{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [f:E(X) 
E(X)].
[e:E(X)]. (prior-f-fixedpoints(e) 
{e':E(X)| (f e') = e'} List)
supposing x:E(X). f x c
x }
{ Proof }
Definitions occuring in Statement :
es-prior-fixedpoints: prior-f-fixedpoints(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causle: e c e',
es-E: E,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
member: t T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t
Definitions :
implies: P 
Q,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
so_lambda: 
x.t[x],
filter: filter(P;l),
l_member: (x l),
fpf: a:A fp-> B[a],
axiom: Ax,
es-prior-fixedpoints: prior-f-fixedpoints(e),
list: type List,
infix_ap: x f y,
es-causl: (e < e'),
or: P 
Q,
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
b,
prop: 
,
es-causle: e c e',
uimplies: b supposing a,
union: left + right,
es-E-interface: E(X),
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
top: Top,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
universe: Type,
member: t T,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
es-fix: f**(e),
list_ind: list_ind def,
length: ||as||,
select: l[i],
cand: A c B,
l_all: (xL.P[x]),
rev_implies: P 
Q,
es-le: e loc e' ,
es-locl: (e <loc e'),
es-p-le: e p e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
record: record(x.T[x]),
tl: tl(l),
hd: hd(l),
nil: [],
cons: [car / cdr],
eclass-val: X(e),
append: as @ bs,
eq_bool: p =b q,
eq_int: (i =
j),
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'),
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,
es-prior-interface: prior(X),
in-eclass: e X,
sq_type: SQType(T),
limited-type: LimitedType,
pair: <a, b>,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
iff: P Q,
bimplies: p q,
band: p q,
bor: p q,
es-eq-E: e = e',
bnot: b,
unit: Unit,
minus: -n,
bool: 
,
subtract: n - m,
grp_car: |g|,
natural_number: $n,
void: Void,
false: False,
real: 
,
rationals: 
,
int: 
,
add: n + m,
nat: 
,
guard: {T},
exists: x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
MaAuto: Error :MaAuto,
BHyp: Error :BHyp,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
SplitOn: Error :SplitOn,
CollapseTHENA: Error :CollapseTHENA,
Repeat: Error :Repeat,
D: Error :D,
RepeatFor: Error :RepeatFor
Lemmas :
es-fix-equal,
es-fix-causle,
ge_wf,
nat_properties,
es-causl-swellfnd,
guard_wf,
nat_wf,
nat_ind_tp,
le_wf,
not_wf,
false_wf,
es-causl_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert-es-eq-E-2,
eqff_to_assert,
assert_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
es-eq-E_wf,
bnot_wf,
es-prior-interface_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-prior-interface_wf1,
es-interface-subtype_rel2,
subtype_rel_wf,
append_wf,
list-subtype,
l_member_wf,
eclass-val_wf2,
es-prior-interface-causl,
l_all_wf,
subtype_base_sq,
set_subtype_base,
length_wf_nat,
length_wf1,
es-fix_wf2,
eclass_wf,
top_wf,
event-ordering+_wf,
es-causle_wf,
subtype_rel_self,
event-ordering+_inc,
es-E-interface-subtype_rel,
list-set-type2,
member_wf,
es-E_wf,
es-E-interface_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. (prior-f-fixedpoints(e) \mmember{} \{e':E(X)| (f e') = e'\} List) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2011_08_16-PM-05_43_30
Last ObjectModification:
2011_06_20-AM-01_31_36
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