Nuprl Lemma : bag-co-restrict-property
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[b:bag(T)]. (¬x ↓∈ (b|¬x))
Proof
Definitions occuring in Statement :
bag-co-restrict: (b|¬x),
bag-member: x ↓∈ bs,
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
bag-co-restrict: (b|¬x),
so_lambda: λ2x.t[x],
deq: EqDecider(T),
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
eqof: eqof(d),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bag-member-filter,
bnot_wf,
bag-member_wf,
bag-co-restrict_wf,
bag_wf,
deq_wf,
assert_wf,
eqof_wf,
not_wf,
equal_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
safe-assert-deq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
cumulativity,
productElimination,
independent_isectElimination,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
isect_memberEquality,
universeEquality,
independent_pairFormation,
impliesFunctionality,
promote_hyp
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[b:bag(T)]. (\mneg{}x \mdownarrow{}\mmember{} (b|\mneg{}x))
Date html generated:
2018_05_21-PM-09_52_45
Last ObjectModification:
2017_07_26-PM-06_32_04
Theory : bags_2
Home
Index