{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [f:E(X) 
E(X)].
[e:E(X)]. (
null(prior-f-fixedpoints(e))) 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',
null: null(as),
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
not: A,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
list: type List,
null: null(as),
es-interface-prior-vals: X(e),
strong-subtype: strong-subtype(A;B),
l_member: (x 
l),
es-prior-fixedpoints: prior-f-fixedpoints(e),
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
void: Void,
false: False,
implies: P 
Q,
not: A,
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,
sq_stable: SqStable(P),
so_apply: x[s],
guard: {T},
fpf: a:A fp-> B[a],
le: A B,
ge: i 
j ,
exists: 
x:A. B[x],
es-fix: f**(e),
IdLnk: IdLnk,
Id: Id,
append: as @ bs,
locl: locl(a),
Knd: Knd,
squash: 
T,
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
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,
limited-type: LimitedType,
so_lambda: x.t[x],
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
pair: <a, b>,
iff: P 
Q,
bool: 
,
true: True,
nil: []
Lemmas :
l_member_wf,
es-fix_wf2,
nil_member,
true_wf,
property-from-l_member,
sq_stable_wf,
sq_stable__equal,
member_null,
member-es-fix-prior-fixedpoints,
subtype_rel_wf,
uiff_inversion,
member_wf,
top_wf,
es-E-interface_wf,
es-E_wf,
es-prior-fixedpoints_wf,
null_wf3,
assert_wf,
false_wf,
not_wf,
pos_length2,
es-E-interface-subtype_rel,
event-ordering+_inc,
subtype_rel_self,
es-causle_wf,
event-ordering+_wf,
eclass_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. (\mneg{}\muparrow{}null(prior-f-fixedpoints(e))) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2011_08_16-PM-05_44_21
Last ObjectModification:
2011_06_20-AM-01_32_09
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