Nuprl Lemma : filter_cons_lemma
∀t,h,f:Top. (filter(f;[h / t]) ~ if f h then [h / filter(f;t)] else filter(f;t) fi )
Proof
Definitions occuring in Statement :
filter: filter(P;l),
cons: [a / b],
ifthenelse: if b then t else f fi ,
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
filter: filter(P;l),
top: Top
Lemmas referenced :
top_wf,
reduce_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}t,h,f:Top. (filter(f;[h / t]) \msim{} if f h then [h / filter(f;t)] else filter(f;t) fi )
Date html generated:
2016_05_14-AM-06_49_04
Last ObjectModification:
2015_12_26-PM-00_24_03
Theory : list_0
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