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Step * 1 of Lemma lattice-extend-wc-join


1. T : Type
2. eq : EqDecider(T)
3. Cs : T ⟶ fset(fset(T))
4. L : BoundedDistributiveLattice
5. eqL : EqDecider(Point(L))
6. f : T ⟶ Point(L)
7. a : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8. b : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
9. lattice-extend(L;eq;eqL;f;a ∨ b) ≤ lattice-extend(L;eq;eqL;f;a) ∨ lattice-extend(L;eq;eqL;f;b)
⊢ a ∨ b ~ a ∨ b
BY
{ ((RWO "free-dl-join free-dlwc-join" 0 THENA Auto) THEN Unfold `fset-constrained-ac-lub` 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.  L  :  BoundedDistributiveLattice
5.  eqL  :  EqDecider(Point(L))
6.  f  :  T  {}\mrightarrow{}  Point(L)
7.  a  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8.  b  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
9.  lattice-extend(L;eq;eqL;f;a  \mvee{}  b)  \mleq{}  lattice-extend(L;eq;eqL;f;a)  \mvee{}  lattice-extend(L;eq;eqL;f;b)
\mvdash{}  a  \mvee{}  b  \msim{}  a  \mvee{}  b


By

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Latex:
((RWO  "free-dl-join  free-dlwc-join"  0  THENA  Auto)  THEN  Unfold  `fset-constrained-ac-lub`  0  THEN  Auto)

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