{ 
[Info,T:Type].
G:es:EO+(Info) 
E bag(T). F:es:EO+(Info)
e':E
T
{e:E| (e' <loc e)}
bag(T). es:EO+(Info). e:E.
(
e 
RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
if e prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
bag-size(F[es;e';RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e');e])
= 1
else bag-size(G[es;e]) = 1
fi ) }
{ Proof }
Definitions occuring in Statement :
es-rec-class: es-rec-class,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e X,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: b,
ifthenelse: if b then t else f fi ,
let: let,
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
all: x:A. B[x],
iff: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
natural_number: $n,
int: 
,
universe: Type,
equal: s = t,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
guard: {T},
sq_type: SQType(T),
eclass-val: X(e),
quotient: x,y:A//B[x; y],
void: Void,
true: True,
rev_implies: P Q,
false: False,
lt_int: i <z j,
le_int: i 
z j,
bfalse: ff,
real: 
,
grp_car: |g|,
nat: 
,
limited-type: LimitedType,
btrue: tt,
null: null(as),
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'),
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,
natural_number: $n,
bag-size: bag-size(bs),
eq_int: (i =
j),
bnot: 
b,
unit: Unit,
union: left + right,
bool: 
,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
top: Top,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_lambda: 
x y.t[x; y],
lambda: x.A[x],
in-eclass: e X,
subtype: S T,
member: t T,
let: let,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
implies: P Q,
product: x:A 
B[x],
and: P Q,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
so_lambda: x.t[x],
all: x:A. B[x],
iff: P Q,
ifthenelse: if b then t else f fi ,
int: ,
prop: 
,
universe: Type,
assert: b,
function: x:A B[x],
set: {x:A| B[x]} ,
es-locl: (e <loc e'),
es-E: E,
event-ordering+: EO+(Info),
event_ordering: EO,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
Auto: Error :Auto,
Unfold: Error :Unfold,
CollapseTHENA: Error :CollapseTHENA,
es-prior-interface: prior(X),
apply: f a,
es-E-interface: E(X),
bag: bag(T),
equal: s = t,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
es-rec-class: es-rec-class,
eclass: EClass(A[eo; e]),
D: Error :D,
RepeatFor: Error :RepeatFor,
tactic: Error :tactic,
es-causl: (e < e')
Lemmas :
eclass-val_wf2,
es-prior-interface_wf1,
assert_elim,
eclass-val_wf,
in-eclass_wf,
es-prior-interface-val,
es-E_wf,
iff_wf,
assert_wf,
ifthenelse_wf,
bag_wf,
event-ordering+_inc,
event-ordering+_wf,
es-locl_wf,
uall_wf,
eclass_wf,
es-rec-class_wf,
es-E-interface_wf,
member_wf,
es-prior-interface_wf,
subtype_rel_wf,
es-interface-top,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
bag-size_wf,
nat_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
eq_int_wf,
assert_witness,
false_wf,
true_wf,
subtype_base_sq,
bool_subtype_base,
eq_int_eq_true
\mforall{}[Info,T:Type].
\mforall{}G:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} bag(T). \mforall{}F:es:EO+(Info) {}\mrightarrow{} e':E {}\mrightarrow{} T {}\mrightarrow{} \{e:E| (e' <loc e)\} {}\mrightarrow{} bag(T).
\mforall{}es:EO+(Info). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
\mLeftarrow{}{}\mRightarrow{} if e \mmember{}\msubb{} prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
bag-size(F[es;e';RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e');e])
= 1
else bag-size(G[es;e]) = 1
fi )
Date html generated:
2011_08_16-PM-05_02_52
Last ObjectModification:
2011_06_20-AM-01_09_19
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