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Step * 1 of Lemma dM-basis


1. I : fset(ℕ)
2. x : Point(dM(I))
3. ∀[x:Point(free-DeMorgan-lattice(names(I);NamesDeq))]
     (x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq)))
⊢ x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(dM(I))
BY
{ Subst' Point(free-DeMorgan-lattice(names(I);NamesDeq)) ~ Point(dM(I)) -1 }

1
.....equality..... 
1. I : fset(ℕ)
2. x : Point(dM(I))
3. ∀[x:Point(free-DeMorgan-lattice(names(I);NamesDeq))]
     (x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq)))
⊢ Point(free-DeMorgan-lattice(names(I);NamesDeq)) ~ Point(dM(I))

2
1. I : fset(ℕ)
2. x : Point(dM(I))
3. ∀[x:Point(dM(I))]. (x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(dM(I)))
⊢ x = \/(λs./\(λx.free-dl-inc(x)"(s))"(x)) ∈ Point(dM(I))

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Latex:

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Latex:

1.  I  :  fset(\mBbbN{})
2.  x  :  Point(dM(I))
3.  \mforall{}[x:Point(free-DeMorgan-lattice(names(I);NamesDeq))].  (x  =  \mbackslash{}/(\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s))"(x)))
\mvdash{}  x  =  \mbackslash{}/(\mlambda{}s./\mbackslash{}(\mlambda{}x.free-dl-inc(x)"(s))"(x))


By

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Latex:
Subst'  Point(free-DeMorgan-lattice(names(I);NamesDeq))  \msim{}  Point(dM(I))  -1

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