Nuprl Lemma : bl-exists-map
∀[f,L,P:Top]. ((∃x∈map(f;L).P[x])_b ~ (∃x∈L.P[f x])_b)
Proof
Definitions occuring in Statement :
bl-exists: (∃x∈L.P[x])_b,
map: map(f;as),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bl-exists: (∃x∈L.P[x])_b,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2]
Lemmas referenced :
reduce-map,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[f,L,P:Top]. ((\mexists{}x\mmember{}map(f;L).P[x])\_b \msim{} (\mexists{}x\mmember{}L.P[f x])\_b)
Date html generated:
2016_05_14-PM-02_11_59
Last ObjectModification:
2015_12_26-PM-05_02_53
Theory : list_1
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