Nuprl Lemma : mapfilter-singleton
∀[x,P,f:Top]. (mapfilter(f;P;[x]) ~ map(f;if P x then [x] else [] fi ))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
map: map(f;as),
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 :
mapfilter: mapfilter(f;P;L),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
filter_cons_lemma,
filter_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,f:Top]. (mapfilter(f;P;[x]) \msim{} map(f;if P x then [x] else [] fi ))
Date html generated:
2016_05_14-PM-01_28_40
Last ObjectModification:
2015_12_26-PM-05_21_40
Theory : list_1
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