Nuprl Lemma : fresh-cname-not-member2
∀I:Cname List. (¬(fresh-cname(I) ∈ I))
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
coordinate_name: Cname,
l_member: (x ∈ l),
list: T List,
all: ∀x:A. B[x],
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
fresh-cname_wf,
set_wf,
coordinate_name_wf,
not_wf,
l_member_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
setElimination,
rename,
independent_functionElimination,
voidElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
applyEquality,
setEquality
Latex:
\mforall{}I:Cname List. (\mneg{}(fresh-cname(I) \mmember{} I))
Date html generated:
2016_05_20-AM-09_28_37
Last ObjectModification:
2015_12_28-PM-04_48_11
Theory : cubical!sets
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