Nuprl Lemma : filter-filter2
∀[P1,P2,L:Top]. (filter(P2;filter(P1;L)) ~ filter(λt.((P1 t) ∧b (P2 t));L))
Proof
Definitions occuring in Statement :
filter: filter(P;l),
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
filter-filter,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[P1,P2,L:Top]. (filter(P2;filter(P1;L)) \msim{} filter(\mlambda{}t.((P1 t) \mwedge{}\msubb{} (P2 t));L))
Date html generated:
2016_05_14-PM-02_57_32
Last ObjectModification:
2015_12_26-PM-02_29_47
Theory : list_1
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