{ 
[M:Type 
Type]
n2m:
pMsg(P.M[P]). l2m:Id pMsg(P.M[P]). S:System(P.M[P]).
env:pEnvType(P.M[P]). x:Id. n,m:
.
(run-event-state-when(pRun(S;env;n2m;l2m);<n, x>)
run-event-state-when(pRun(S;env;n2m;l2m);<m, x>)) supposing
((a:runEvents(pRun(S;env;n2m;l2m))
((n 
run-event-step(a)) 
(run-event-step(a) < m))
supposing run-event-loc(a) = x) and
(n m))
supposing Continuous+(P.M[P]) }
{ Proof }
Definitions occuring in Statement :
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
run-event-state-when: run-event-state-when(r;e),
runEvents: runEvents(r),
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Process: Process(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
le: A B,
all: x:A. B[x],
not: A,
and: P Q,
less_than: a < b,
function: x:A B[x],
pair: <a, b>,
universe: Type,
equal: s = t,
l_contains: A B
Definitions :
void: Void,
fpf-dom: x 
dom(f),
false: False,
guard: {T},
pInTransit: pInTransit(P.M[P]),
unit: Unit,
int: 
,
subtype: S T,
tag-by: z
T,
rev_implies: P 
Q,
or: P 
Q,
iff: P 
Q,
labeled-graph: LabeledGraph(T),
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
union: left + right,
top: Top,
true: True,
fpf: a:A fp-> B[a],
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
fpf-cap: f(x)?z,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
uiff: uiff(P;Q),
ldag: LabeledDAG(T),
list: type List,
atom: Atom$n,
pEnvType: pEnvType(T.M[T]),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
apply: f a,
lambda: 
x.A[x],
subtype_rel: A r B,
ext-eq: A 
B,
prop: 
,
strong-type-continuous: Continuous+(T.F[T]),
set: {x:A| B[x]} ,
exists: 
x:A. B[x],
l_member: (x l),
l_all: (xL.P[x]),
universe: Type,
uall: [x:A]. B[x],
function: x:A B[x],
uimplies: b supposing a,
isect: x:A. B[x],
product: x:A B[x],
so_lambda: 
x.t[x],
fulpRunType: fulpRunType(T.M[T]),
add: n + m,
pair: <a, b>,
pRun: pRun(S0;env;nat2msg;loc2msg),
run-event-state-when: run-event-state-when(r;e),
so_apply: x[s],
Process: Process(P.M[P]),
l_contains: A B,
run-event-step: run-event-step(e),
less_than: a < b,
le: A B,
and: P Q,
not: A,
run-event-loc: run-event-loc(e),
Id: Id,
equal: s = t,
implies: P Q,
runEvents: runEvents(r),
all: x:A. B[x],
nat_plus: ,
nat: ,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
pRunType: pRunType(T.M[T]),
member: t T,
AssertBY: Error :AssertBY,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
subtract: n - m,
grp_car: |g|,
int_nzero: 
,
real: 
,
limited-type: LimitedType,
natural_number: $n,
minus: -n,
sq_type: SQType(T),
sqequal: s ~ t,
Subst': Error :Subst',
tactic: Error :tactic,
length: ||as||,
rationals: 
,
ParallelOp: Error :ParallelOp,
BHyp: Error :BHyp,
pi1: fst(t),
eq_id: a = b,
pi2: snd(t),
mapfilter: mapfilter(f;P;L),
deliver-msg: deliver-msg(t;m;x;Cs;L),
spread: spread def,
assert: 
b,
component: component(P.M[P]),
is-dag: is-dag(g),
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
map: map(f;as),
in-eclass: e 
X,
eq_knd: a = b,
filter: filter(P;l),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
corec: corec(T.F[T]),
process: process(P.M[P];P.E[P]),
bool: 
,
nil: [],
append: as @ bs,
intensional-universe: IType,
pExt: pExt(P.M[P]),
so_lambda: x y.t[x; y],
listp: A List,
combination: Combination(n;T),
Com: Com(P.M[P]),
add-cause: add-cause(ev;ext),
lg-append: lg-append(g1;g2),
Process-apply: Process-apply(P;m),
list_accum: list_accum(x,a.f[x; a];y;l),
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
eq_lnk: a = b,
es-eq-E: e = e',
bimplies: p q,
band: p q,
bor: p q,
bnot: b,
deliver-msg-to-comp: deliver-msg-to-comp(t;m;x;S;C),
cand: A c B,
atom: Atom,
int_seg: {i..j},
quotient: x,y:A//B[x; y],
divides: b | a,
assoced: a ~ b,
set_car: |p|,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
