Nuprl Lemma : cubical-equiv-p
∀[H:j⊢]. ∀[T,A,E:{H ⊢ _}]. ((Equiv(A;E))p = Equiv((A)p;(E)p) ∈ {H.T ⊢ _})
Proof
Definitions occuring in Statement :
cubical-equiv: Equiv(T;A),
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
csm-cubical-equiv,
cubical_set_cumulativity-i-j,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cc-fst_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
inhabitedIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[T,A,E:\{H \mvdash{} \_\}]. ((Equiv(A;E))p = Equiv((A)p;(E)p))
Date html generated:
2020_05_20-PM-03_26_33
Last ObjectModification:
2020_04_07-PM-00_59_41
Theory : cubical!type!theory
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