Nuprl Lemma : gluetype_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[T:{Gamma, phi ⊢ _}]. ∀[f:{Gamma, phi ⊢ _:Equiv(T;A)}].
Gamma ⊢ gluetype(Gamma;A;phi;T;f)
Proof
Definitions occuring in Statement :
gluetype: gluetype(Gamma;A;phi;T;f),
cubical-equiv: Equiv(T;A),
context-subset: Gamma, phi,
face-type: 𝔽,
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,
gluetype: gluetype(Gamma;A;phi;T;f)
Lemmas referenced :
glue-type_wf,
equiv-fun_wf,
context-subset_wf,
thin-context-subset,
istype-cubical-term,
cubical-equiv_wf,
cubical-type_wf,
face-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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[T:\{Gamma, phi \mvdash{} \_\}].
\mforall{}[f:\{Gamma, phi \mvdash{} \_:Equiv(T;A)\}].
Gamma \mvdash{} gluetype(Gamma;A;phi;T;f)
Date html generated:
2020_05_20-PM-07_05_00
Last ObjectModification:
2020_04_21-PM-07_53_53
Theory : cubical!type!theory
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