Nuprl Lemma : equiv-fun_wf
∀[G:j⊢]. ∀[A,T:{G ⊢ _}]. ∀[f:{G ⊢ _:Equiv(T;A)}]. (equiv-fun(f) ∈ {G ⊢ _:(T ⟶ A)})
Proof
Definitions occuring in Statement :
equiv-fun: equiv-fun(f),
cubical-equiv: Equiv(T;A),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _: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),
equiv-fun: equiv-fun(f),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
cubical-fst_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-term_wf,
cubical-equiv_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
because_Cache,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,T:\{G \mvdash{} \_\}]. \mforall{}[f:\{G \mvdash{} \_:Equiv(T;A)\}]. (equiv-fun(f) \mmember{} \{G \mvdash{} \_:(T {}\mrightarrow{} A)\})
Date html generated:
2020_05_20-PM-03_26_56
Last ObjectModification:
2020_04_06-PM-06_45_16
Theory : cubical!type!theory
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