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

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[Cs:T ⟶ fset(fset(T))]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))].
∀[f:T ⟶ Point(L)]. ∀[x,y:Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))].
  lattice-extend-wc(L;eq;eqL;f;x) ≤ lattice-extend-wc(L;eq;eqL;f;y) supposing x ≤ y
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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)

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[Cs:T  {}\mrightarrow{}  fset(fset(T))].  \mforall{}[L:BoundedDistributiveLattice].
\mforall{}[eqL:EqDecider(Point(L))].  \mforall{}[f:T  {}\mrightarrow{}  Point(L)].
\mforall{}[x,y:Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))].
    lattice-extend-wc(L;eq;eqL;f;x)  \mleq{}  lattice-extend-wc(L;eq;eqL;f;y)  supposing  x  \mleq{}  y


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