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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