Nuprl Lemma : pRun-invariant1
∀[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]).
let r = pRun(S0;env;n2m;l2m) in
∀e:runEvents(r)
(fst(fst(run-info(r;e))) < run-event-step(e)
∨ (∃m:ℕlg-size(snd(S0)). ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))) ∈ (ℤ × Id))))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
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]),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
System: System(P.M[P]),
let: let,
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
runEvents: runEvents(r),
top: Top,
decidable: Dec(P),
or: P ∨ Q,
pi1: fst(t),
run-event-step: run-event-step(e),
not: ¬A,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
false: False,
prop: ℙ,
run-info: run-info(r;e),
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
is-run-event: is-run-event(r;t;x),
nat: ℕ,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
isl: isl(x),
outl: outl(x),
bfalse: ff,
band: p ∧b q,
assert: ↑b,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
le: A ≤ B,
less_than': less_than'(a;b),
ge: i ≥ j ,
int_upper: {i...},
spreadn: spread3,
satisfiable_int_formula: satisfiable_int_formula(fmla),
ldag: LabeledDAG(T),
lg-is-source: lg-is-source(g;i),
int_seg: {i..j-},
lelt: i ≤ j < k,
pInTransit: pInTransit(P.M[P]),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
fulpRunType: fulpRunType(T.M[T]),
lg-all: ∀x∈G.P[x],
Id: Id,
true: True
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]).
let r = pRun(S0;env;n2m;l2m) in
\mforall{}e:runEvents(r)
(fst(fst(run-info(r;e))) < run-event-step(e)
\mvee{} (\mexists{}m:\mBbbN{}lg-size(snd(S0)). ((fst(run-info(r;e))) = (fst(lg-label(snd(S0);m))))))
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_48_25
Last ObjectModification:
2016_01_18-AM-00_24_32
Theory : process-model
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