Nuprl Lemma : bag-co-restrict-disjoint
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[b:bag(T)]. (b|¬x) = b ∈ bag(T) supposing ¬x ↓∈ b
Proof
Definitions occuring in Statement :
bag-co-restrict: (b|¬x),
bag-member: x ↓∈ bs,
bag: bag(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
bag-co-restrict: (b|¬x),
bag-filter: [x∈b|p[x]],
deq: EqDecider(T),
so_apply: x[s],
so_lambda: λ2x.t[x],
uiff: uiff(P;Q),
eqof: eqof(d),
subtype_rel: A ⊆r B,
false: False
Lemmas referenced :
bag_to_squash_list,
not_wf,
bag-member_wf,
bag-member-list,
decidable-equal-deq,
l_member_wf,
equal_wf,
bag_wf,
bag-co-restrict_wf,
deq_wf,
filter_trivial,
bnot_wf,
l_all_iff,
assert_wf,
iff_transitivity,
eqof_wf,
iff_weakening_uiff,
assert_of_bnot,
safe-assert-deq,
list-subtype-bag,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
cumulativity,
rename,
lambdaFormation,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
universeEquality,
lambdaEquality,
applyEquality,
setElimination,
independent_isectElimination,
setEquality,
addLevel,
independent_pairFormation,
impliesFunctionality,
dependent_set_memberEquality,
voidElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[b:bag(T)]. (b|\mneg{}x) = b supposing \mneg{}x \mdownarrow{}\mmember{} b
Date html generated:
2018_05_21-PM-09_52_52
Last ObjectModification:
2017_07_26-PM-06_32_08
Theory : bags_2
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