Nuprl Lemma : reduce-fast-mapfilter2
∀[L,z,k,c,d,f,p:Top].
(reduce(λx,a. if c[x;a]=d[x;a] then z else a;k;fast-mapfilter(p;f;L)) ~ reduce(λx,a. if p x
then if c[f x;a]=d[f x;a]
then z
else a
else a
fi ;k;L))
Proof
Definitions occuring in Statement :
fast-mapfilter: fast-mapfilter(p;f;L),
reduce: reduce(f;k;as),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
int_eq: if a=b then c else d,
apply: f a,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
so_apply: x[s1;s2],
fast-mapfilter: fast-mapfilter(p;f;L),
so_apply: x[s],
uall: ∀[x:A]. B[x],
member: t ∈ T,
reduce: reduce(f;k;as),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
strict1: strict1(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
list_ind: list_ind,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top
Lemmas referenced :
sqequal-list_ind,
has-value_wf_base,
istype-base,
is-exception_wf,
istype-universe,
reduce-ifthenelse,
istype-void,
reduce_cons_lemma,
sqle_wf_base,
reduce_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation_alt,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
universeIsType,
callbyvalueExceptionCases,
inlFormation_alt,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inrFormation_alt,
isect_memberEquality_alt,
voidElimination,
dependent_functionElimination,
divergentSqle,
sqleRule,
sqleReflexivity,
instantiate,
inhabitedIsType,
because_Cache,
axiomSqEquality,
isectIsTypeImplies
Latex:
\mforall{}[L,z,k,c,d,f,p:Top].
(reduce(\mlambda{}x,a. if c[x;a]=d[x;a] then z else a;k;fast-mapfilter(p;f;L))
\msim{} reduce(\mlambda{}x,a. if p x then if c[f x;a]=d[f x;a] then z else a else a fi ;k;L))
Date html generated:
2019_10_15-AM-11_09_36
Last ObjectModification:
2018_10_16-AM-09_34_18
Theory : general
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