Nuprl Lemma : fresh-cname-not-member
∀[I:Cname List]. (¬(fresh-cname(I) ∈ nameset(I)))
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
nameset: nameset(L),
squash: ↓T,
subtype_rel: A ⊆r B,
coordinate_name: Cname,
int_upper: {i...},
uimplies: b supposing a
Lemmas referenced :
list_wf,
coordinate_name_wf,
fresh-cname_wf,
set_wf,
not_wf,
l_member_wf,
equal_wf,
set_subtype_base,
le_wf,
int_subtype_base,
base_wf,
equal-wf-base,
nameset_wf,
list_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaFormation,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
voidElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
setElimination,
rename,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
intEquality,
natural_numberEquality,
independent_isectElimination,
because_Cache,
baseApply,
closedConclusion
Latex:
\mforall{}[I:Cname List]. (\mneg{}(fresh-cname(I) \mmember{} nameset(I)))
Date html generated:
2017_10_05-AM-10_05_06
Last ObjectModification:
2017_07_28-AM-11_15_56
Theory : cubical!sets
Home
Index