Step * of Lemma equals-transprt

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[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 +⊢ Compositon(A)]. ∀[a:{Gamma ⊢ _:(A)[0(𝕀)]}]. ∀[xx:Top].
  (comp cA [0(𝔽) ⊢→ xx] transprt(Gamma;cA;a) ∈ {Gamma ⊢ _:(A)[1(𝕀)]})
BY
(Auto THEN Unfold `transprt` THEN Symmetry) }

1
1. Gamma CubicalSet{j}
2. {Gamma.𝕀 ⊢ _}
3. cA Gamma.𝕀 +⊢ Compositon(A)
4. {Gamma ⊢ _:(A)[0(𝕀)]}
5. xx Top
⊢ comp cA [0(𝔽) ⊢→ discr(⋅)] comp cA [0(𝔽) ⊢→ xx] a ∈ {Gamma ⊢ _:(A)[1(𝕀)]}


Latex:


Latex:
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\mforall{}[Gamma:j\mvdash{}].  \mforall{}[A:\{Gamma.\mBbbI{}  \mvdash{}  \_\}].  \mforall{}[cA:Gamma.\mBbbI{}  +\mvdash{}  Compositon(A)].  \mforall{}[a:\{Gamma  \mvdash{}  \_:(A)[0(\mBbbI{})]\}].
\mforall{}[xx:Top].
    (comp  cA  [0(\mBbbF{})  \mvdash{}\mrightarrow{}  xx]  a  =  transprt(Gamma;cA;a))


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Latex:
(Auto  THEN  Unfold  `transprt`  0  THEN  Symmetry)




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