Nuprl Lemma : empty-bag-union
∀[T:Type]. ∀[bbs:bag(bag(T))]. ∀bs:bag(T). (bs ↓∈ bbs ⇒ (bs = {} ∈ bag(T))) supposing bag-union(bbs) = {} ∈ bag(T)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag-union: bag-union(bbs),
empty-bag: {},
bag: bag(T)
Lemmas :
bag-size_wf,
bag_wf,
nat_wf,
equal_wf,
equal-wf-base-T,
int_subtype_base,
equal-wf-T-base,
empty-bag-union,
subtype_base_sq,
bag-rep_wf,
empty-bag_wf,
list-subtype-bag,
member-bag-rep,
bag-member_wf,
squash_wf,
true_wf,
iff_weakening_equal
Latex:
\mforall{}[T:Type]. \mforall{}[bbs:bag(bag(T))]. \mforall{}bs:bag(T). (bs \mdownarrow{}\mmember{} bbs {}\mRightarrow{} (bs = \{\})) supposing bag-union(bbs) = \{\}
Date html generated:
2015_07_23-AM-11_25_32
Last ObjectModification:
2015_02_04-PM-04_46_31
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