Nuprl Lemma : empty-context-lemma
∀[Gamma:j⊢]. ∀[A,x:Top]. (x ∈ {Gamma ⊢ _:A}) supposing ∀I:fset(ℕ). (¬Gamma(I))
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
istype-top,
fset_wf,
nat_wf,
I_cube_wf,
istype-void,
cubical_set_wf,
empty-context-eq-lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
functionIsType,
universeIsType,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,x:Top]. (x \mmember{} \{Gamma \mvdash{} \_:A\}) supposing \mforall{}I:fset(\mBbbN{}). (\mneg{}Gamma(I))
Date html generated:
2020_05_20-PM-04_12_20
Last ObjectModification:
2020_04_10-PM-04_48_08
Theory : cubical!type!theory
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