Nuprl Lemma : run-initialization-property
∀[M:Type ⟶ Type]
∀[n2m:ℕ ⟶ pMsg(P.M[P])]. ∀[l2m:Id ⟶ pMsg(P.M[P])]. ∀[S0:System(P.M[P])]. ∀[env:pEnvType(P.M[P])].
∀[e:runEvents(pRun(S0;env;n2m;l2m))]. fst(fst(run-info(pRun(S0;env;n2m;l2m);e))) < run-event-step(e)
supposing run-initialization(pRun(S0;env;n2m;l2m);snd(S0))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
run-initialization: run-initialization(r;G),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
let: let,
System: System(P.M[P]),
pi2: snd(t),
implies: P ⇒ Q,
pi1: fst(t),
nat: ℕ,
prop: ℙ,
ldag: LabeledDAG(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
run-initialization: run-initialization(r;G),
lg-all: ∀x∈G.P[x],
runEvents: runEvents(r),
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
is-run-event: is-run-event(r;t;x),
run-event-step: run-event-step(e),
top: Top,
decidable: Dec(P),
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
and: P ∧ Q,
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
isl: isl(x),
outl: outl(x),
band: p ∧b q,
assert: ↑b,
Id: Id,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
pInTransit: pInTransit(P.M[P]),
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[l2m:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[S0:System(P.M[P])].
\mforall{}[env:pEnvType(P.M[P])].
\mforall{}[e:runEvents(pRun(S0;env;n2m;l2m))]
fst(fst(run-info(pRun(S0;env;n2m;l2m);e))) < run-event-step(e)
supposing run-initialization(pRun(S0;env;n2m;l2m);snd(S0))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_51_25
Last ObjectModification:
2016_01_18-AM-00_13_24
Theory : process-model
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