Nuprl Lemma : bag_filter_cons_lemma
∀p,v,u:Top. ([x∈u.v|p[x]] ~ if p[u] then u.[x∈v|p[x]] else [x∈v|p[x]] fi )
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
cons-bag: x.b,
ifthenelse: if b then t else f fi ,
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
cons-bag: x.b,
bag-filter: [x∈b|p[x]],
all: ∀x:A. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
filter_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation
Latex:
\mforall{}p,v,u:Top. ([x\mmember{}u.v|p[x]] \msim{} if p[u] then u.[x\mmember{}v|p[x]] else [x\mmember{}v|p[x]] fi )
Date html generated:
2016_05_15-PM-02_23_27
Last ObjectModification:
2015_12_27-AM-09_54_06
Theory : bags
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