Nuprl Lemma : empty-context-eq-lemma
∀[Gamma:j⊢]. ∀[A,x,y:Top]. (x = y ∈ {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,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
cubical-term: {X ⊢ _:A}
Lemmas referenced :
istype-top,
fset_wf,
nat_wf,
I_cube_wf,
istype-void,
cubical_set_wf,
names-hom_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,
because_Cache,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
functionIsType,
universeIsType,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
functionExtensionality,
dependent_functionElimination,
functionExtensionality_alt,
independent_functionElimination,
voidElimination,
lambdaFormation_alt,
dependent_set_memberEquality_alt,
equalityIstype,
applyEquality
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,x,y:Top]. (x = y) supposing \mforall{}I:fset(\mBbbN{}). (\mneg{}Gamma(I))
Date html generated:
2020_05_20-PM-04_12_06
Last ObjectModification:
2020_04_10-PM-04_40_54
Theory : cubical!type!theory
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