{ 
[Info,T,S:Type]. [x:T].
f:T 
EClass(S). (return-class(x) >z> f[z] = f[x]) }
{ Proof }
Definitions occuring in Statement :
return-class: return-class(x),
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
implies: P 
Q,
record-select: r.x,
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
bag: bag(T),
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
top: Top,
so_lambda: 
x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
all: x:A. B[x],
lambda: x.A[x],
so_lambda: x y.t[x; y],
function: x:A B[x],
member: t 
T,
apply: f a,
axiom: Ax,
equal: s = t,
bind-class: X >x> Y[x],
return-class: return-class(x),
so_apply: x[s],
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
BHyp: Error :BHyp,
Auto: Error :Auto,
eclass: EClass(A[eo; e]),
ORELSE: Error :ORELSE,
Try: Error :Try,
CollapseTHENA: Error :CollapseTHENA,
nil: [],
cons: [car / cdr],
bag-append: as + bs,
es-le-before: loc(e),
es-le: e loc e' ,
es-first: first(e),
exists: 
x:A. B[x],
iff: P 
Q,
real: 
,
grp_car: |g|,
int: 
,
list_ind: list_ind def,
length: ||as||,
select: l[i],
record: record(x.T[x]),
sq_type: SQType(T),
es-loc: loc(e),
Id: Id,
es-causl: (e < e'),
es-causle: e c e',
eclass-val: X(e),
es-init: es-init(es;e),
true: True,
es-pred: pred(e),
nat: 
,
null: null(as),
es-locl: (e <loc e'),
union: left + right,
or: P 
Q,
filter: filter(P;l),
l_member: (x l),
void: Void,
false: False,
l_all: (xL.P[x]),
cand: A c B,
prop: 
,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
bnot: 
b,
bfalse: ff,
sqequal: s ~ t,
list: type List,
tl: tl(l),
btrue: tt,
hd: hd(l),
bool: 
,
add: n + m,
natural_number: $n,
fpf-dom: x dom(f),
rcv: rcv(l,tg),
locl: locl(a),
Knd: Knd,
squash: 
T,
tag-by: zT,
rev_implies: P Q,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 T2,
b-union: A 
B,
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
es-E-interface: Error :es-E-interface,
fpf-cap: f(x)?z,
permutation: permutation(T;L1;L2),
listp: A List
,
ndlist: ndlist(T),
limited-type: LimitedType,
quotient: x,y:A//B[x; y],
guard: {T},
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: Error :collect-event,
decidable: Dec(P),
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),
valueall-type: valueall-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),
sq_stable: SqStable(P),
label: ...$L... t,
MaAuto: Error :MaAuto,
intensional-universe: IType,
record-update: r[x := v],
eo-restrict: eo-restrict(eo;P),
eo-forward: eo.e,
bag-combine: xbs.f[x],
empty-bag: {},
IdLnk: IdLnk,
rationals: 
,
tactic: Error :tactic,
single-bag: {x},
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
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_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p q,
SplitOn: Error :SplitOn,
RepeatFor: Error :RepeatFor,
AssertBY: Error :AssertBY
Lemmas :
bag-combine-empty-left,
bag-combine-empty-right,
empty-bag_wf,
eo-forward-trivial,
single-bag_wf,
bool_cases,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
bag-combine-single-left,
rev_implies_wf,
iff_wf,
bag-combine-append-left,
bag-append-empty,
bag-combine_wf,
eo-forward_wf,
intensional-universe_wf,
member-eo-forward-E,
list_subtype_base,
length_nil,
pos_length3,
sq_stable_from_decidable,
decidable__es-le,
hd_wf,
bag-append_wf,
bool_wf,
bool_subtype_base,
true_wf,
ifthenelse_wf,
permutation_wf,
squash_wf,
subtype_rel_bag,
subtype_rel_set,
subtype_rel_sets,
es-le-before_wf,
es-loc_wf,
bfalse_wf,
ge_wf,
le_wf,
btrue_neq_bfalse,
non_neg_length,
length_wf1,
es-le-before-not-null,
assert_wf,
l_member_wf,
es-le_wf,
not_wf,
l_all_wf,
subtype_rel_self,
es-base-E_wf,
es-first_wf,
es-le-before_wf2,
tl_wf,
list_set_type,
btrue_wf,
hd-es-le-before-is-first,
false_wf,
es-locl_wf,
es-causle-le,
es-causl_wf,
Id_wf,
subtype_base_sq,
set_subtype_base,
length_wf_nat,
nat_wf,
top_wf,
tl-es-le-before,
list-subtype-bag,
es-E_wf,
bag_wf,
eclass_wf,
Error :es-interface-top,
subtype_rel_wf,
event-ordering+_wf,
member_wf,
event-ordering+_inc,
bind-class_wf,
return-class_wf
\mforall{}[Info,T,S:Type]. \mforall{}[x:T]. \mforall{}f:T {}\mrightarrow{} EClass(S). (return-class(x) >z> f[z] = f[x])
Date html generated:
2011_08_16-AM-11_36_00
Last ObjectModification:
2011_06_20-AM-00_29_32
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