Nuprl Lemma : single-valued-sub-bag
∀[T:Type]. ∀[as,bs:bag(T)]. (single-valued-bag(bs;T) ⇒ sub-bag(T;as;bs) ⇒ single-valued-bag(as;T))
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
sub-bag: sub-bag(T;as;bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
single-valued-bag: single-valued-bag(b;T),
all: ∀x:A. B[x],
prop: ℙ,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
sub-bag-member,
bag-member_wf,
sub-bag_wf,
single-valued-bag_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
sqequalRule,
lambdaEquality,
axiomEquality,
isect_memberEquality,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)].
(single-valued-bag(bs;T) {}\mRightarrow{} sub-bag(T;as;bs) {}\mRightarrow{} single-valued-bag(as;T))
Date html generated:
2016_05_15-PM-02_45_31
Last ObjectModification:
2015_12_27-AM-09_37_18
Theory : bags
Home
Index