### Nuprl Lemma : bag-restrict-append

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[b,c:bag(T)].  ((b + c|x) ~ (b|x) + (c|x))`

Proof

Definitions occuring in Statement :  bag-restrict: `(b|x)` bag-append: `as + bs` bag: `bag(T)` deq: `EqDecider(T)` uall: `∀[x:A]. B[x]` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` bag-restrict: `(b|x)` so_lambda: `λ2x.t[x]` top: `Top` so_apply: `x[s]`
Lemmas referenced :  bag-filter-append bag_wf deq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin isect_memberEquality voidElimination voidEquality hypothesis sqequalAxiom hypothesisEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[x:T].  \mforall{}[b,c:bag(T)].    ((b  +  c|x)  \msim{}  (b|x)  +  (c|x))

Date html generated: 2016_05_15-PM-08_10_17
Last ObjectModification: 2015_12_27-PM-04_12_10

Theory : bags_2

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