Nuprl Lemma : cubical-equiv_wf
∀[X:j⊢]. ∀[T,A:{X ⊢ _}]. X ⊢ Equiv(T;A)
Proof
Definitions occuring in Statement :
cubical-equiv: Equiv(T;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-equiv: Equiv(T;A),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
cubical-sigma_wf,
cubical-fun_wf,
is-cubical-equiv_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
cc-snd_wf-cubical-fun,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
because_Cache,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[T,A:\{X \mvdash{} \_\}]. X \mvdash{} Equiv(T;A)
Date html generated:
2020_05_20-PM-03_26_07
Last ObjectModification:
2020_04_06-PM-06_44_01
Theory : cubical!type!theory
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