Nuprl Lemma : cubical-id-equiv_wf
∀X:j⊢. ∀T:{X ⊢ _}. (IdEquiv(X;T) ∈ {X ⊢ _:Equiv(T;T)})
Proof
Definitions occuring in Statement :
cubical-id-equiv: IdEquiv(X;T),
cubical-equiv: Equiv(T;A),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
cubical-id-equiv: IdEquiv(X;T)
Lemmas referenced :
cubical-id-fun_wf,
cubical-type_wf,
cubical_set_wf,
cubical-id-is-equiv_wf,
equiv-witness_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
because_Cache,
dependent_functionElimination
Latex:
\mforall{}X:j\mvdash{}. \mforall{}T:\{X \mvdash{} \_\}. (IdEquiv(X;T) \mmember{} \{X \mvdash{} \_:Equiv(T;T)\})
Date html generated:
2020_05_20-PM-03_34_10
Last ObjectModification:
2020_04_06-PM-06_55_53
Theory : cubical!type!theory
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