Nuprl Lemma : bag-restrict-split
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[b:bag(T)]. (b = ((b|x) + (b|¬x)) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-co-restrict: (b|¬x),
bag-restrict: (b|x),
bag-append: as + bs,
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
deq: EqDecider(T),
so_apply: x[s],
bag-co-restrict: (b|¬x),
bag-restrict: (b|x)
Lemmas referenced :
bag-filter-split,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
setElimination,
rename,
hypothesisEquality,
equalitySymmetry,
hypothesis,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[b:bag(T)]. (b = ((b|x) + (b|\mneg{}x)))
Date html generated:
2016_05_15-PM-08_10_53
Last ObjectModification:
2015_12_27-PM-04_11_24
Theory : bags_2
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