Step
*
1
of Lemma
ps-sigma-unelim-elim-type
1. C : SmallCategory
2. X : ps_context{j:l}(C)
3. A : {X ⊢ _}
4. B : {X.A ⊢ _}
5. SigmaUnElim o SigmaElim = 1(X.Σ A B) ∈ psc_map{[i | j]:l}(C; X.Σ A B; X.Σ A B)
6. T : {X.Σ A B ⊢ _}
7. (T)SigmaUnElim o SigmaElim = (T)1(X.Σ A B) ∈ {X.Σ A B ⊢ _}
⊢ ((T)SigmaUnElim)SigmaElim = T ∈ {X.Σ A B ⊢ _}
BY
{ (NthHypEqGen (-1) THEN EqCDA THEN Auto) }
Latex:
Latex:
1. C : SmallCategory
2. X : ps\_context\{j:l\}(C)
3. A : \{X \mvdash{} \_\}
4. B : \{X.A \mvdash{} \_\}
5. SigmaUnElim o SigmaElim = 1(X.\mSigma{} A B)
6. T : \{X.\mSigma{} A B \mvdash{} \_\}
7. (T)SigmaUnElim o SigmaElim = (T)1(X.\mSigma{} A B)
\mvdash{} ((T)SigmaUnElim)SigmaElim = T
By
Latex:
(NthHypEqGen (-1) THEN EqCDA THEN Auto)
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