Nuprl Lemma : bag-mapfilter-null
∀P,f,bs:Top.  (null(bag-mapfilter(f;P;bs)) ~ null([x∈bs|P x]))
Proof
Definitions occuring in Statement : 
bag-mapfilter: bag-mapfilter(f;P;bs)
, 
bag-filter: [x∈b|p[x]]
, 
null: null(as)
, 
top: Top
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
sqequal: s ~ t
Definitions unfolded in proof : 
bag-mapfilter: bag-mapfilter(f;P;bs)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
top: Top
Lemmas referenced : 
bag-map-null, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis
Latex:
\mforall{}P,f,bs:Top.    (null(bag-mapfilter(f;P;bs))  \msim{}  null([x\mmember{}bs|P  x]))
Date html generated:
2016_05_15-PM-02_23_49
Last ObjectModification:
2015_12_27-AM-09_53_51
Theory : bags
Home
Index