{ 
[Info,A1,B1,A2,B2,C:Type]. [X1:EClass(A1)]. [X2:EClass(A2)]. [b1:B1].
[b2:B2]. [acc1:B1 
A1 B1]. [acc2:B2 A2 B2]. [F1:B1 C].
[F2:B2 C].
((F1[x] where x from es-interface-accum(acc1;b1;X1))
= (F2[x] where x from es-interface-accum(acc2;b2;X2))) supposing
((a:B1. b:B2.
(((F1 a) = (F2 b))
(es:EO+(Info). e:E.
((
e 
X1)
(e X1)
(F1[acc1 a X1(e)] = F2[acc2 b X2(e)]))))) and
(F1[b1] = F2[b2]) and
(es:EO+(Info). e:E. (e X1 
e X2))) }
{ Proof }
Definitions occuring in Statement :
es-interface-accum: es-interface-accum(f;x;X),
map-class: (f[v] where v from X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
axiom: Ax,
es-interface-accum: es-interface-accum(f;x;X),
map-class: (f[v] where v from X),
guard: {T},
true: True,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
es-E-interface: E(X),
eclass-val: X(e),
so_apply: x[s],
limited-type: LimitedType,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
list: type List,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
apply: f a,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
subtype_rel: A 
r B,
top: Top,
rev_implies: P Q,
in-eclass: e X,
implies: P Q,
product: x:A 
B[x],
and: P 
Q,
prop: 
,
assert: b,
iff: P Q,
uimplies: b supposing a,
subtype: S T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
universe: Type,
eclass: EClass(A[eo; e]),
all: x:A. B[x],
function: x:A B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
so_lambda: 
x y.t[x; y],
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
sq_type: SQType(T),
sqequal: s ~ t,
tag-by: zT,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
b-union: A 
B,
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
fpf-cap: f(x)?z,
intensional-universe: IType,
inr: inr x ,
es-loc: loc(e),
set: {x:A| B[x]} ,
unit: Unit,
list_accum: list_accum(x,a.f[x; a];y;l),
inl: inl x ,
bfalse: ff,
btrue: tt,
es-interface-at: X@i,
cond-class: [X?Y],
cand: A c B,
void: Void,
suptype: suptype(S; T),
isl: isl(x),
can-apply: can-apply(f;x),
atom: Atom,
token: "$token",
bool: 
,
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
sq_stable: SqStable(P),
or: P 
Q,
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
union: left + right,
so_lambda: x.t[x],
pair: <a, b>,
es-interface-predecessors: (X)(e)
Lemmas :
list_accum_equality,
es-interface-predecessors-equal,
map-class_wf,
es-interface-accum_wf,
uiff_inversion,
subtype_rel_self,
map-class_functionality,
top_wf,
rev_implies_wf,
btrue_wf,
bfalse_wf,
bool_wf,
unit_wf,
es-interface-predecessors_wf,
Id_wf,
es-E-interface_wf,
list_accum_wf,
es-loc_wf,
intensional-universe_wf,
es-interface-subtype_rel,
is-interface-accum,
es-interface-accum-val,
subtype_base_sq,
list_subtype_base,
set_subtype_base,
list-equal-set2,
bool_subtype_base,
assert_elim,
event-ordering+_wf,
es-E_wf,
assert_wf,
es-interface-top,
subtype_rel_wf,
eclass_wf,
member_wf,
in-eclass_wf,
iff_wf,
event-ordering+_inc,
eclass-val_wf,
false_wf,
ifthenelse_wf,
true_wf
\mforall{}[Info,A1,B1,A2,B2,C:Type]. \mforall{}[X1:EClass(A1)]. \mforall{}[X2:EClass(A2)]. \mforall{}[b1:B1]. \mforall{}[b2:B2]. \mforall{}[acc1:B1
{}\mrightarrow{} A1
{}\mrightarrow{} B1].
\mforall{}[acc2:B2 {}\mrightarrow{} A2 {}\mrightarrow{} B2]. \mforall{}[F1:B1 {}\mrightarrow{} C]. \mforall{}[F2:B2 {}\mrightarrow{} C].
((F1[x] where x from es-interface-accum(acc1;b1;X1))
= (F2[x] where x from es-interface-accum(acc2;b2;X2))) supposing
((\mforall{}a:B1. \mforall{}b:B2.
(((F1 a) = (F2 b))
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X1) {}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X1) {}\mRightarrow{} (F1[acc1 a X1(e)] = F2[acc2 b X2(e)]))))) and
(F1[b1] = F2[b2]) and
(\mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X1 \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} X2)))
Date html generated:
2011_08_16-PM-05_17_30
Last ObjectModification:
2011_06_20-AM-01_19_19
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