Nuprl Lemma : bag-remove-append
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. ∀[x:T]. (as + bs - x ~ as - x + bs - x)
Proof
Definitions occuring in Statement :
bag-remove: bs - 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-remove: bs - 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{}[as,bs:bag(T)]. \mforall{}[x:T]. (as + bs - x \msim{} as - x + bs - x)
Date html generated:
2016_05_15-PM-08_03_19
Last ObjectModification:
2015_12_27-PM-04_15_13
Theory : bags_2
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