Nuprl Lemma : constrained-cubical-term_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[t:{Gamma, phi ⊢ _:A}]. ({Gamma ⊢ _:A[phi |⟶ t]} ∈ 𝕌{[i | j']})
Proof
Definitions occuring in Statement :
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]},
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,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]},
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T}
Lemmas referenced :
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
equal_wf,
context-subset-term-subtype,
context-subset_wf,
thin-context-subset,
face-type_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[t:\{Gamma, phi \mvdash{} \_:A\}].
(\{Gamma \mvdash{} \_:A[phi |{}\mrightarrow{} t]\} \mmember{} \mBbbU{}\{[i | j']\})
Date html generated:
2020_05_20-PM-02_58_04
Last ObjectModification:
2020_04_06-AM-11_22_25
Theory : cubical!type!theory
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