Nuprl Lemma : bag-no-repeats-list
∀[T:Type]. ∀[L:T List]. uiff(bag-no-repeats(T;L);no_repeats(T;L))
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
no_repeats: no_repeats(T;l),
list: T List,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bag-no-repeats: bag-no-repeats(T;bs),
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
squash: ↓T,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
cand: A c∧ B
Lemmas referenced :
no_repeats_witness,
bag-no-repeats_wf,
list-subtype-bag,
no_repeats_wf,
list_wf,
sq_stable__no_repeats,
no_repeats-bag,
equal_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
cumulativity,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
sqequalRule,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_pairFormation,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. uiff(bag-no-repeats(T;L);no\_repeats(T;L))
Date html generated:
2017_10_01-AM-09_01_23
Last ObjectModification:
2017_07_26-PM-04_42_43
Theory : bags
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