{ 
[E:Type]. [dom:E 
]. [l:E Id]. [R:E E 
]. [a:e1,e2:E.
((e1 = e2)
(
(e1
= e2)))].
[b:
f:E 
. x,y:E. ((x R y) 
((f x) < (f y)))]. [c:e1,e2:E.
((e1 R e2)
((e1 R e2)))].
[d:x,y,z:E. ((x R y) (y R z) (x R z))]. [e:x:E
L:E List
z:E
((z R x)
(z 
L))].
[f:e1,e2:E. (e1 = e2) (e1 R e2) (e2 R e1) supposing (l e1) = (l e2)].
(mk-eo(E;dom;l;R;a;b;c;d;e;f) EO) }
{ Proof }
Definitions occuring in Statement :
mk-eo: mk-eo(E;dom;l;R;a;b;c;d;e;f),
event_ordering: EO,
Id: Id,
bool: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
infix_ap: x f y,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
or: P Q,
member: t T,
less_than: a < b,
apply: f a,
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
rec_select_update: rec_select_update{rec_select_update_compseq_tag_def:o}(y; v; x; r),
guard: {T},
sq_type: SQType(T),
lt_int: i <z j,
le_int: i 
z j,
bfalse: ff,
btrue: tt,
iff: P 
Q,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
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$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
bimplies: p q,
band: p 
q,
bor: p q,
assert: 
b,
bnot: b,
unit: Unit,
void: Void,
record-update: r[x := v],
token: "$token",
eq_atom: x =a y,
top: Top,
ifthenelse: if b then t else f fi ,
lambda: 
x.A[x],
atom: Atom,
record+: record+,
record-select: r.x,
limited-type: LimitedType,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S 
T,
int: 
,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
axiom: Ax,
mk-eo: mk-eo(E;dom;l;R;a;b;c;d;e;f),
event_ordering: EO,
uimplies: b supposing a,
list: type List,
l_member: (x l),
nat: ,
apply: f a,
infix_ap: x f y,
less_than: a < b,
implies: P Q,
product: x:A 
B[x],
exists: x:A. B[x],
not: A,
union: left + right,
or: P Q,
equal: s = t,
bool: ,
Id: Id,
prop: ,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
all: x:A. B[x],
function: x:A B[x],
record: record(x.T[x])
Lemmas :
bnot_wf,
assert_wf,
not_wf,
bool_wf,
assert_of_eq_atom,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
iff_weakening_uiff,
eqtt_to_assert,
top_wf,
eq_atom_wf,
ifthenelse_wf,
Id_wf,
nat_wf,
l_member_wf,
event_ordering_wf,
member_wf,
subtype_base_sq,
atom_subtype_base
\mforall{}[E:Type]. \mforall{}[dom:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[l:E {}\mrightarrow{} Id]. \mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}[a:\mforall{}e1,e2:E. ((e1 = e2) \mvee{} (\mneg{}(e1 = e2)))]. \mforall{}[b:\mexists{}f:E {}\mrightarrow{} \mBbbN{}. \mforall{}x,y:E. ((x R y) {}\mRightarrow{} ((f x) < (f y)))].
\mforall{}[c:\mforall{}e1,e2:E. ((e1 R e2) \mvee{} (\mneg{}(e1 R e2)))]. \mforall{}[d:\mforall{}x,y,z:E. ((x R y) {}\mRightarrow{} (y R z) {}\mRightarrow{} (x R z))].
\mforall{}[e:\mforall{}x:E. \mexists{}L:E List. \mforall{}z:E. ((z R x) {}\mRightarrow{} (z \mmember{} L))]. \mforall{}[f:\mforall{}e1,e2:E.
(e1 = e2) \mvee{} (e1 R e2) \mvee{} (e2 R e1)
supposing (l e1) = (l e2)].
(mk-eo(E;dom;l;R;a;b;c;d;e;f) \mmember{} EO)
Date html generated:
2011_08_16-AM-10_19_57
Last ObjectModification:
2011_06_18-AM-09_08_12
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