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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
run-event-interval: run-event-interval(r;e1;e2),
let: let,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
uimplies: b supposing a,
implies: P ⇒ Q,
cand: A c∧ B,
squash: ↓T,
guard: {T},
sq_stable: SqStable(P),
decidable: Dec(P),
or: P ∨ Q,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
le: A ≤ B,
less_than: a < b,
pi1: fst(t),
pi2: snd(t),
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
runEvents: runEvents(r),
is-run-event: is-run-event(r;t;x),
rev_implies: P ⇐ Q,
Id: Id,
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
uiff: uiff(P;Q)
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:
2016_05_17-AM-10_43_51
Last ObjectModification:
2016_01_18-AM-00_21_11
Theory : process-model
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