{ 
es:EO
[T:Type]
f:T 
T. ((x:T. f x c
x) 
retraction(T;f))
supposing strong-subtype(T;E) }
{ Proof }
Definitions occuring in Statement :
es-causle: e c e',
es-E: E,
event_ordering: EO,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
strong-subtype: strong-subtype(A;B),
retraction: retraction(T;f)
Definitions :
intensional-universe: IType,
record: record(x.T[x]),
es-causl: (e < e'),
sq_stable: SqStable(P),
pair: <a, b>,
so_apply: x[s],
guard: {T},
l_member: (x 
l),
assert: 
b,
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
apply: f a,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record-select: r.x,
infix_ap: x f y,
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: 
A,
and: P 
Q,
uiff: uiff(P;Q),
less_than: a < b,
union: left + right,
or: P 
Q,
es-causle: e c e',
event_ordering: EO,
universe: Type,
uimplies: b supposing a,
prop: 
,
retraction: retraction(T;f),
exists: 
x:A. B[x],
nat: 
,
set: {x:A| B[x]} ,
strong-subtype: strong-subtype(A;B),
cand: A c B,
product: x:A 
B[x],
subtype_rel: A 
r B,
es-E: E,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
equal: s = t,
all: x:A. B[x],
function: x:A B[x],
implies: P Q,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
strongwellfounded: SWellFounded(R[x; y]),
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
void: Void,
real: 
,
false: False,
iff: P 
Q,
atom: Atom,
int_seg: {i..j
},
bool: 
,
quotient: x,y:A//B[x; y],
divides: b | a,
assoced: a ~ b,
set_car: |p|,
set_leq: a b,
set_lt: a <p b,
grp_car: |g|,
grp_lt: a < b,
rng_car: |r|,
unit: Unit,
int: 
,
nat_plus: 
,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
limited-type: LimitedType,
rationals: 
,
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
atom: Atom$n,
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset: FSet{T},
fset-closed: (s closed under fs),
string: Error :string,
Id: Id,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
consensus-rcv: consensus-rcv(V;A),
decidable: Dec(P),
es-locl: (e <loc e'),
list: type List,
top: Top,
true: True,
fpf-cap: f(x)?z,
subtype: S T,
suptype: suptype(S; T),
D: Error :D,
tactic: Error :tactic
Lemmas :
subtype_rel_function,
subtype_rel_self,
decidable__lt,
es-causl-swellfnd,
retraction_wf,
nat_wf,
es-causle_wf,
strong-subtype_witness,
es-E_wf,
strong-subtype_wf,
event_ordering_wf,
uall_wf,
subtype_rel_wf,
member_wf,
uiff_inversion,
assert_wf,
intensional-universe_wf,
es-causl_wf
\mforall{}es:EO. \mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. ((\mforall{}x:T. f x c\mleq{} x) {}\mRightarrow{} retraction(T;f)) supposing strong-subtype(T;E)
Date html generated:
2011_08_16-AM-10_32_22
Last ObjectModification:
2011_06_18-AM-09_13_58
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