Nuprl Lemma : same-cubical-type_wf
∀[Gamma:j⊢]. ∀[A,B:{Gamma ⊢ _}]. (Gamma ⊢ A = B ∈ 𝕌{[i' | j']})
Proof
Definitions occuring in Statement :
same-cubical-type: Gamma ⊢ A = B,
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,
same-cubical-type: Gamma ⊢ A = B,
prop: ℙ
Lemmas referenced :
equal_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,B:\{Gamma \mvdash{} \_\}]. (Gamma \mvdash{} A = B \mmember{} \mBbbU{}\{[i' | j']\})
Date html generated:
2020_05_20-PM-02_59_37
Last ObjectModification:
2020_04_06-AM-10_52_11
Theory : cubical!type!theory
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