{ 
[M:Type 
Type]
S0:System(P.M[P]). r:pRunType(P.M[P]). e1,e2:runEvents(r).
(((run-event-local-pred(r;e2) = run-event-local-pred(r;e1))
(run-event-interval(r;e1;e2) = [e2]))
(
e:runEvents(r)
((run-event-step(e) < run-event-step(e2))
(run-event-step(e1) 
run-event-step(e))
((run-event-loc(e1) = run-event-loc(e))
(run-event-local-pred(r;e2) = (inl e )))
(run-event-interval(r;e1;e2)
= (run-event-interval(r;e1;e) @ [e2]))))) supposing
((run-event-step(e1) run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2))) }
{ Proof }
Definitions occuring in Statement :
run-event-local-pred: run-event-local-pred(r;e),
run-event-interval: run-event-interval(r;e1;e2),
run-event-step: run-event-step(e),
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
System: System(P.M[P]),
Id: Id,
append: as @ bs,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
or: P Q,
and: P Q,
unit: Unit,
less_than: a < b,
function: x:A B[x],
inl: inl x ,
union: left + right,
cons: [car / cdr],
nil: [],
list: type List,
universe: Type,
equal: s = t
Definitions :
limited-type: LimitedType,
strong-subtype: strong-subtype(A;B),
tl: tl(l),
hd: hd(l),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
ldag: LabeledDAG(T),
ge: i 
j ,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
exists: x:A. B[x],
unit: Unit,
list: type List,
product: x:A 
B[x],
and: P Q,
apply: f a,
so_apply: x[s],
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S T,
int: 
,
nat: 
,
run-event-step: run-event-step(e),
less_than: a < b,
lambda: 
x.A[x],
void: Void,
false: False,
implies: P 
Q,
not: 
A,
le: A B,
uall: [x:A]. B[x],
universe: Type,
all: x:A. B[x],
function: x:A B[x],
so_lambda: 
x.t[x],
prop: 
,
uimplies: b supposing a,
isect: 
x:A. B[x],
or: P Q,
union: left + right,
axiom: Ax,
Id: Id,
run-event-loc: run-event-loc(e),
runEvents: runEvents(r),
pRunType: pRunType(T.M[T]),
member: t 
T,
equal: s = t,
System: System(P.M[P]),
guard: {T},
atom: Atom,
sq_type: SQType(T),
atom: Atom$n,
bool: 
,
true: True,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
squash: 
T,
sq_stable: SqStable(P),
run-event-local-pred: run-event-local-pred(r;e),
run-event-interval: run-event-interval(r;e1;e2),
run-event-history: run-event-history(r;e),
let: let,
sqequal: s ~ t,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
is-run-event: is-run-event(r;t;x),
AssertBY: Error :AssertBY,
RepeatFor: Error :RepeatFor,
tactic: Error :tactic,
eq_bool: p =b q,
quotient: x,y:A//B[x; y],
has-value: has-value(a),
callbyvalue: callbyvalue,
bfalse: ff,
iff: P 
Q,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
bimplies: p q,
bor: p q,
lt_int: i <z j,
bnot: b,
btrue: tt,
listp: A List
,
combination: Combination(n;T),
map: map(f;as),
length: ||as||,
select: l[i],
l_all: (xL.P[x]),
filter: filter(P;l),
spread: spread def,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
lelt: i j < k,
pMsg: pMsg(P.M[P]),
rationals: 
,
l_member: (x l),
cand: A c B,
top: Top,
band: p q,
append: as @ bs,
inl: inl x ,
last: last(L),
inr: inr x ,
it: 
,
null: null(as),
Repeat: Error :Repeat,
RepUR: Error :RepUR,
Try: Error :Try,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
nil: [],
cons: [car / cdr],
natural_number: $n,
add: n + m,
from-upto: [n, m),
pair: <a, b>,
mapfilter: mapfilter(f;P;L),
pi2: snd(t),
pi1: fst(t),
int_seg: {i..j
},
ycomb: Y,
