Nuprl Lemma : mapfilter-class-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[P:A ─→ 𝔹]. ∀[f:A ─→ B]. ∀[X:EClass(A)]. ∀[e:E].
(f[v] where v from X such that P[v])(e) ~ f[X(e)] supposing ↑e ∈b (f[v] where v from X such that P[v])
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
bag_size_single_lemma,
bag_only_single_lemma,
true_wf,
bag_size_empty_lemma,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
assert_wf,
in-eclass_wf,
mapfilter-class_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
bag-only_wf2,
decidable__lt,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
single-valued-bag-if-le1,
le_weakening
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(f[v] where v from X such that P[v])(e) \msim{} f[X(e)]
supposing \muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v])
Date html generated:
2015_07_17-PM-01_07_37
Last ObjectModification:
2015_01_27-PM-10_34_32
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