Step * of Lemma discrete-function-injection

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[A:Type]. ∀[B:A ⟶ Type]. ∀[X:j⊢].
  ∀f,g:{X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}.
    g ∈ {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])} 
    supposing discrete-function(f) discrete-function(g) ∈ {X ⊢ _:discr(a:A ⟶ B[a])}
BY
(Auto
   THEN (CubicalTermEqual THEN Auto)
   THEN Fold `cubical-term-at` 0
   THEN (Assert f(a) ∈ Πdiscr(A) discrete-family(A;a.B[a])(a) BY
               Auto)) }

1
1. Type
2. A ⟶ Type
3. CubicalSet{j}
4. {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}
5. {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}
6. discrete-function(f) discrete-function(g) ∈ {X ⊢ _:discr(a:A ⟶ B[a])}
7. fset(ℕ)
8. X(I)
9. f(a) ∈ Πdiscr(A) discrete-family(A;a.B[a])(a)
⊢ f(a) g(a) ∈ Πdiscr(A) discrete-family(A;a.B[a])(a)


Latex:


Latex:
No  Annotations
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[X:j\mvdash{}].
    \mforall{}f,g:\{X  \mvdash{}  \_:\mPi{}discr(A)  discrete-family(A;a.B[a])\}.
        f  =  g  supposing  discrete-function(f)  =  discrete-function(g)


By


Latex:
(Auto
  THEN  (CubicalTermEqual  THEN  Auto)
  THEN  Fold  `cubical-term-at`  0
  THEN  (Assert  f(a)  \mmember{}  \mPi{}discr(A)  discrete-family(A;a.B[a])(a)  BY
                          Auto))




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