Nuprl Lemma : filter_nil_lemma
∀P:Top. (filter(P;[]) ~ [])
Proof
Definitions occuring in Statement : 
filter: filter(P;l)
, 
nil: []
, 
top: Top
, 
all: ∀x:A. B[x]
, 
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_nil_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{}P:Top.  (filter(P;[])  \msim{}  [])
Date html generated:
2016_05_14-AM-06_48_59
Last ObjectModification:
2015_12_26-PM-00_24_07
Theory : list_0
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