Nuprl Lemma : es-local-pred-property2
∀[Info:Type]
∀es:EO+(Info). ∀e:E. ∀P:{e':E| (e' <loc e)} ─→ 𝔹.
((↑can-apply(last(P);e) ⇐⇒ ∃a:E. ((a <loc e) ∧ (↑(P a))))
∧ (do-apply(last(P);e) <loc e)
∧ (↑(P do-apply(last(P);e)))
∧ (∀e'':E. ((e'' <loc e) ⇒ (do-apply(last(P);e) <loc e'') ⇒ (¬↑(P e''))))
supposing ↑can-apply(last(P);e))
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
event-ordering+: EO+(Info),
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,
function: x:A ─→ B[x],
universe: Type,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x)
Lemmas :
es-local-pred_wf2,
set_wf,
es-E_wf,
event-ordering+_subtype,
es-locl_wf,
bool_wf,
event-ordering+_wf,
or_wf,
sq_exists_wf,
assert_wf,
all_wf,
not_wf,
true_wf,
exists_wf,
assert_elim,
subtype_base_sq,
bool_subtype_base,
assert_witness,
false_wf,
equal_wf,
sq_stable_from_decidable,
decidable__es-locl
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}.
((\muparrow{}can-apply(last(P);e) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. ((a <loc e) \mwedge{} (\muparrow{}(P a))))
\mwedge{} (do-apply(last(P);e) <loc e)
\mwedge{} (\muparrow{}(P do-apply(last(P);e)))
\mwedge{} (\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (do-apply(last(P);e) <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}(P e''))))
supposing \muparrow{}can-apply(last(P);e))
Date html generated:
2015_07_20-PM-04_06_03
Last ObjectModification:
2015_01_27-PM-09_52_52
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