Nuprl Lemma : mapfilter-reverse
∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[f:Top]. ∀[L:T List]. (mapfilter(f;P;rev(L)) ~ rev(mapfilter(f;P;L)))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
reverse: rev(as),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
mapfilter: mapfilter(f;P;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
filter-reverse,
map-reverse,
filter_wf_top,
subtype_rel_dep_function,
bool_wf,
l_member_wf,
subtype_rel_self,
set_wf,
list_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
lambdaFormation,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:Top]. \mforall{}[L:T List]. (mapfilter(f;P;rev(L)) \msim{} rev(mapfilter(f;P;L)))
Date html generated:
2016_05_14-PM-03_10_54
Last ObjectModification:
2015_12_26-PM-01_49_14
Theory : list_1
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