Nuprl Lemma : es-is-filter-image
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[f:A ─→ bag(B)]. ∀[X:EClass(A)]. ∀[e:E].
uiff(↑e ∈b f[X];(↑e ∈b X) ∧ (#(f X(e)) = 1 ∈ ℤ))
Proof
Definitions occuring in Statement :
es-filter-image: f[X],
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Lemmas :
is-filter-image-sq,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
in-eclass_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
bag-size_wf,
eclass-val_wf,
assert_wf,
eq_int_wf,
assert_witness,
true_wf,
equal-wf-T-base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
event-ordering+_wf,
es-filter-image_wf,
subtype_rel_dep_function,
bag_wf,
subtype_rel_bag,
nat_wf,
eclass_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} f[X];(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\#(f X(e)) = 1))
Date html generated:
2015_07_17-PM-01_06_30
Last ObjectModification:
2015_01_27-PM-10_35_45
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