Nuprl Lemma : es-interface-local-pred-bool
∀[Info:Type]
∀P:es:EO+(Info) ─→ E ─→ 𝔹
∃X:EClass({e':E| (e' <loc e) ∧ (↑(P es e')) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P es e''))))} )
∀es:EO+(Info). ∀e:E.
((↑e ∈b X ⇐⇒ ∃a:E. ((a <loc e) ∧ (↑(P es a)))) ∧ es-p-local-pred(es;λe.(↑(P es e))) e X(e) supposing ↑e ∈b X)
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-local-pred-property,
local-pred-class_wf,
subtype_rel_dep_function,
es-E_wf,
event-ordering+_subtype,
bool_wf,
es-locl_wf,
subtype_rel_self,
set_wf,
es-local-pred_wf,
or_wf,
sq_exists_wf,
assert_wf,
all_wf,
not_wf,
bag_size_single_lemma,
bag_only_single_lemma,
iff_wf,
true_wf,
exists_wf,
bag_size_empty_lemma,
false_wf,
assert_witness,
equal_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
es-p-local-pred_wf,
eclass-val_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]
\mforall{}P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}
\mexists{}X:EClass(\{e':E|
(e' <loc e)
\mwedge{} (\muparrow{}(P es e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P es e''))))\} )
\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. ((a <loc e) \mwedge{} (\muparrow{}(P es a))))
\mwedge{} es-p-local-pred(es;\mlambda{}e.(\muparrow{}(P es e))) e X(e) supposing \muparrow{}e \mmember{}\msubb{} X)
Date html generated:
2015_07_20-PM-04_07_13
Last ObjectModification:
2015_01_27-PM-09_51_16
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