rng_car: |r|,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (xL. P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
string: Error :string,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
consensus-rcv: consensus-rcv(V;A),
infix_ap: x f y,
es-E: E,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
lg-edge: lg-edge(g;a;b),
decidable: Dec(P),
es-locl: (e <loc e'),
es-causl: (e < e'),
last: last(L),
remove-repeats: remove-repeats(eq;L),
select: l[i],
primrec: primrec(n;b;c),
it: 
,
is-run-event: is-run-event(r;t;x),
decision: Decision,
pCom: pCom(P.M[P]),
lg-size: lg-size(g),
inr: inr x ,
lg-remove: lg-remove(g;n),
comm-create: comm-create(c),
create-component: create-component(t;P;x;Cs;L),
comm-msg: comm-msg(c),
inl: inl x ,
token: "$token",
com-kind: com-kind(c),
let: let,
lg-label: lg-label(g;x),
eq_bool: p =b q,
lg-is-source: lg-is-source(g;i),
lelt: i j < k,
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
outl: outl(x),
spreadn: spread3,
isl: isl(x),
eq_atom: x =a y,
null: null(as),
set_blt: a < b,
grp_blt: a < b,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_int: (i =
j),
RepUR: Error :RepUR,
Try: Error :Try,
Repeat: Error :Repeat,
SplitOn: Error :SplitOn,
D: Error :D,
Complete: Error :Complete,
Unfold: Error :Unfold
Lemmas :
isl_wf,
bfalse_wf,
band_wf,
eq_int_wf,
assert_of_eq_int,
pRun_wf2,
int_seg_wf,
nat_plus_properties,
int_seg_properties,
lg-is-source_wf_dag,
lg-label_wf_dag,
lg-size_wf_dag,
bool_cases,
bool_subtype_base,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
lt_int_wf,
le_int_wf,
assert_elim,
assert_of_eq_atom,
com-kind_wf,
eq_atom_wf,
create-component_wf,
comm-create_wf,
lg-remove_wf_dag,
deliver-msg_wf,
comm-msg_wf,
mapfilter-contains,
pi1_wf,
atom2_subtype_base,
is-run-event_wf,
true_wf,
pi2_wf,
pExt_wf,
append_assoc_sq,
Com_wf,
primrec_wf,
isect_subtype_base,
member_singleton,
rev_implies_wf,
iff_wf,
or_functionality_wrt_iff,
member_append,
iff_transitivity,
l_member_subtype,
cons_member,
decidable__l_member,
bnot_wf,
assert-eq-id,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
iff_weakening_uiff,
eqtt_to_assert,
btrue_neq_bfalse,
eq_id_self,
btrue_wf,
not_assert_elim,
map_wf,
list-subtype,
deliver-msg-to-comp_wf,
list_accum_wf,
Process-apply_wf,
lg-append_wf_dag,
add-cause_wf,
bool_wf,
append_wf,
intensional-universe_wf,
append-nil,
pi1_wf_top,
mapfilter_wf,
uiff_inversion,
filter_wf,
ifthenelse_wf,
assert_wf,
eq_id_wf,
component_wf,
false_wf,
l_contains_transitivity,
subtype_base_sq,
int_subtype_base,
l_contains_weakening,
run-event-state-when_wf,
ge_wf,
nat_properties,
l_member_wf,
l_all_wf,
runEvents_wf,
nat_plus_wf,
run-event-step_wf,
run-event-loc_wf,
nat_ind_tp,
pRun_wf,
Id_wf,
not_wf,
le_wf,
l_contains_wf,
Process_wf,
System_wf,
pMsg_wf,
nat_wf,
strong-type-continuous_wf,
uall_wf,
pEnvType_wf,
pRunType_wf,
fulpRunType_wf,
subtype_rel_wf,
member_wf,
pInTransit_wf,
ldag_wf,
top_wf,
unit_wf,
subtype_rel_function,
subtype_rel_self,
subtype_rel_simple_product
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}n2m:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P]). \mforall{}l2m:Id {}\mrightarrow{} pMsg(P.M[P]). \mforall{}S:System(P.M[P]). \mforall{}env:pEnvType(P.M[P]). \mforall{}x:Id.
\mforall{}n,m:\mBbbN{}\msupplus{}.
(run-event-state-when(pRun(S;env;n2m;l2m);<n, x>) \msubseteq{} run-event-state-when(pRun(S;env;n2m;l2m);<m
, x
>)) supposing
((\mforall{}a:runEvents(pRun(S;env;n2m;l2m))
\mneg{}((n \mleq{} run-event-step(a)) \mwedge{} (run-event-step(a) < m)) supposing run-event-loc(a) = x) and
(n \mleq{} m))
supposing Continuous+(P.M[P])
Date html generated:
2011_08_16-PM-07_02_16
Last ObjectModification:
2011_06_18-AM-11_15_56
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