{ 
[Info,A,T:Type].
es:EO+(Info). X:EClass(T 
A). e:E.
{(fst(MaxFst(X)(e)) ~ imax-list(map(
e.(fst(X(e)));
(X)(e))))
(
mxe:E(X)
(mxe loc e
(MaxFst(X)(e) = X(mxe))
(e':E(X). (e' loc e 
((fst(X(e'))) (fst(X(mxe))))))))}
supposing 
e 
MaxFst(X)
supposing T 
r 
}
{ Proof }
Definitions occuring in Statement :
max-fst-class: MaxFst(X),
es-interface-predecessors: (X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-E: E,
map: map(f;as),
subtype_rel: A r B,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
pi1: fst(t),
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
lambda: x.A[x],
product: x:A B[x],
int: ,
universe: Type,
sqequal: s ~ t,
equal: s = t,
imax-list: imax-list(L)
Definitions :
eclass-val: X(e),
pi1: fst(t),
le: A B,
es-le: e loc e' ,
implies: P Q,
es-E-interface: E(X),
all: x:A. B[x],
max-fst-class: MaxFst(X),
int: ,
product: x:A B[x],
equal: s = t,
and: P Q,
exists: x:A. B[x],
es-interface-predecessors: (X)(e),
lambda: x.A[x],
map: map(f;as),
imax-list: imax-list(L),
sqequal: s ~ t,
guard: {T},
in-eclass: e X,
assert: b,
es-E: E,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
universe: Type,
uall: [x:A]. B[x],
void: Void,
subtype: S T,
atom: Atom,
apply: f a,
es-base-E: es-base-E(es),
token: "$token",
subtype_rel: A r B,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
top: Top,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
union: left + right,
record-select: r.x,
member: t T,
isect: 
x:A. B[x],
so_lambda: 
x y.t[x; y],
event_ordering: EO,
function: x:A 
B[x],
prop: 
,
set: {x:A| B[x]} ,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
THENM: Error :THENM,
CollapseTHENA: Error :CollapseTHENA,
MaAuto: Error :MaAuto,
Unfold: Error :Unfold,
tactic: Error :tactic,
cand: A c B,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
sq_type: SQType(T),
Id: Id,
so_lambda: x.t[x],
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
list: type List,
lt_int: i <z j,
list_accum: list_accum(x,a.f[x; a];y;l),
imax: imax(a;b),
unit: Unit,
bool: 
,
bnot: b,
bor: p 
q,
band: p q,
bimplies: p q,
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_int: (i =
j),
le_int: i z j,
iff: P 
Q,
btrue: tt,
limited-type: LimitedType,
false: False,
true: True,
bfalse: ff,
combination: Combination(n;T),
listp: A List
,
squash: 
T,
tl: tl(l),
hd: hd(l),
es-loc: loc(e),
nil: [],
record: record(x.T[x]),
nat: 
,
length: ||as||,
natural_number: $n,
grp_car: |g|,
real: 
,
cons: [car / cdr],
l_member: (x l),
or: P Q,
can-apply: can-apply(f;x),
isl: isl(x),
select: l[i],
remove-repeats: remove-repeats(eq;L),
last: last(L),
rev_implies: P Q,
es-causl: (e < e'),
es-locl: (e <loc e'),
decidable: Dec(P),
append: as @ bs,
intensional-universe: IType,
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
es-fset-loc: i locs(s),
existse-between3: e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
alle-lt: e<e'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
l_disjoint: l_disjoint(T;l1;l2),
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
i-closed: i-closed(I),
i-finite: i-finite(I),
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
accum_list_cons: accum_list_cons_compseq_tag_def,
D: Error :D,
ParallelOp: Error :ParallelOp,
Subst': Error :Subst',
proper-iseg: L1 < L2,
iseg: l1 l2,
multiply: n * m,
gt: i > j,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
atom: Atom$n,
Knd: Knd,
locl: locl(a),
so_apply: x[s],
atom_eq: atomeqn def,
filter: filter(P;l),
RepeatFor: Error :RepeatFor,
MaAuto: Error :MaAuto,
IdLnk: IdLnk,
rationals: 
,
pi2: snd(t)
Lemmas :
pi2_wf,
assert_witness,
uall_wf,
guard_wf,
member-interface-predecessors-subtype,
l_member-settype,
es-le-loc,
list-subtype,
assert-eq-id,
uiff_inversion,
member_map,
imax-list-ub,
sq_stable__assert,
length-map,
pos-length,
equal-nil-sq-nil,
l_exists_wf,
pos_length2,
member-interface-predecessors,
not_wf,
es-locl_wf,
decidable__l_member,
es-interface-val_wf2,
bool_sq,
es-interface-subtype_rel,
intensional-universe_wf,
l_member_subtype,
cons_member,
decidable__equal_es-E-interface,
bool_subtype_base,
l_member_wf,
list_subtype_base,
set_subtype_base,
nat_wf,
length_wf_nat,
length_wf1,
es-interface-predecessors-nonempty,
is-max-fst,
es-loc_wf,
squash_wf,
bnot_of_le_int,
lt_int_wf,
bnot_wf,
le_int_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
bool_wf,
pi1_wf_top,
false_wf,
true_wf,
assert_elim,
list_accum_wf,
map_wf,
pi1_wf,
eclass-val_wf,
imax_wf,
es-E-interface_wf,
Id_wf,
ifthenelse_wf,
es-interface-predecessors_wf,
int_subtype_base,
subtype_base_sq,
imax-list_wf,
accum_list_wf,
le_wf,
es-le_wf,
assert_wf,
in-eclass_wf,
member_wf,
es-interface-top,
es-interface-subtype_rel2,
max-fst-class_wf,
top_wf,
eclass_wf,
es-E_wf,
es-base-E_wf,
event-ordering+_inc,
event-ordering+_wf,
max-fst-val,
subtype_rel_wf,
subtype_rel_self
\mforall{}[Info,A,T:Type].
\mforall{}es:EO+(Info). \mforall{}X:EClass(T \mtimes{} A). \mforall{}e:E.
\{(fst(MaxFst(X)(e)) \msim{} imax-list(map(\mlambda{}e.(fst(X(e)));\mleq{}(X)(e))))
\mwedge{} (\mexists{}mxe:E(X)
(mxe \mleq{}loc e
\mwedge{} (MaxFst(X)(e) = X(mxe))
\mwedge{} (\mforall{}e':E(X). (e' \mleq{}loc e {}\mRightarrow{} ((fst(X(e'))) \mleq{} (fst(X(mxe))))))))\}
supposing \muparrow{}e \mmember{}\msubb{} MaxFst(X)
supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2011_08_16-PM-05_21_46
Last ObjectModification:
2011_06_20-AM-01_21_36
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