Nuprl Lemma : is-mapfilter-class
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[P:A ─→ 𝔹]. ∀[f:Top]. ∀[X:EClass(A)]. ∀[e:E].
uiff(↑e ∈b (f[v] where v from X such that P[v]);(↑e ∈b X) ∧ (↑P[X(e)]))
Proof
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
bag_size_single_lemma,
true_wf,
bag_size_empty_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
assert_witness,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
eclass-val_wf,
assert_wf,
mapfilter-class_wf,
eclass_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:Top]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v]);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[X(e)]))
Date html generated:
2015_07_17-PM-01_07_28
Last ObjectModification:
2015_01_27-PM-10_34_45
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