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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
runEvents: runEvents(r),
run-event-step: run-event-step(e),
run_local_pred: run_local_pred(r;e),
pi2: snd(t),
pi1: fst(t),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
run-event-loc: run-event-loc(e),
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
run-local-pred: run-local-pred(r;i;t;t'),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
has-value: (a)↓,
nequal: a ≠ b ∈ T ,
true: True
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:
2016_05_17-AM-10_50_01
Last ObjectModification:
2016_01_18-AM-00_13_18
Theory : process-model
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