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Step * 1 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
⊢ x ≤ y
BY
{ ((RWO "free-dlwc-le" (-1) THENA Auto) THEN RWO "free-dl-le" 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.  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{}  x  \mleq{}  y


By

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Latex:
((RWO  "free-dlwc-le"  (-1)  THENA  Auto)  THEN  RWO  "free-dl-le"  0  THEN  Auto)

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