Nuprl Lemma : assert-is-filter-image
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(Top)]. ∀[e:E].
(↑e ∈b f[X] ~ if e ∈b X then ↑(#(f X(e)) =z 1) else False fi )
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,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
false: False,
apply: f a,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs)
Lemmas :
is-filter-image-sq,
in-eclass_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
event-ordering+_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Top]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\muparrow{}e \mmember{}\msubb{} f[X] \msim{} if e \mmember{}\msubb{} X then \muparrow{}(\#(f X(e)) =\msubz{} 1) else False fi )
Date html generated:
2015_07_17-PM-01_06_22
Last ObjectModification:
2015_01_27-PM-10_35_21
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