Nuprl Lemma : empty-context-subset-lemma1
∀[Gamma:j⊢]. ∀[A,x:Top]. (x ∈ {Gamma, 0(𝔽).𝕀 ⊢ _:A})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-0: 0(𝔽),
interval-type: 𝕀,
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
context-subset: Gamma, phi,
cube-context-adjoin: X.A,
false: False,
face-0: 0(𝔽),
cubical-term-at: u(a)
Lemmas referenced :
empty-context-lemma,
cube-context-adjoin_wf,
context-subset_wf,
cubical_set_cumulativity-i-j,
face-0_wf,
interval-type_wf,
istype-top,
cubical_set_wf,
I_cube_wf,
fset_wf,
nat_wf,
I_cube_pair_redex_lemma,
face-lattice-0-not-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
independent_isectElimination,
because_Cache,
universeIsType,
lambdaFormation_alt,
dependent_functionElimination,
Error :memTop,
productElimination,
setElimination,
rename,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,x:Top]. (x \mmember{} \{Gamma, 0(\mBbbF{}).\mBbbI{} \mvdash{} \_:A\})
Date html generated:
2020_05_20-PM-04_12_32
Last ObjectModification:
2020_04_10-AM-04_37_36
Theory : cubical!type!theory
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