Nuprl Lemma : fresh-cname-not-equal2
∀I:Cname List. ∀[x:nameset(I)]. (¬(x = fresh-cname(I) ∈ Cname))
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
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],
nameset: nameset(L),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
coordinate_name: Cname,
int_upper: {i...},
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
fresh-cname_wf,
set_wf,
coordinate_name_wf,
not_wf,
l_member_wf,
equal_wf,
nameset_wf,
list_wf,
subtype_base_sq,
set_subtype_base,
le_wf,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
setElimination,
rename,
applyEquality,
setEquality,
because_Cache,
instantiate,
cumulativity,
independent_isectElimination,
intEquality,
natural_numberEquality
Latex:
\mforall{}I:Cname List. \mforall{}[x:nameset(I)]. (\mneg{}(x = fresh-cname(I)))
Date html generated:
2017_10_05-AM-10_05_13
Last ObjectModification:
2017_07_28-AM-11_15_58
Theory : cubical!sets
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