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Step * 2 of Lemma free-dlwc-1-join-irreducible


1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
5. y : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
6. (x = 1 ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
∨ (y = 1 ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])))
⊢ x ∨ y = 1 ∈ Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
BY
{ (D -1 THEN HypSubst' (-1) 0 THEN Auto) }

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Latex:

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Latex:

1.  T  :  Type
2.  eq  :  EqDecider(T)
3.  Cs  :  T  {}\mrightarrow{}  fset(fset(T))
4.  x  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
5.  y  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
6.  (x  =  1)  \mvee{}  (y  =  1)
\mvdash{}  x  \mvee{}  y  =  1


By

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Latex:
(D  -1  THEN  HypSubst'  (-1)  0  THEN  Auto)

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