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Step * 1 of Lemma nh-id-right


1. I : fset(ℕ)
2. J : fset(ℕ)
3. f : names(J) ⟶ Point(dM(I))
4. x : names(J)
5. v : {g:dma-hom(free-DeMorgan-algebra(names(J);NamesDeq);free-DeMorgan-algebra(names(I);NamesDeq))| 
        ∀i:names(J). ((g <i>) = (f i) ∈ Point(free-DeMorgan-algebra(names(I);NamesDeq)))} 
6. free-dma-lift(names(J);NamesDeq;free-DeMorgan-algebra(names(I);NamesDeq);free-dml-deq(names(I);NamesDeq);f)
= v
∈ {g:dma-hom(free-DeMorgan-algebra(names(J);NamesDeq);free-DeMorgan-algebra(names(I);NamesDeq))| 
   ∀i:names(J). ((g <i>) = (f i) ∈ Point(free-DeMorgan-algebra(names(I);NamesDeq)))} 
⊢ ((v o (λx.<x>)) x) = (f x) ∈ Point(dM(I))
BY
{ (D -2 THEN Reduce 0 THEN Auto) }

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Latex:

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Latex:

1.  I  :  fset(\mBbbN{})
2.  J  :  fset(\mBbbN{})
3.  f  :  names(J)  {}\mrightarrow{}  Point(dM(I))
4.  x  :  names(J)
5.  v  :  \{g:dma-hom(free-DeMorgan-algebra(names(J);NamesDeq);free-DeMorgan-algebra(names(I);...))| 
                \mforall{}i:names(J).  ((g  <i>)  =  (f  i))\} 
6.  free-dma-lift(names(J);NamesDeq;free-DeMorgan-algebra(names(I);NamesDeq);free-dml-deq(...;...);f)
=  v
\mvdash{}  ((v  o  (\mlambda{}x.<x>))  x)  =  (f  x)


By

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Latex:
(D  -2  THEN  Reduce  0  THEN  Auto)

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