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Step * 2 1 of Lemma dM-to-FL-properties


1. ∀[I:fset(ℕ)]. (λz.dM-to-FL(I;z) ∈ Hom(free-DeMorgan-lattice(names(I);NamesDeq);face_lattice(I)))
2. I : fset(ℕ)
3. λz.dM-to-FL(I;z) ∈ Hom(free-DeMorgan-lattice(names(I);NamesDeq);face_lattice(I))
4. ∀x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq)).
     (dM-to-FL(I;x ∨ y) = dM-to-FL(I;x) ∨ dM-to-FL(I;y) ∈ Point(face_lattice(I)))
5. x : Point(free-DeMorgan-lattice(names(I);NamesDeq))
6. y : Point(free-DeMorgan-lattice(names(I);NamesDeq))
⊢ ((λz.dM-to-FL(I;z)) x ∧ y) = (λz.dM-to-FL(I;z)) x ∧ (λz.dM-to-FL(I;z)) y ∈ Point(face_lattice(I))
BY
{ (GenConclTerm ⌜λz.dM-to-FL(I;z)⌝⋅ THEN Auto THEN D -2 THEN D -3 THEN RWO "-3.1 -3.2" 0 THEN Auto) }

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Latex:

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Latex:

1.  \mforall{}[I:fset(\mBbbN{})].  (\mlambda{}z.dM-to-FL(I;z)  \mmember{}  Hom(free-DeMorgan-lattice(names(I);NamesDeq);face\_lattice(I)))
2.  I  :  fset(\mBbbN{})
3.  \mlambda{}z.dM-to-FL(I;z)  \mmember{}  Hom(free-DeMorgan-lattice(names(I);NamesDeq);face\_lattice(I))
4.  \mforall{}x,y:Point(free-DeMorgan-lattice(names(I);NamesDeq)).
          (dM-to-FL(I;x  \mvee{}  y)  =  dM-to-FL(I;x)  \mvee{}  dM-to-FL(I;y))
5.  x  :  Point(free-DeMorgan-lattice(names(I);NamesDeq))
6.  y  :  Point(free-DeMorgan-lattice(names(I);NamesDeq))
\mvdash{}  ((\mlambda{}z.dM-to-FL(I;z))  x  \mwedge{}  y)  =  (\mlambda{}z.dM-to-FL(I;z))  x  \mwedge{}  (\mlambda{}z.dM-to-FL(I;z))  y


By

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Latex:
(GenConclTerm  \mkleeneopen{}\mlambda{}z.dM-to-FL(I;z)\mkleeneclose{}\mcdot{}  THEN  Auto  THEN  D  -2  THEN  D  -3  THEN  RWO  "-3.1  -3.2"  0  THEN  Auto)

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