Nuprl Lemma : es-local-pred_wf2
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[P:{e':E| (e' <loc e)} ─→ 𝔹].
(last(P) e ∈ (∃e':{E| ((e' <loc e) ∧ (↑(P e')) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P e'')))))})
∨ (¬(∃e':{E| ((e' <loc e) ∧ (↑(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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-locl_wf,
bool_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-first_wf2,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
it_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
sq_exists_wf,
all_wf,
es-pred-locl,
es-pred_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-locl-iff,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
squash_wf,
true_wf,
event_ordering_wf,
iff_weakening_equal,
es-le_weakening,
es-causl_weakening,
subtype_rel_dep_function,
subtype_rel_sets,
subtype_rel_self,
set_wf,
subtype_rel_union,
sq_exists_subtype_rel,
subtype_rel_not,
assert_functionality_wrt_uiff,
es-locl_transitivity1,
not_assert_elim
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[P:\{e':E| (e' <loc e)\} {}\mrightarrow{} \mBbbB{}].
(last(P) e \mmember{} (\mexists{}e':\{E| ((e' <loc e)
\mwedge{} (\muparrow{}(P e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P e'')))))\})
\mvee{} (\mneg{}(\mexists{}e':\{E| ((e' <loc e) \mwedge{} (\muparrow{}(P e')))\})))
Date html generated:
2015_07_20-PM-03_57_03
Last ObjectModification:
2015_02_04-PM-05_30_06
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