{ 
[M:Type 
Type]
r:pRunType(P.M[P])
e1,e2:runEvents(r). Dec(e1 run-lt(r) e2)
supposing e:runEvents(r)
((fst(fst(run-info(r;e)))) < run-event-step(e)) }
{ Proof }
Definitions occuring in Statement :
run-lt: run-lt(r),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRunType: pRunType(T.M[T]),
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
pi1: fst(t),
all: x:A. B[x],
less_than: a < b,
function: x:A B[x],
universe: Type
Definitions :
list: type List,
rel_finite: rel_finite(T;R),
so_lambda: 
x y.t[x; y],
strongwellfounded: SWellFounded(R[x; y]),
void: Void,
real: 
,
grp_car: |g|,
nat: 
,
run-event-step: run-event-step(e),
subtype: S 
T,
pMsg: pMsg(P.M[P]),
Id: Id,
run-info: run-info(r;e),
top: Top,
int: 
,
pi1: fst(t),
strong-subtype: strong-subtype(A;B),
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
ge: i 
j ,
uiff: uiff(P;Q),
subtype_rel: A r B,
prop: 
,
false: False,
not: 
A,
and: P 
Q,
iff: P 
Q,
le: A 
B,
assert: 
b,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c B,
l_member: (x 
l),
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
llex: llex(A;a,b.<[a; b]),
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
rel_exp: R^n,
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,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
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,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-le: e loc e' ,
es-causle: e c e',
rel_plus: R
,
rel_star: R^*,
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-p-local-pred: es-p-local-pred(es;P),
es-p-le-pred: es-p-le-pred(es;P),
es-fset-loc: i locs(s),
product: x:A 
B[x],
exists: x:A. B[x],
es-p-immediate-pred: es-p-immediate-pred(es;P),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
implies: P Q,
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),
run-pred: run-pred(r),
run-lt: run-lt(r),
infix_ap: x f y,
apply: f a,
so_apply: x[s],
uall: [x:A]. B[x],
universe: Type,
uimplies: b supposing a,
isect: 
x:A. B[x],
decidable: Dec(P),
or: P 
Q,
union: left + right,
lambda: x.A[x],
so_lambda: x.t[x],
less_than: a < b,
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
equal: s = t,
member: t T,
axiom: Ax,
function: x:A B[x],
all: x:A. B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
Unfold: Error :Unfold
Lemmas :
run-pred_wf,
decidable__equal_runEvents,
decidable_wf,
runEvents_wf,
decidable__rel_plus,
pRunType_wf,
pMsg_wf,
member_wf,
top_wf,
Id_wf,
nat_wf,
run-event-step_wf,
run-info_wf,
pi1_wf_top,
run-lt_wf,
not_wf,
strongwellfounded_wf,
well-founded-run-pred,
rel_finite_wf,
l_member_wf,
finite-run-pred,
decidable__run-pred
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}r:pRunType(P.M[P])
\mforall{}e1,e2:runEvents(r). Dec(e1 run-lt(r) e2)
supposing \mforall{}e:runEvents(r). ((fst(fst(run-info(r;e)))) < run-event-step(e))
Date html generated:
2011_08_16-PM-07_05_25
Last ObjectModification:
2011_06_18-AM-11_18_29
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