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Step * of Lemma order-preserving-map-is-lattice-hom

No Annotations
∀[l1,l2:Lattice]. ∀[f:Point(l1) ⟶ Point(l2)].
  f ∈ Hom(l1;l2) 
  supposing (∀x,y:Point(l1).  (x ≤ y ⇒ f x ≤ f y))
  ∧ (∀a,b:Point(l1).  f a ∧ f b ≤ f a ∧ b)
  ∧ (∀a,b:Point(l1).  f a ∨ b ≤ f a ∨ f b)
BY
{ (Auto
   THEN ((InstLemma `lattice-le-order` [⌜l2⌝]⋅ THENA Auto)
         THEN D -1
         THEN InstLemma `order-preserving-map-lattice-lemma` [⌜l1⌝;⌜l2⌝;⌜f⌝]⋅
         THEN Auto)
   THEN MemTypeCD
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[l1,l2:Lattice].  \mforall{}[f:Point(l1)  {}\mrightarrow{}  Point(l2)].
    f  \mmember{}  Hom(l1;l2) 
    supposing  (\mforall{}x,y:Point(l1).    (x  \mleq{}  y  {}\mRightarrow{}  f  x  \mleq{}  f  y))
    \mwedge{}  (\mforall{}a,b:Point(l1).    f  a  \mwedge{}  f  b  \mleq{}  f  a  \mwedge{}  b)
    \mwedge{}  (\mforall{}a,b:Point(l1).    f  a  \mvee{}  b  \mleq{}  f  a  \mvee{}  f  b)


By

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Latex:
(Auto
  THEN  ((InstLemma  `lattice-le-order`  [\mkleeneopen{}l2\mkleeneclose{}]\mcdot{}  THENA  Auto)
              THEN  D  -1
              THEN  InstLemma  `order-preserving-map-lattice-lemma`  [\mkleeneopen{}l1\mkleeneclose{};\mkleeneopen{}l2\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}
              THEN  Auto)
  THEN  MemTypeCD
  THEN  Auto)

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