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Step * of Lemma face_lattice-hom-equal

∀[I,J:fset(ℕ)]. ∀[g,h:Hom(face_lattice(I);face_lattice(J))].
  g = h ∈ Hom(face_lattice(I);face_lattice(J)) 
  supposing (∀x:names(I). ((g (x=0)) = (h (x=0)) ∈ Point(face_lattice(J))))
  ∧ (∀x:names(I). ((g (x=1)) = (h (x=1)) ∈ Point(face_lattice(J))))
BY
{ (Auto
   THEN Unfold `face_lattice` 0
   THEN Using [`eqL', ⌜face_lattice-deq()⌝;`f0',⌜λx.(g (x=0))⌝;`f1',⌜λx.(g (x=1))⌝] (BLemma `face-lattice-hom-unique`)⋅
   THEN Auto
   THEN Fold `face_lattice` 0
   THEN Auto
   THEN Folds  ``fl0 fl1`` 0
   THEN Auto
   THEN RepeatFor 2 (DVar `g')
   THEN RWW "4.1 FL-meet-0-1.1" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[I,J:fset(\mBbbN{})].  \mforall{}[g,h:Hom(face\_lattice(I);face\_lattice(J))].
    g  =  h  supposing  (\mforall{}x:names(I).  ((g  (x=0))  =  (h  (x=0))))  \mwedge{}  (\mforall{}x:names(I).  ((g  (x=1))  =  (h  (x=1))))


By

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Latex:
(Auto
  THEN  Unfold  `face\_lattice`  0
  THEN  Using  [`eqL',  \mkleeneopen{}face\_lattice-deq()\mkleeneclose{};`f0',\mkleeneopen{}\mlambda{}x.(g  (x=0))\mkleeneclose{};`f1',\mkleeneopen{}\mlambda{}x.(g  (x=1))\mkleeneclose{}
  ]  (BLemma  `face-lattice-hom-unique`)\mcdot{}
  THEN  Auto
  THEN  Fold  `face\_lattice`  0
  THEN  Auto
  THEN  Folds    ``fl0  fl1``  0
  THEN  Auto
  THEN  RepeatFor  2  (DVar  `g')
  THEN  RWW  "4.1  FL-meet-0-1.1"  0
  THEN  Auto)

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