Nuprl Lemma : fresh-cname-not-member-list-diff
∀I:Cname List. ∀[L:Cname List]. (¬(fresh-cname(I) ∈ I-L))
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
fresh-cname_wf,
member-list-diff,
l_member_wf,
coordinate_name_wf,
list-diff_wf,
cname_deq_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
inhabitedIsType,
setElimination,
rename,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
productElimination,
voidElimination,
universeIsType,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
applyEquality,
sqequalRule,
lambdaEquality_alt,
functionIsTypeImplies
Latex:
\mforall{}I:Cname List. \mforall{}[L:Cname List]. (\mneg{}(fresh-cname(I) \mmember{} I-L))
Date html generated:
2020_05_21-AM-10_48_12
Last ObjectModification:
2020_01_05-AM-00_09_17
Theory : cubical!sets
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