Nuprl Lemma : member-run-event-interval
∀[M:Type ─→ Type]
∀r:pRunType(P.M[P]). ∀e1,e2,e:runEvents(r).
((e ∈ run-event-interval(r;e1;e2))
⇐⇒ (run-event-loc(e) = run-event-loc(e1) ∈ Id)
∧ (run-event-step(e1) ≤ run-event-step(e))
∧ (run-event-step(e) ≤ run-event-step(e2)))
Proof
Definitions occuring in Statement :
run-event-interval: run-event-interval(r;e1;e2),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
Id: Id,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
member-mapfilter,
le_wf,
run-event-step_wf,
nat_wf,
less_than_wf,
from-upto_wf,
l_member_wf,
set_wf,
is-run-event_wf,
subtype_rel_sets,
zero-le-nat,
run-event-loc_wf,
assert_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
mapfilter_wf,
iff_wf,
exists_wf,
Id_wf,
runEvents_wf,
pRunType_wf,
set_subtype_base,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
sq_stable__le,
add_functionality_wrt_le,
le-add-cancel,
less-iff-le,
add-associates,
zero-add,
le-add-cancel2,
decidable__lt,
member-from-upto,
sq_stable__assert
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}r:pRunType(P.M[P]). \mforall{}e1,e2,e:runEvents(r).
((e \mmember{} run-event-interval(r;e1;e2))
\mLeftarrow{}{}\mRightarrow{} (run-event-loc(e) = run-event-loc(e1))
\mwedge{} (run-event-step(e1) \mleq{} run-event-step(e))
\mwedge{} (run-event-step(e) \mleq{} run-event-step(e2)))
Date html generated:
2015_07_23-AM-11_11_30
Last ObjectModification:
2015_01_29-AM-00_12_14
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