebra(I;eqi))].  \mforall{}[g:K  {}\mrightarrow{}  Point(free-DeMorgan-algebra(J;eqj))].
\mforall{}[h:H  {}\mrightarrow{}  Point(free-DeMorgan-algebra(K;eqk))].
    (dma-lift-compose(I;K;eqi;eqk;dma-lift-compose(I;J;eqi;eqj;f;g);h)
    =  dma-lift-compose(I;J;eqi;eqj;f;dma-lift-compose(J;K;eqj;eqk;g;h)))


By

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Latex:
(Auto  THEN  (FunExt  THENA  Auto)  THEN  RepUR  ``dma-lift-compose``  0)

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