{ 
[Info:Type]
es:EO+(Info)
[T:Type]
X:EClass(T). P:E(X) 
. i:Id.
[R:Id E(X) 
]
n:
. L:Id List.
((x
L.
y:E(X). (R[x;y] 
(
P[y])))
(e:E(X)
((P[e])
e is first@ i s.t. q.||filter(
e.P[e];
(X)(q))||
= n))) supposing
((n ||L||) and
no_repeats(Id;L))
supposing x1,x2:Id. y:E(X). (R[x1;y] R[x2;y] (x1 = x2))
supposing e:E(X). loc(e) = i supposing P[e] }
{ Proof }
Definitions occuring in Statement :
es-interface-predecessors: (X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
es-loc: loc(e),
Id: Id,
length: ||as||,
assert: b,
bool: ,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
lambda: x.A[x],
function: x:A B[x],
list: type List,
int: 
,
universe: Type,
equal: s = t,
l_all: (xL.P[x]),
no_repeats: no_repeats(T;l),
filter: filter(P;l)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
uimplies: b supposing a,
so_apply: x[s],
prop: ,
implies: P Q,
so_apply: x[s1;s2],
no_repeats: no_repeats(T;l),
le: A B,
exists: x:A. B[x],
and: P Q,
member: t T,
not: 
A,
false: False,
rev_implies: P 
Q,
iff: P Q,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
assert: b,
cand: A c B,
btrue: tt,
ifthenelse: if b then t else f fi ,
true: True,
nat: ,
guard: {T},
ge: i 
j ,
top: Top,
squash: 
T,
es-E-interface: E(X),
length: ||as||,
label: ...$L... t,
ycomb: Y,
subtype: S 
T,
nat_plus: ,
sq_type: SQType(T),
strongwellfounded: SWellFounded(R[x; y]),
decidable: Dec(P),
or: P 
Q,
bfalse: ff,
filter: filter(P;l),
reduce: reduce(f;k;as),
append: as @ bs,
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e]
Lemmas :
assert_wf,
es-E-interface_wf,
es-interface-top,
Id_wf,
select_wf,
not_wf,
nat_wf,
length_wf1,
filter-interface-predecessors-lower-bound2,
l_all_wf2,
l_member_wf,
le_wf,
no_repeats_wf,
nat_plus_wf,
es-loc_wf,
event-ordering+_inc,
bool_wf,
eclass_wf,
es-E_wf,
event-ordering+_wf,
subtype_base_sq,
bool_subtype_base,
filter_wf,
es-interface-predecessors_wf,
assert_elim,
es-causl-swellfnd,
es-causl_wf,
nat_properties,
ge_wf,
decidable__equal_int,
in-eclass_wf,
es-prior-interface_wf,
es-interface-subtype_rel2,
top_wf,
bnot_wf,
squash_wf,
true_wf,
es-interface-predecessors-general-step,
bool_cases,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
eclass-val_wf2,
es-prior-interface-causl,
es-loc-prior-interface,
length_nil,
non_neg_length,
length_wf_nat,
filter_wf_top,
append_wf,
length_append,
filter_append_sq,
filter_type,
subtype_rel_list,
length_cons,
length-append,
es-first-at-exists,
es-prior-interface-locl,
append-nil,
assert_witness,
es-first-at_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[T:Type]
\mforall{}X:EClass(T). \mforall{}P:E(X) {}\mrightarrow{} \mBbbB{}. \mforall{}i:Id.
\mforall{}[R:Id {}\mrightarrow{} E(X) {}\mrightarrow{} \mBbbP{}]
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}L:Id List.
((\mforall{}x\mmember{}L.\mexists{}y:E(X). (R[x;y] \mwedge{} (\muparrow{}P[y])))
{}\mRightarrow{} (\mexists{}e:E(X)
((\muparrow{}P[e]) \mwedge{} e is first@ i s.t. q.||filter(\mlambda{}e.P[e];\mleq{}(X)(q))|| = n))) supposing
((n \mleq{} ||L||) and
no\_repeats(Id;L))
supposing \mforall{}x1,x2:Id. \mforall{}y:E(X). (R[x1;y] {}\mRightarrow{} R[x2;y] {}\mRightarrow{} (x1 = x2))
supposing \mforall{}e:E(X). loc(e) = i supposing \muparrow{}P[e]
Date html generated:
2011_08_16-PM-05_23_55
Last ObjectModification:
2011_06_20-AM-01_22_56
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