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Step * 1 1 of Lemma discrete-sigma-equiv


1. A : Type
2. B : A ⟶ Type
3. X : CubicalSet{j}
4. (Σ discr(A) discrete-family(A;a.B[a]))p
= Σ discr(A) (discrete-family(A;a.B[a]))(p o p;q)
∈ {X.Σ discr(A) discrete-family(A;a.B[a]) ⊢ _}
⊢ discrete-pair(q) ∈ {X.Σ discr(A) discrete-family(A;a.B[a]) ⊢ _:(discr(a:A × B[a]))p}
BY
{ ((RWO "csm-discrete-cubical-type" 0) CollapseTHEN (Auto⋅))⋅ }

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Latex:

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Latex:

1.  A  :  Type
2.  B  :  A  {}\mrightarrow{}  Type
3.  X  :  CubicalSet\{j\}
4.  (\mSigma{}  discr(A)  discrete-family(A;a.B[a]))p  =  \mSigma{}  discr(A)  (discrete-family(A;a.B[a]))(p  o  p;q)
\mvdash{}  discrete-pair(q)  \mmember{}  \{X.\mSigma{}  discr(A)  discrete-family(A;a.B[a])  \mvdash{}  \_:(discr(a:A  \mtimes{}  B[a]))p\}


By

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Latex:
((RWO  "csm-discrete-cubical-type"  0)  CollapseTHEN  (Auto\mcdot{}))\mcdot{}

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