Nuprl Lemma : pRun-intransit-invariant
∀[M:Type ─→ Type]
∀n2m:ℕ ─→ pMsg(P.M[P]). ∀l2m:Id ─→ pMsg(P.M[P]). ∀Cs0:component(P.M[P]) List. ∀G0:LabeledDAG(pInTransit(P.M[P])).
∀env:pEnvType(P.M[P]). ∀t:ℕ.
let r = pRun(<Cs0, G0>;env;n2m;l2m) in
let info,Cs,G = r t in
∀x∈G.let ev = fst(x) in
((fst(ev)) ≤ t) ∨ (∃m:ℕlg-size(G0). (ev = (fst(lg-label(G0;m))) ∈ (ℤ × Id)))
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pInTransit: pInTransit(P.M[P]),
component: component(P.M[P]),
pMsg: pMsg(P.M[P]),
lg-all: ∀x∈G.P[x],
ldag: LabeledDAG(T),
lg-label: lg-label(g;x),
lg-size: lg-size(g),
Id: Id,
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
int_seg: {i..j-},
nat: ℕ,
let: let,
spreadn: spread3,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
nat_wf,
or_wf,
le_wf,
exists_wf,
int_seg_wf,
lg-size_wf,
equal_wf,
lg-label_wf,
pRun-System-invariant,
lg-all_wf,
System_wf,
pEnvType_wf,
ldag_wf,
pInTransit_wf,
list_wf,
component_wf,
Id_wf,
pMsg_wf,
strong-type-continuous_wf,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
less_than_wf,
pRun_wf2,
subtype_rel_dep_function,
unit_wf2,
top_wf,
int_seg_subtype-nat,
subtype_rel_self,
lg-is-source_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
lt_int_wf,
lelt_wf,
lg-remove_wf_dag,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
lg-all-remove,
decidable__le,
not-le-2,
add-swap,
list_induction,
all_wf,
list_accum_wf,
deliver-msg-to-comp_wf,
list_accum_cons_lemma,
subtype_rel_product,
subtype_top,
eq_id_wf,
assert-eq-id,
Process-apply_wf,
Process_wf,
pExt_wf,
lg-all-append,
add-cause_wf,
lg-all-map,
pCom_wf,
add-mul-special,
zero-mul,
eq_atom_wf,
com-kind_wf,
assert_of_eq_atom,
trivial-int-eq1,
sq_stable__le,
comm-msg_wf,
nil_wf,
neg_assert_of_eq_atom,
pRun_wf,
fulpRunType_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}Cs0:component(P.M[P]) List.
\mforall{}G0:LabeledDAG(pInTransit(P.M[P])). \mforall{}env:pEnvType(P.M[P]). \mforall{}t:\mBbbN{}.
let r = pRun(<Cs0, G0>env;n2m;l2m) in
let info,Cs,G = r t in
\mforall{}x\mmember{}G.let ev = fst(x) in
((fst(ev)) \mleq{} t) \mvee{} (\mexists{}m:\mBbbN{}lg-size(G0). (ev = (fst(lg-label(G0;m)))))
supposing Continuous+(P.M[P])
Date html generated:
2015_07_23-AM-11_14_19
Last ObjectModification:
2015_01_29-AM-00_12_02
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