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Step * of Lemma lattice-extend-is-hom-constrained

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[Cs:T ⟶ fset(fset(T))]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))].
∀[f:T ⟶ Point(L)].
  λac.lattice-extend-wc(L;eq;eqL;f;ac) ∈ Hom(free-dist-lattice-with-constraints(T;eq;x.Cs[x]);L) 
  supposing ∀x:T. ∀c:fset(T).  (c ∈ Cs[x] ⇒ (/\(f"(c)) = 0 ∈ Point(L)))
BY
{ (Auto THEN (BLemma `order-preserving-map-is-bounded-lattice-hom` THEN Auto) THEN Reduce 0 THEN EAuto 1) }

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Latex:

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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)].
    \mlambda{}ac.lattice-extend-wc(L;eq;eqL;f;ac)  \mmember{}  Hom(free-dist-lattice-with-constraints(T;eq;x.Cs[x]);L) 
    supposing  \mforall{}x:T.  \mforall{}c:fset(T).    (c  \mmember{}  Cs[x]  {}\mRightarrow{}  (/\mbackslash{}(f"(c))  =  0))


By

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Latex:
(Auto
  THEN  (BLemma  `order-preserving-map-is-bounded-lattice-hom`  THEN  Auto)
  THEN  Reduce  0
  THEN  EAuto  1)

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