Nuprl Lemma : mapfilter-cons
∀[u,v,P,f:Top]. (mapfilter(f;P;[u / v]) ~ mapfilter(f;P;[u]) @ mapfilter(f;P;v))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
append: as @ bs,
cons: [a / b],
nil: [],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_ind_cons_lemma,
list_ind_nil_lemma,
mapfilter-append,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[u,v,P,f:Top]. (mapfilter(f;P;[u / v]) \msim{} mapfilter(f;P;[u]) @ mapfilter(f;P;v))
Date html generated:
2016_05_14-PM-01_28_47
Last ObjectModification:
2015_12_26-PM-05_21_44
Theory : list_1
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