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Step * 1 1 of Lemma term-A-face_wf

.....assertion..... 
1. X : CubicalSet
2. A : {X ⊢ _}
3. a : {X ⊢ _:A}
4. I : Cname List
5. alpha : X(I)
6. i : ℕ2
⊢ alpha = (fresh-cname(I):=i)(iota(fresh-cname(I))(alpha)) ∈ X(I)
BY
{ ((InstLemma `cube-set-restriction-comp` [⌜X⌝;⌜I⌝;⌜[fresh-cname(I) / I]⌝;⌜I⌝;⌜iota(fresh-cname(I))⌝;
    ⌜(fresh-cname(I):=i)⌝;⌜alpha⌝]⋅
    THENA Auto
    )
   THEN (Subst ⌜(iota(fresh-cname(I)) o (fresh-cname(I):=i)) = 1 ∈ name-morph(I;I)⌝ (-1)⋅ THENA Auto)
   ) }

1
1. X : CubicalSet
2. A : {X ⊢ _}
3. a : {X ⊢ _:A}
4. I : Cname List
5. alpha : X(I)
6. i : ℕ2
7. (fresh-cname(I):=i)(iota(fresh-cname(I))(alpha)) = 1(alpha) ∈ X(I)
⊢ alpha = (fresh-cname(I):=i)(iota(fresh-cname(I))(alpha)) ∈ X(I)

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Latex:

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Latex:
.....assertion..... 
1.  X  :  CubicalSet
2.  A  :  \{X  \mvdash{}  \_\}
3.  a  :  \{X  \mvdash{}  \_:A\}
4.  I  :  Cname  List
5.  alpha  :  X(I)
6.  i  :  \mBbbN{}2
\mvdash{}  alpha  =  (fresh-cname(I):=i)(iota(fresh-cname(I))(alpha))


By

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Latex:
((InstLemma  `cube-set-restriction-comp`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}[fresh-cname(I)  /  I]\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}iota(fresh-cname(I))\mkleeneclose{};
    \mkleeneopen{}(fresh-cname(I):=i)\mkleeneclose{};\mkleeneopen{}alpha\mkleeneclose{}]\mcdot{}
    THENA  Auto
    )
  THEN  (Subst  \mkleeneopen{}(iota(fresh-cname(I))  o  (fresh-cname(I):=i))  =  1\mkleeneclose{}  (-1)\mcdot{}  THENA  Auto)
  )

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