Nuprl Lemma : filter-singleton
∀[x,P:Top].  (filter(P;[x]) ~ if P x then [x] else [] fi )
Proof
Definitions occuring in Statement : 
filter: filter(P;l)
, 
cons: [a / b]
, 
nil: []
, 
ifthenelse: if b then t else f fi 
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
apply: f a
, 
sqequal: s ~ t
Definitions unfolded in proof : 
filter: filter(P;l)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
top: Top
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
reduce_cons_lemma, 
reduce_nil_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, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
isectElimination, 
hypothesisEquality, 
because_Cache
Latex:
\mforall{}[x,P:Top].    (filter(P;[x])  \msim{}  if  P  x  then  [x]  else  []  fi  )
Date html generated:
2016_05_14-PM-02_57_45
Last ObjectModification:
2015_12_26-PM-02_30_06
Theory : list_1
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