Nuprl Lemma : same-cubical-type-0
∀[Gamma:j⊢]. ∀[A,B:{Gamma, 0(𝔽) ⊢ _}]. Gamma, 0(𝔽) ⊢ A = B
Proof
Definitions occuring in Statement :
same-cubical-type: Gamma ⊢ A = B,
context-subset: Gamma, phi,
face-0: 0(𝔽),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
context-subset: Gamma, phi,
false: False,
face-0: 0(𝔽),
cubical-term-at: u(a),
same-cubical-type: Gamma ⊢ A = B,
uimplies: b supposing a,
cubical-type: {X ⊢ _}
Lemmas referenced :
I_cube_pair_redex_lemma,
face-lattice-0-not-1,
I_cube_wf,
context-subset_wf,
face-0_wf,
fset_wf,
nat_wf,
cubical-type_wf,
cubical_set_wf,
cubical-type-equal2,
names-hom_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
extract_by_obid,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
setElimination,
rename,
sqequalRule,
isectElimination,
hypothesisEquality,
independent_functionElimination,
voidElimination,
universeIsType,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
independent_isectElimination,
productElimination,
dependent_pairEquality_alt,
functionExtensionality,
applyEquality,
because_Cache,
functionIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,B:\{Gamma, 0(\mBbbF{}) \mvdash{} \_\}]. Gamma, 0(\mBbbF{}) \mvdash{} A = B
Date html generated:
2020_05_20-PM-03_00_51
Last ObjectModification:
2020_04_04-PM-05_15_35
Theory : cubical!type!theory
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