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Step * 1 of Lemma lattice-extend-wc-order-preserving


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. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8. y : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
9. x ≤ y
⊢ lattice-extend-wc(L;eq;eqL;f;x) ≤ lattice-extend-wc(L;eq;eqL;f;y)
BY
{ (Unfold `lattice-extend-wc` 0 THEN BLemma `lattice-extend-order-preserving` THEN Auto) }

1
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. x : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8. y : Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
9. x ≤ y
⊢ x ≤ y

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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.  x  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
8.  y  :  Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
9.  x  \mleq{}  y
\mvdash{}  lattice-extend-wc(L;eq;eqL;f;x)  \mleq{}  lattice-extend-wc(L;eq;eqL;f;y)


By

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Latex:
(Unfold  `lattice-extend-wc`  0  THEN  BLemma  `lattice-extend-order-preserving`  THEN  Auto)

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