Nuprl Lemma : es-is-interface-filter
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[P:A ─→ 𝔹]. ∀[e:E].
uiff(↑e ∈b X|a.P[a];{(↑e ∈b X) ∧ (↑P[X(e)])})
Proof
Definitions occuring in Statement :
es-interface-filter: X|a.P[a],
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],
guard: {T},
so_apply: x[s],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_witness,
eclass-val_wf,
es-E_wf,
event-ordering+_subtype,
assert_wf,
bool_wf,
eclass_wf,
event-ordering+_wf,
bag_wf,
eq_int_wf,
bag-size_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
bag-size-one,
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_only_single_lemma,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bag_size_empty_lemma,
filter_cons_lemma,
filter_nil_lemma,
length_of_cons_lemma,
length_of_nil_lemma,
true_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} X|a.P[a];\{(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[X(e)])\})
Date html generated:
2015_07_20-PM-03_33_21
Last ObjectModification:
2015_01_27-PM-10_23_12
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