{ 
[Info,A:Type]. [X:EClass(A)]. [Y:EClass(Top)].
((X until Y) = 
xs,ys.if bag-null(ys) then xs else {} fi |X;Prior(Y)|) }
{ Proof }
Definitions occuring in Statement :
simple-comb2: x,y.F[x; y]|X;Y|,
primed-class: Prior(X),
until-class: (X until Y),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
top: Top,
universe: Type,
equal: s = t,
bag-null: bag-null(bs),
empty-bag: {}
Definitions :
Unfold: Error :Unfold,
RepUR: Error :RepUR,
RepeatFor: Error :RepeatFor,
top: Top,
Repeat: Error :Repeat,
D: Error :D,
ExRepD: Error :ExRepD,
Try: Error :Try,
Complete: Error :Complete,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
isect: 
x:A. B[x],
member: t 
T,
function: x:A 
B[x],
event-ordering+: EO+(Info),
event_ordering: EO,
es-E: E,
bag: bag(T),
uall: [x:A]. B[x],
universe: Type,
equal: s = t,
eclass: EClass(A[eo; e]),
until-class: (X until Y),
simple-comb2: x,y.F[x; y]|X;Y|,
ifthenelse: if b then t else f fi ,
bag-null: bag-null(bs),
empty-bag: {},
primed-class: Prior(X),
axiom: Ax,
all: x:A. B[x],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
product: x:A 
B[x],
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
fpf: a:A fp-> B[a],
pair: <a, b>,
subtype: S T,
simple-comb: simple-comb(F;Xs),
lambda: x.A[x],
select: l[i],
record+: record+,
dep-isect: Error :dep-isect,
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
class-pred: class-pred(X;es;e),
union: left + right,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
apply: f a,
so_lambda: 
x y.t[x; y],
bool: 
,
assert: 
b,
set: {x:A| B[x]} ,
record-select: r.x,
inr: inr x ,
or: P 
Q,
existse-before: 
e<e'.P[e],
alle-lt: e<e'.P[e],
exists: x:A. B[x],
cand: A c B,
es-locl: (e <loc e'),
squash: 
T,
sq_type: SQType(T),
so_lambda: x.t[x],
record: record(x.T[x]),
void: Void,
prop: 
,
inl: inl x ,
es-causl: (e < e'),
infix_ap: x f y,
es-le: e loc e' ,
implies: P 
Q,
unit: Unit,
int: 
,
bnot: 
b,
bor: p q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
btrue: tt,
limited-type: LimitedType,
bfalse: ff,
le_int: i z j,
lt_int: i <z j,
classrel: v X(e),
Id: Id,
guard: {T},
es-E-interface: E(X),
atom: Atom,
token: "$token",
it: 
,
natural_number: $n,
false: False,
nat: 
,
list: type List,
l_member: (x l),
length: ||as||,
ycomb: Y,
list_ind: list_ind def,
add: n + m,
nil: [],
subtract: n - m,
es-base-E: es-base-E(es),
true: True,
permutation: permutation(T;L1;L2),
int_seg: {i..j
},
lelt: i j < k,
inject: Inj(A;B;f),
permute_list: (L o f),
atom_eq: if a=b then c else d,
atom: Atom$n,
less: if (a) < (b) then c else d,
quotient: x,y:A//B[x; y],
mklist: mklist(n;f),
append: as @ bs,
cons: [car / cdr],
primrec: primrec(n;b;c),
eq_int: (i =
j),
int_eq: if a=b then c else d,
Knd: Knd,
locl: locl(a),
so_apply: x[s],
rationals: 
,
IdLnk: IdLnk,
es-loc: loc(e),
fpf-dom: x dom(f),
eq_knd: a = b,
in-eclass: e X,
intensional-universe: IType,
rev_uimplies: rev_uimplies(P;Q),
bag-member: bag-member(T;x;bs)
Lemmas :
es-locl_wf,
Id_wf,
es-loc_wf,
squash_wf,
existse-before_wf,
alle-lt_wf,
es-le_wf,
primed-classrel,
false_wf,
intensional-universe_wf,
no-classrel-iff-empty,
uiff_wf,
classrel_wf,
permutation_wf,
bnot_wf,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
not_wf,
assert-bag-null,
eqtt_to_assert,
uiff_transitivity,
isect_subtype_base,
set_subtype_base,
assert_wf,
union_subtype_base,
subtype_base_sq,
class-pred-cases,
es-interface-top,
subtype_rel_wf,
primed-class_wf,
bag-null_wf,
bool_wf,
top_wf,
class-pred_wf,
empty-bag_wf,
event-ordering+_inc,
member_wf,
eclass_wf,
event-ordering+_wf,
es-E_wf,
bag_wf,
ifthenelse_wf
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(Top)].
((X until Y) = \mlambda{}xs,ys.if bag-null(ys) then xs else \{\} fi |X;Prior(Y)|)
Date html generated:
2011_08_16-PM-05_05_15
Last ObjectModification:
2011_06_17-AM-10_59_48
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