Nuprl Lemma : bag-no-repeats-filter
∀[T:Type]. ∀[b:bag(T)]. ∀[p:T ⟶ 𝔹]. bag-no-repeats(T;[x∈b|p[x]]) supposing bag-no-repeats(T;b)
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
bag-filter: [x∈b|p[x]],
bag: bag(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
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,
bag-filter: [x∈b|p[x]],
uiff: uiff(P;Q),
and: P ∧ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
bag-no-repeats: bag-no-repeats(T;bs)
Lemmas referenced :
bag_to_squash_list,
bag-no-repeats_wf,
bag-no-repeats-list,
no_repeats_filter,
filter_wf5,
l_member_wf,
squash_wf,
no_repeats_wf,
bag-filter_wf,
subtype_rel_bag,
assert_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
sqequalRule,
rename,
independent_isectElimination,
lambdaEquality,
applyEquality,
functionExtensionality,
imageMemberEquality,
baseClosed,
addLevel,
setElimination,
setEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. bag-no-repeats(T;[x\mmember{}b|p[x]]) supposing bag-no-repeats(T;b)
Date html generated:
2016_10_25-AM-10_35_16
Last ObjectModification:
2016_07_12-AM-06_49_43
Theory : bags
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