### Nuprl Lemma : bag-member-size

`∀[T:Type]. ∀[bs:bag(T)]. ∀[x:T].  0 < #(bs) supposing x ↓∈ bs`

Proof

Definitions occuring in Statement :  bag-member: `x ↓∈ bs` bag-size: `#(bs)` bag: `bag(T)` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` exists: `∃x:A. B[x]` prop: `ℙ` squash: `↓T` subtype_rel: `A ⊆r B` nat: `ℕ`
Lemmas referenced :  bag_wf nat_wf bag-size_wf member-less_than bag-member_wf bag-size-bag-member
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality hypothesis productElimination independent_functionElimination dependent_pairFormation sqequalRule imageMemberEquality baseClosed isect_memberEquality natural_numberEquality applyEquality lambdaEquality setElimination rename independent_isectElimination equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[bs:bag(T)].  \mforall{}[x:T].    0  <  \#(bs)  supposing  x  \mdownarrow{}\mmember{}  bs

Date html generated: 2016_05_15-PM-02_40_30
Last ObjectModification: 2016_01_16-AM-08_47_22

Theory : bags

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