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Step * of Lemma lattice-extend-is-hom

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))]. ∀[f:T ⟶ Point(L)].
  (λac.lattice-extend(L;eq;eqL;f;ac) ∈ Hom(free-dist-lattice(T; eq);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{}[L:BoundedDistributiveLattice].  \mforall{}[eqL:EqDecider(Point(L))].
\mforall{}[f:T  {}\mrightarrow{}  Point(L)].
    (\mlambda{}ac.lattice-extend(L;eq;eqL;f;ac)  \mmember{}  Hom(free-dist-lattice(T;  eq);L))


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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