Nuprl Lemma : csm-type-ap_wf
∀[Gamma,Delta:CubicalSet]. ∀[s:Delta ⟶ Gamma]. ∀[A:{Gamma ⊢ _}]. Delta ⊢ csm-type-ap(A;s)
Proof
Definitions occuring in Statement :
csm-type-ap: csm-type-ap(A;s),
cubical-type: {X ⊢ _},
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
csm-type-ap: csm-type-ap(A;s)
Lemmas referenced :
cubical-set_wf,
cube-set-map_wf,
cubical-type_wf,
csm-ap-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[Gamma,Delta:CubicalSet]. \mforall{}[s:Delta {}\mrightarrow{} Gamma]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. Delta \mvdash{} csm-type-ap(A;s)
Date html generated:
2016_06_16-PM-05_39_29
Last ObjectModification:
2016_03_13-PM-03_20_15
Theory : cubical!sets
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