Nuprl Lemma : empty-context-subset-lemma6
∀[Gamma:j⊢]. ∀[x,y:Top × Top]. (x = y ∈ {Gamma, 0(𝔽) ⊢ _})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-0: 0(𝔽),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
equal: s = t ∈ T
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),
cubical-type: {X ⊢ _},
guard: {T},
and: P ∧ Q
Lemmas referenced :
istype-top,
cubical_set_wf,
I_cube_pair_redex_lemma,
face-lattice-0-not-1,
I_cube_wf,
context-subset_wf,
face-0_wf,
fset_wf,
nat_wf,
names-hom_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
hypothesis,
because_Cache,
productIsType,
introduction,
extract_by_obid,
universeIsType,
instantiate,
thin,
lambdaFormation_alt,
sqequalHypSubstitution,
dependent_functionElimination,
Error :memTop,
setElimination,
rename,
sqequalRule,
isectElimination,
hypothesisEquality,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality_alt,
productElimination,
dependent_pairEquality_alt,
functionExtensionality,
functionIsType,
applyEquality,
independent_pairFormation
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[x,y:Top \mtimes{} Top]. (x = y)
Date html generated:
2020_05_20-PM-04_13_55
Last ObjectModification:
2020_04_10-PM-04_48_22
Theory : cubical!type!theory
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