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Step * 3 1 of Lemma dM-neg-properties


1. I : fset(ℕ)
2. ∀[x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq))].
     (dm-neg(names(I);NamesDeq;x ∧ y) = ¬(x) ∨ ¬(y) ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq)))
3. ∀[x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq))].
     (dm-neg(names(I);NamesDeq;x ∨ y) = ¬(x) ∧ ¬(y) ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq)))
4. dm-neg(names(I);NamesDeq;0) = 1 ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq))
5. dm-neg(names(I);NamesDeq;1) = 0 ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq))
6. ∀[x:Point(free-DeMorgan-lattice(names(I);NamesDeq))]
     (dm-neg(names(I);NamesDeq;¬(x)) = x ∈ Point(free-DeMorgan-lattice(names(I);NamesDeq)))
⊢ ∀[x:Point(dM(I))]. (dm-neg(names(I);NamesDeq;¬(x)) = x ∈ Point(dM(I)))
BY
{ (NthHypSq (-1) THEN RepUR ``dM free-DeMorgan-algebra mk-DeMorgan-algebra lattice-point`` 0 THEN Auto) }

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Latex:

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Latex:

1.  I  :  fset(\mBbbN{})
2.  \mforall{}[x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq))].
          (dm-neg(names(I);NamesDeq;x  \mwedge{}  y)  =  \mneg{}(x)  \mvee{}  \mneg{}(y))
3.  \mforall{}[x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq))].
          (dm-neg(names(I);NamesDeq;x  \mvee{}  y)  =  \mneg{}(x)  \mwedge{}  \mneg{}(y))
4.  dm-neg(names(I);NamesDeq;0)  =  1
5.  dm-neg(names(I);NamesDeq;1)  =  0
6.  \mforall{}[x:Point(free-DeMorgan-lattice(names(I);NamesDeq))].  (dm-neg(names(I);NamesDeq;\mneg{}(x))  =  x)
\mvdash{}  \mforall{}[x:Point(dM(I))].  (dm-neg(names(I);NamesDeq;\mneg{}(x))  =  x)


By

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Latex:
(NthHypSq  (-1)
  THEN  RepUR  ``dM  free-DeMorgan-algebra  mk-DeMorgan-algebra  lattice-point``  0
  THEN  Auto)

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