Nuprl Lemma : glue-type-1
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[T:{Gamma, 1(𝔽) ⊢ _}]. ∀[w:{Gamma, 1(𝔽) ⊢ _:(T ⟶ A)}].
(Gamma ⊢ Glue [1(𝔽) ⊢→ (T;w)] A = T ∈ {Gamma ⊢ _})
Proof
Definitions occuring in Statement :
glue-type: Glue [phi ⊢→ (T;w)] A,
context-subset: Gamma, phi,
face-1: 1(𝔽),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
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,
same-cubical-type: Gamma ⊢ A = B,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
glue-type-constraint,
face-1_wf,
subset-cubical-type,
context-subset_wf,
context-1-subset,
istype-cubical-term,
cubical-fun_wf,
thin-context-subset,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
independent_isectElimination,
because_Cache,
sqequalRule,
universeIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[T:\{Gamma, 1(\mBbbF{}) \mvdash{} \_\}]. \mforall{}[w:\{Gamma, 1(\mBbbF{}) \mvdash{} \_:(T {}\mrightarrow{} A)\}].
(Gamma \mvdash{} Glue [1(\mBbbF{}) \mvdash{}\mrightarrow{} (T;w)] A = T)
Date html generated:
2020_05_20-PM-05_42_44
Last ObjectModification:
2020_04_21-PM-06_58_44
Theory : cubical!type!theory
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