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Step * of Lemma fl-morph-face-lattice-tube1

∀[J:fset(ℕ)]. ∀[k:names(J)]. ∀[I:fset(ℕ)]. ∀[phi:Point(face_lattice(I))]. ∀[j:ℕ]. ∀[g:J ⟶ I+j].
  (face-lattice-tube(I;phi;j))<g> = (s(phi))<g> ∨ (k=0) ∨ (k=1) ∈ Point(face_lattice(J)) 
  supposing (g j) = <k> ∈ Point(dM(J))
BY
{ (Auto
   THEN Unfold `face-lattice-tube` 0
   THEN (RWW "fl-morph-join fl-morph-fl0 fl-morph-fl1" 0 THENA Auto)
   THEN EqCD
   THEN Auto
   THEN EqCD
   THEN HypSubst' (-1)0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[J:fset(\mBbbN{})].  \mforall{}[k:names(J)].  \mforall{}[I:fset(\mBbbN{})].  \mforall{}[phi:Point(face\_lattice(I))].  \mforall{}[j:\mBbbN{}].  \mforall{}[g:J  {}\mrightarrow{}  I+j].
    (face-lattice-tube(I;phi;j))<g>  =  (s(phi))<g>  \mvee{}  (k=0)  \mvee{}  (k=1)  supposing  (g  j)  =  <k>


By

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Latex:
(Auto
  THEN  Unfold  `face-lattice-tube`  0
  THEN  (RWW  "fl-morph-join  fl-morph-fl0  fl-morph-fl1"  0  THENA  Auto)
  THEN  EqCD
  THEN  Auto
  THEN  EqCD
  THEN  HypSubst'  (-1)0
  THEN  Auto)

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