{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [e:E(X)].
(
(X)(e) = if e 
prior(X) then (X)(prior(X)(e)) @ [e] else [e] fi ) }
{ Proof }
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: (X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
append: as @ bs,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
cons: [car / cdr],
nil: [],
list: type List,
universe: Type,
equal: s = t
Definitions :
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),
implies: P 
Q,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f 
g,
sq_stable: SqStable(P),
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
pair: <a, b>,
l_member: (x l),
tl: tl(l),
hd: hd(l),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
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),
axiom: Ax,
nil: [],
cons: [car / cdr],
eclass-val: X(e),
append: as @ bs,
es-prior-interface: prior(X),
in-eclass: e X,
es-interface-predecessors: (X)(e),
es-loc: loc(e),
Id: Id,
set: {x:A| B[x]} ,
list: type List,
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,
exists: 
x:A. B[x],
void: Void,
false: False,
bfalse: ff,
limited-type: LimitedType,
btrue: tt,
prop: 
,
iff: P 
Q,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
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_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
bimplies: p q,
band: p q,
bor: p 
q,
bnot: b,
int: 
,
unit: Unit,
bool: 
,
sqequal: s ~ t,
es-locl: (e <loc e'),
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
guard: {T},
es-causl: (e < e'),
sq_type: SQType(T),
atom: Atom$n,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN
Lemmas :
eclass-val_wf,
eclass-val_wf2,
atom2_subtype_base,
subtype_base_sq,
es-E-interface-subtype_rel,
es-prior-interface-locl,
es-prior-interface_wf1,
es-prior-interface_wf,
es-prior-interface_wf0,
in-eclass_wf,
bnot_wf,
assert_wf,
not_wf,
bool_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
es-interface-predecessors-step-sq,
subtype_rel_wf,
append_wf,
es-interface-subtype_rel2,
list-subtype,
l_member_wf,
btrue_neq_bfalse,
assert_elim,
not_assert_elim,
eclass_wf,
top_wf,
subtype_rel_self,
event-ordering+_wf,
es-interface-predecessors_wf,
ifthenelse_wf,
list-equal-set2,
sq_stable_wf,
sq_stable__equal,
event-ordering+_inc,
es-loc_wf,
member_wf,
es-E_wf,
Id_wf,
es-E-interface_wf,
list-equal-set
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)].
(\mleq{}(X)(e) = if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) @ [e] else [e] fi )
Date html generated:
2011_08_16-PM-05_16_50
Last ObjectModification:
2011_06_20-AM-01_18_43
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