Nuprl Lemma : empty-context-subset-lemma4
∀[Gamma:j⊢]. ∀[B:{Gamma ⊢ _}]. ∀[A,x,y:Top]. (x = y ∈ {Gamma, 0(𝔽).B ⊢ _:A})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-0: 0(𝔽),
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cubical-term: {X ⊢ _:A},
context-subset: Gamma, phi,
cube-context-adjoin: X.A,
all: ∀x:A. B[x],
member: t ∈ T,
face-0: 0(𝔽),
cubical-term-at: u(a),
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
I_cube_pair_redex_lemma,
face-lattice-0-not-1,
I_cube_wf,
cube-context-adjoin_wf,
context-subset_wf,
cubical_set_cumulativity-i-j,
face-0_wf,
thin-context-subset,
cubical-type-cumulativity2,
fset_wf,
nat_wf,
names-hom_wf,
istype-top,
cubical-type_wf,
cubical_set_wf,
istype-cubical-type-at,
cube-set-restriction_wf,
cubical-type-ap-morph_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
dependent_set_memberEquality_alt,
functionExtensionality,
sqequalHypSubstitution,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
sqequalRule,
productElimination,
setElimination,
rename,
isectElimination,
hypothesisEquality,
independent_functionElimination,
voidElimination,
instantiate,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
universeIsType,
inhabitedIsType,
functionIsType,
equalityIstype
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[B:\{Gamma \mvdash{} \_\}]. \mforall{}[A,x,y:Top]. (x = y)
Date html generated:
2020_05_20-PM-04_13_25
Last ObjectModification:
2020_04_10-AM-04_40_46
Theory : cubical!type!theory
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