Nuprl Lemma : sub-bag-remove-repeats-if-no-repeats
∀[T:Type]
∀eq:EqDecider(T). ∀b1,b2:bag(T).
(bag-no-repeats(T;b1) ⇒ sub-bag(T;b1;b2) ⇒ sub-bag(T;b1;bag-remove-repeats(eq;b2)))
Proof
Definitions occuring in Statement :
bag-remove-repeats: bag-remove-repeats(eq;bs),
sub-bag: sub-bag(T;as;bs),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q
Lemmas referenced :
deq_wf,
bag-no-repeats_wf,
sub-bag_wf,
bag-remove-repeats_wf,
sub-bag-no-repeats-iff,
bag-member_wf,
sub-bag-member,
bag-member-remove-repeats
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
productElimination,
independent_pairFormation,
independent_isectElimination,
sqequalRule,
imageElimination,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]
\mforall{}eq:EqDecider(T). \mforall{}b1,b2:bag(T).
(bag-no-repeats(T;b1) {}\mRightarrow{} sub-bag(T;b1;b2) {}\mRightarrow{} sub-bag(T;b1;bag-remove-repeats(eq;b2)))
Date html generated:
2016_05_15-PM-08_08_53
Last ObjectModification:
2016_01_16-PM-01_27_36
Theory : bags_2
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