{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [f:E(X) 
E(X)].
[e,e':E(X)]. (f e') = e' supposing (e' 
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',
es-E: E,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
implies: P 
Q,
in-eclass: e 
X,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
pair: <a, b>,
exists: 
x:A. B[x],
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
axiom: Ax,
list: type List,
es-prior-fixedpoints: prior-f-fixedpoints(e),
l_member: (x l),
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,
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,
sq_stable: SqStable(P),
limited-type: LimitedType,
so_lambda: x.t[x],
so_apply: x[s],
cons: [car / cdr],
nil: [],
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},
strongwellfounded: SWellFounded(R[x; y]),
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor
Lemmas :
ge_wf,
nat_properties,
subtype_rel_wf,
es-causl-swellfnd,
guard_wf,
nat_wf,
nat_ind_tp,
le_wf,
not_wf,
false_wf,
es-causl_wf,
property-from-l_member,
sq_stable_wf,
sq_stable__equal,
eclass_wf,
top_wf,
event-ordering+_wf,
es-causle_wf,
l_member_wf,
es-prior-fixedpoints_wf,
subtype_rel_self,
event-ordering+_inc,
es-E-interface_wf,
member_wf,
es-E-interface-subtype_rel,
es-E_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e,e':E(X)]. (f e') = e' supposing (e' \mmember{} prior-f-fixedpoints(e)) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2011_08_16-PM-05_45_20
Last ObjectModification:
2011_06_20-AM-01_32_40
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