{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [e:E].
((X)' es e ~ if first(e) then {}
if pred(e) 
X then {X(pred(e))}
else (X)' es pred(e)
fi ) }
{ Proof }
Definitions occuring in Statement :
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-pred: pred(e),
es-first: first(e),
es-E: E,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t,
single-bag: {x},
empty-bag: {}
Definitions :
sqequal: s ~ t,
subtype: S 
T,
top: Top,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
event-ordering+: EO+(Info),
universe: Type,
eclass: EClass(A[eo; e]),
all: x:A. B[x],
function: x:A 
B[x],
member: t T,
equal: s = t,
so_lambda: 
x y.t[x; y],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
es-pred: pred(e),
bag-size: bag-size(bs),
record: record(x.T[x]),
es-locl: (e <loc e'),
sq_exists: 
x:{A| B[x]},
or: P 
Q,
so_lambda: x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
guard: {T},
quotient: x,y:A//B[x; y],
sq_type: SQType(T),
bag: bag(T),
bag-only: only(bs),
single-bag: {x},
empty-bag: {},
subtype_rel: A r B,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bfalse: ff,
btrue: tt,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
eq_int: (i =
j),
eq_atom: x =a y,
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'),
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_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-first: first(e),
assert: 
b,
bnot: 
b,
unit: Unit,
union: left + right,
bool: 
,
true: True,
squash: 
T,
es-causl: (e < e'),
apply: f a,
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
not: A,
natural_number: $n,
prop: 
,
le: A B,
ge: i 
j ,
int: 
,
set: {x:A| B[x]} ,
less_than: a < b,
nat: 
,
implies: P Q,
product: x:A 
B[x],
exists: x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
eclass-val: X(e),
es-local-pred: last(P),
local-pred-class: local-pred-class(P),
es-prior-interface: prior(X),
in-eclass: e X,
es-prior-val: (X)'
Lemmas :
nat_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
le_wf,
member_wf,
es-causl_wf,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
es-first_wf,
bag-only_wf,
single-bag_wf,
bag_wf,
ifthenelse_wf,
subtype_base_sq,
eq_int_wf,
bool_subtype_base,
isect_subtype_base,
es-local-pred_wf,
es-locl_wf,
set_subtype_base,
assert_of_eq_int,
bag-size_wf,
es-pred_wf,
not_functionality_wrt_uiff,
eclass_wf,
event-ordering+_wf,
top_wf,
es-E_wf,
event-ordering+_inc
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
((X)' es e \msim{} if first(e) then \{\}
if pred(e) \mmember{}\msubb{} X then \{X(pred(e))\}
else (X)' es pred(e)
fi )
Date html generated:
2011_08_16-PM-05_03_44
Last ObjectModification:
2011_06_20-AM-01_09_42
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