list_ind: list_ind def,
intensional-universe: IType,
es-E-interface: E(X),
eq_knd: a = b,
IdLnk: IdLnk,
Knd: Knd,
labeled-graph: LabeledGraph(T),
dep-isect: Error :dep-isect,
fpf-dom: x dom(f),
rev_implies: P Q,
Complete: Error :Complete,
no_repeats: no_repeats(T;l),
prime_ideal_p: IsPrimeIdeal(R;P),
integ_dom_p: IsIntegDom(r),
grp_leq: a b,
monoid_hom_p: IsMonHom{M1,M2}(f),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
action_p: IsAction(A;x;e;S;f),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
bilinear: BiLinear(T;pl;tm),
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
coprime: CoPrime(a,b),
connex: Connex(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
path-goes-thru: x-f*-y thru i,
cut-order: a (X;f) b,
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
es-fset-loc: i locs(s),
existse-between3: e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
alle-lt: e<e'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
es-le: e loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_disjoint: l_disjoint(T;l1;l2),
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
l_exists: (xL. P[x]),
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
decidable: Dec(P),
subtract: n - m,
minus: -n,
qabs: |r|,
es-interface-prior-vals: X(e),
i-finite: i-finite(I),
i-closed: i-closed(I),
lg-edge: lg-edge(g;a;b)
Lemmas :
append-nil,
last_append,
mapfilter-singleton,
rev_implies_wf,
iff_wf,
iff_transitivity,
decidable__le,
equal-nil-sq-nil,
guard_wf,
nat_sq,
nat_ind_tp,
not_functionality_wrt_iff,
ge_wf,
decidable__assert,
sq_stable_from_decidable,
squash_wf,
last_wf,
pos_length2,
bfalse_wf,
subtype_rel_wf,
append_wf,
it_wf,
list-equal-set2,
sq_stable_wf,
list-equal-set,
pi1_wf,
intensional-universe_wf,
uiff_inversion,
nat_properties,
from-upto_wf,
mapfilter_wf,
top_wf,
l_member_wf,
member_wf,
mapfilter-append,
null_append,
from-upto-split,
bool_wf,
int_seg_wf,
pi1_wf_top,
pi2_wf,
list-subtype,
list-set-type2,
l_all_wf,
product_subtype_base,
set_subtype_base,
int_subtype_base,
filter_wf,
map_wf,
length_wf1,
length_wf_nat,
bool_subtype_base,
assert_elim,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
le_int_wf,
bnot_wf,
lt_int_wf,
list_subtype_base,
rational-has-value,
int_inc,
assert_of_null,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
null_wf3,
assert_wf,
false_wf,
ifthenelse_wf,
true_wf,
sq_stable__assert,
is-run-event_wf,
subtype_base_sq,
atom2_subtype_base,
unit_wf,
le_wf,
run-event-step_wf,
nat_wf,
Id_wf,
run-event-loc_wf,
runEvents_wf,
pRunType_wf,
System_wf
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}S0:System(P.M[P]). \mforall{}r:pRunType(P.M[P]). \mforall{}e1,e2:runEvents(r).
(((run-event-local-pred(r;e2) = run-event-local-pred(r;e1))
\mwedge{} (run-event-interval(r;e1;e2) = [e2]))
\mvee{} (\mexists{}e:runEvents(r)
((run-event-step(e) < run-event-step(e2))
\mwedge{} (run-event-step(e1) \mleq{} run-event-step(e))
\mwedge{} ((run-event-loc(e1) = run-event-loc(e)) \mwedge{} (run-event-local-pred(r;e2) = (inl e )))
\mwedge{} (run-event-interval(r;e1;e2) = (run-event-interval(r;e1;e) @ [e2]))))) supposing
((run-event-step(e1) \mleq{} run-event-step(e2)) and
(run-event-loc(e1) = run-event-loc(e2)))
Date html generated:
2011_08_16-PM-07_00_57
Last ObjectModification:
2011_06_18-AM-11_15_13
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