Nuprl Lemma : sub-bag-lub
∀[T:Type]
∀eq:EqDecider(T). ∀as,bs,cs:bag(T). ((sub-bag(T;cs;as) ∨ sub-bag(T;cs;bs)) ⇒ sub-bag(T;cs;bag-lub(eq;as;bs)))
Proof
Definitions occuring in Statement :
bag-lub: bag-lub(eq;b1;b2),
sub-bag: sub-bag(T;as;bs),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
bag-lub-property,
sub-bag_transitivity,
bag-lub_wf,
or_wf,
sub-bag_wf,
bag_wf,
deq_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
productElimination,
unionElimination,
independent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}eq:EqDecider(T). \mforall{}as,bs,cs:bag(T).
((sub-bag(T;cs;as) \mvee{} sub-bag(T;cs;bs)) {}\mRightarrow{} sub-bag(T;cs;bag-lub(eq;as;bs)))
Date html generated:
2016_05_15-PM-08_09_39
Last ObjectModification:
2015_12_27-PM-04_12_31
Theory : bags_2
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