Nuprl Lemma : bag-co-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-co-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-co-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|\mneg{}x) \msim{} (b|\mneg{}x) + (c|\mneg{}x))
Date html generated:
2016_05_15-PM-08_10_36
Last ObjectModification:
2015_12_27-PM-04_12_02
Theory : bags_2
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