Nuprl Lemma : cubical-term-eqcd
∀[X:j⊢]. ∀[A,B:{X ⊢ _}]. {X ⊢ _:A} = {X ⊢ _:B} ∈ 𝕌{[i | j']} supposing A = B ∈ {X ⊢ _}
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
equalitySymmetry,
dependent_set_memberEquality_alt,
hypothesis,
independent_pairFormation,
equalityTransitivity,
sqequalRule,
productIsType,
equalityIstype,
inhabitedIsType,
hypothesisEquality,
applyLambdaEquality,
setElimination,
thin,
rename,
sqequalHypSubstitution,
productElimination,
instantiate,
extract_by_obid,
isectElimination,
applyEquality,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
because_Cache
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A,B:\{X \mvdash{} \_\}]. \{X \mvdash{} \_:A\} = \{X \mvdash{} \_:B\} supposing A = B
Date html generated:
2020_05_20-PM-01_51_21
Last ObjectModification:
2020_04_18-AM-10_13_33
Theory : cubical!type!theory
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