### Nuprl Lemma : bag-member-evidence

`∀[T:Type]. ∀[b:bag(T)]. ∀[x:T].  Ax ∈ x ↓∈ b supposing x ↓∈ b`

Proof

Definitions occuring in Statement :  bag-member: `x ↓∈ bs` bag: `bag(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type` axiom: `Ax`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` bag-member: `x ↓∈ bs` squash: `↓T` prop: `ℙ`
Lemmas referenced :  bag_wf bag-member_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution imageElimination hypothesis imageMemberEquality hypothesisEquality thin baseClosed axiomEquality equalityTransitivity equalitySymmetry lemma_by_obid isectElimination isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[b:bag(T)].  \mforall{}[x:T].    Ax  \mmember{}  x  \mdownarrow{}\mmember{}  b  supposing  x  \mdownarrow{}\mmember{}  b

Date html generated: 2016_05_15-PM-02_39_40
Last ObjectModification: 2016_01_16-AM-08_48_06

Theory : bags

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