Nuprl Lemma : run_local_pred_maximal
∀M:Type ─→ Type. ∀r:pRunType(P.M[P]). ∀e,x:runEvents(r).
(run-event-step(x) < run-event-step(e)
⇒ run-event-step(run_local_pred(r;e)) < run-event-step(x)
⇒ (¬(run-event-loc(x) = run-event-loc(e) ∈ Id)))
Proof
Definitions occuring in Statement :
run_local_pred: run_local_pred(r;e),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
Id: Id,
less_than: a < b,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
equal_wf,
Id_wf,
run-event-loc_wf,
less_than_wf,
run-event-step_wf,
run_local_pred_wf,
nat_wf,
runEvents_wf,
pRunType_wf,
less_than_transitivity1,
run-local-pred_wf,
less_than_irreflexivity,
nat_properties,
ge_wf,
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,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_weakening,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
value-type-has-value,
int-value-type,
is-run-event_wf,
not-le-2,
not-equal-2,
le_wf,
int_subtype_base,
and_wf,
assert_elim,
equal-wf-T-base
Latex:
\mforall{}M:Type {}\mrightarrow{} Type. \mforall{}r:pRunType(P.M[P]). \mforall{}e,x:runEvents(r).
(run-event-step(x) < run-event-step(e)
{}\mRightarrow{} run-event-step(run\_local\_pred(r;e)) < run-event-step(x)
{}\mRightarrow{} (\mneg{}(run-event-loc(x) = run-event-loc(e))))
Date html generated:
2015_07_23-AM-11_15_16
Last ObjectModification:
2015_01_29-AM-00_06_54
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