Nuprl Lemma : glue-type-term-subtype2
∀[Gamma:j⊢]. ∀[psi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma, psi ⊢ _}]. ∀[phi:{Gamma, psi ⊢ _:𝔽}]. ∀[T:{Gamma, psi, phi ⊢ _}].
∀[w:{Gamma, psi, phi ⊢ _:(T ⟶ A)}].
({Gamma, psi ⊢ _:Glue [phi ⊢→ (T;w)] A} ⊆r {Gamma, psi, phi ⊢ _:T})
Proof
Definitions occuring in Statement :
glue-type: Glue [phi ⊢→ (T;w)] A,
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
glue-type-term-subtype,
istype-cubical-term,
context-subset_wf,
cubical-fun_wf,
thin-context-subset,
cubical-type_wf,
face-type_wf,
cubical_set_wf,
glue-type-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
sqequalRule,
Error :memTop
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[psi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{Gamma, psi \mvdash{} \_\}]. \mforall{}[phi:\{Gamma, psi \mvdash{} \_:\mBbbF{}\}].
\mforall{}[T:\{Gamma, psi, phi \mvdash{} \_\}]. \mforall{}[w:\{Gamma, psi, phi \mvdash{} \_:(T {}\mrightarrow{} A)\}].
(\{Gamma, psi \mvdash{} \_:Glue [phi \mvdash{}\mrightarrow{} (T;w)] A\} \msubseteq{}r \{Gamma, psi, phi \mvdash{} \_:T\})
Date html generated:
2020_05_20-PM-05_42_29
Last ObjectModification:
2020_04_21-PM-06_58_27
Theory : cubical!type!theory
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