Nuprl Lemma : new-name-property
∀[I:fset(ℕ)]. (¬new-name(I) ∈ I)
Proof
Definitions occuring in Statement :
new-name: new-name(I),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
new-name_wf,
not_wf,
fset_wf,
set_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
introduction,
extract_by_obid,
isectElimination,
applyEquality,
intEquality,
independent_isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
setElimination,
rename,
setEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. (\mneg{}new-name(I) \mmember{} I)
Date html generated:
2017_01_09-AM-09_12_11
Last ObjectModification:
2016_12_08-PM-06_25_04
Theory : cubical!type!theory
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