{ 
[Info,T:Type]. [es:EO+(Info)]. [X:EClass(T)]. [e,p:E].
(((X)' es e) = ((X)
es p)) supposing
((e'':E. ((e'' <loc e) 
(p <loc e'') (
e'' 
X))) and
(p <loc e)) }
{ Proof }
Definitions occuring in Statement :
es-latest-val: (X),
es-prior-val: (X)',
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
not: A,
implies: P Q,
apply: f a,
universe: Type,
equal: s = t,
bag: bag(T)
Definitions :
axiom: Ax,
es-latest-val: (X),
es-prior-val: (X)',
bag: bag(T),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
apply: f a,
infix_ap: x f y,
es-causl: (e < e'),
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
top: Top,
in-eclass: e X,
assert: b,
not: A,
implies: P Q,
prop: 
,
es-locl: (e <loc e'),
uimplies: b supposing a,
subtype: S T,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
isect: 
x:A. B[x],
event-ordering+: EO+(Info),
universe: Type,
equal: s = t,
member: t T,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
record: record(x.T[x]),
eclass-val: X(e),
single-bag: {x},
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
set_blt: a < b,
grp_blt: a < b,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p 
q,
es-pred: pred(e),
bnot: b,
unit: Unit,
union: left + right,
fpf-dom: x dom(f),
es-loc: loc(e),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
guard: {T},
bfalse: ff,
sq_type: SQType(T),
es-first: first(e),
null: null(as),
Id: Id,
bool: 
,
sqequal: s ~ t,
pair: <a, b>,
true: True,
squash: 
T,
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
natural_number: $n,
int: 
,
nat: 
,
exists: x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
or: P Q,
iff: P 
Q,
es-E-interface: E(X),
so_apply: x[s1;s2],
so_lambda: x.t[x],
so_apply: x[s],
l_member: (x l),
es-le: e loc e' ,
es-p-le: e p e',
es-causle: e c e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p)
Lemmas :
es-locl_transitivity2,
es-le_weakening,
es-causl_weakening,
es-pred-causl,
set_subtype_base,
squash_wf,
true_wf,
es-interface-subtype_rel2,
top_wf,
Id_wf,
es-pred-locl,
es-locl-iff,
bag_wf,
es-causl-swellfnd,
nat_wf,
nat_properties,
ge_wf,
le_wf,
es-causl_wf,
es-prior-val_wf,
es-latest-val_wf,
prior-val-pred,
false_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
es-locl-first,
es-base-E_wf,
subtype_rel_self,
ifthenelse_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
eclass-val_wf,
single-bag_wf,
bnot_wf,
not_assert_elim,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
es-locl_wf,
not_wf,
assert_wf,
in-eclass_wf,
member_wf,
eclass_wf,
subtype_rel_wf,
es-interface-top
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e,p:E].
(((X)' es e) = ((X)\msupminus{} es p)) supposing
((\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (p <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X))) and
(p <loc e))
Date html generated:
2011_08_16-PM-05_08_54
Last ObjectModification:
2011_06_20-AM-01_11_56
Home
Index