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Step * 1 of Lemma discrete-pi-bijection


1. A : Type
2. B : A ⟶ Type
3. X : CubicalSet{j}
4. a1 : {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}
5. a2 : {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}
6. discrete-function(a1) = discrete-function(a2) ∈ {X ⊢ _:discr(a:A ⟶ B[a])}
⊢ a1 = a2 ∈ {X ⊢ _:Πdiscr(A) discrete-family(A;a.B[a])}
BY
{ (FLemma `discrete-function-injection` [-1] THEN Auto) }

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Latex:

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Latex:

1.  A  :  Type
2.  B  :  A  {}\mrightarrow{}  Type
3.  X  :  CubicalSet\{j\}
4.  a1  :  \{X  \mvdash{}  \_:\mPi{}discr(A)  discrete-family(A;a.B[a])\}
5.  a2  :  \{X  \mvdash{}  \_:\mPi{}discr(A)  discrete-family(A;a.B[a])\}
6.  discrete-function(a1)  =  discrete-function(a2)
\mvdash{}  a1  =  a2


By

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Latex:
(FLemma  `discrete-function-injection`  [-1]  THEN  Auto)

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