Nuprl Lemma : fast-mapfilter_wf
∀[A,B:Type]. ∀[L:A List]. ∀[p:{x:A| (x ∈ L)} ⟶ 𝔹]. ∀[f:{x:A| (x ∈ L) ∧ (↑p[x])} ⟶ B].
(fast-mapfilter(p;f;L) ∈ B List)
Proof
Definitions occuring in Statement :
fast-mapfilter: fast-mapfilter(p;f;L),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fast-mapfilter: fast-mapfilter(p;f;L),
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff
Lemmas referenced :
reduce_wf,
l_member_wf,
list_wf,
bool_wf,
eqtt_to_assert,
cons_wf,
assert_wf,
equal_wf,
nil_wf,
list-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
functionExtensionality,
dependent_functionElimination,
dependent_set_memberEquality,
unionElimination,
equalityElimination,
sqequalRule,
productElimination,
independent_isectElimination,
because_Cache,
productEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
functionEquality,
universeEquality,
isect_memberFormation,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:A List]. \mforall{}[p:\{x:A| (x \mmember{} L)\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\{x:A| (x \mmember{} L) \mwedge{} (\muparrow{}p[x])\} {}\mrightarrow{} B].
(fast-mapfilter(p;f;L) \mmember{} B List)
Date html generated:
2018_05_21-PM-06_52_11
Last ObjectModification:
2017_07_26-PM-04_58_17
Theory : general
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