Nuprl Lemma : csm-ap-cubical-fst
∀[X,Delta:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}]. ∀[p:{X ⊢ _:Σ A B}]. ∀[s:Delta ⟶ X].
((p.1)s = (p)s.1 ∈ {Delta ⊢ _:(A)s})
Proof
Definitions occuring in Statement :
cubical-fst: p.1,
cubical-sigma: Σ A B,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:AF},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
csm-cubical-fst,
csm-ap-term_wf,
cubical-fst_wf,
cube-set-map_wf,
cubical-term_wf,
cubical-sigma_wf,
cubical-type_wf,
cube-context-adjoin_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality
Latex:
\mforall{}[X,Delta:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[B:\{X.A \mvdash{} \_\}]. \mforall{}[p:\{X \mvdash{} \_:\mSigma{} A B\}]. \mforall{}[s:Delta {}\mrightarrow{} X].
((p.1)s = (p)s.1)
Date html generated:
2018_05_23-PM-06_31_05
Last ObjectModification:
2018_05_20-PM-04_17_58
Theory : cubical!sets
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