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Step * 2 of Lemma adjacent-compatible-iff


1. [X] : CubicalSet
2. I : Cname List
3. L : I-face(X;I) List
4. ∀f1,f2:I-face(X;I).
     ((f1 ∈ L)
     ⇒ (f2 ∈ L)
     ⇒ (¬(dimension(f1) = dimension(f2) ∈ Cname))
     ⇒ ((dimension(f2):=direction(f2))(cube(f1))
        = (dimension(f1):=direction(f1))(cube(f2))
        ∈ X(I-[dimension(f1); dimension(f2)])))
⊢ adjacent-compatible(X;I;L)
BY
{ (D 0 THEN Auto) }

1
1. [X] : CubicalSet
2. I : Cname List
3. L : I-face(X;I) List
4. ∀f1,f2:I-face(X;I).
     ((f1 ∈ L)
     ⇒ (f2 ∈ L)
     ⇒ (¬(dimension(f1) = dimension(f2) ∈ Cname))
     ⇒ ((dimension(f2):=direction(f2))(cube(f1))
        = (dimension(f1):=direction(f1))(cube(f2))
        ∈ X(I-[dimension(f1); dimension(f2)])))
5. i : ℕ||L||
6. j : ℕi
⊢ face-compatible(X;I;L[j];L[i])

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Latex:

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Latex:

1.  [X]  :  CubicalSet
2.  I  :  Cname  List
3.  L  :  I-face(X;I)  List
4.  \mforall{}f1,f2:I-face(X;I).
          ((f1  \mmember{}  L)
          {}\mRightarrow{}  (f2  \mmember{}  L)
          {}\mRightarrow{}  (\mneg{}(dimension(f1)  =  dimension(f2)))
          {}\mRightarrow{}  ((dimension(f2):=direction(f2))(cube(f1))  =  (dimension(f1):=direction(f1))(cube(f2))))
\mvdash{}  adjacent-compatible(X;I;L)


By

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Latex:
(D  0  THEN  Auto)

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