Nuprl Lemma : decidable__nameset
∀L:Cname List. ∀a:Cname. Dec(a ∈ nameset(L))
Proof
Definitions occuring in Statement :
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
decidable: Dec(P),
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
nameset: nameset(L),
prop: ℙ,
not: ¬A,
squash: ↓T,
false: False,
subtype_rel: A ⊆r B,
coordinate_name: Cname,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
coordinate_name_wf,
list_wf,
decidable__l_member,
decidable__equal-coordinate_name,
l_member_wf,
not_wf,
member_wf,
nameset_wf,
set_subtype_base,
le_wf,
int_subtype_base,
base_wf,
equal-wf-base,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
inlFormation,
dependent_set_memberEquality,
inrFormation,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
voidElimination,
applyEquality,
intEquality,
lambdaEquality,
natural_numberEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}L:Cname List. \mforall{}a:Cname. Dec(a \mmember{} nameset(L))
Date html generated:
2017_10_05-AM-10_04_55
Last ObjectModification:
2017_07_28-AM-11_15_52
Theory : cubical!sets
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