{ 
[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)].
X;Y
= eclass-compose2(
ys,xs.
if (bag-size(ys) =
1)
then if (bag-size(xs) = 1)
then {<only(xs), only(ys)>}
else {}
fi
else {}
fi ;Y;Prior(X))
supposing Singlevalued(X) }
{ Proof }
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
primed-class: Prior(X),
eclass-compose2: eclass-compose2(f;X;Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
eq_int: (i = j),
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: [x:A]. B[x],
lambda: x.A[x],
pair: <a, b>,
product: x:A 
B[x],
natural_number: $n,
universe: Type,
equal: s = t,
bag-only: only(bs),
bag-size: bag-size(bs),
single-bag: {x},
empty-bag: {}
Definitions :
iff: P 
Q,
es-prior-val: (X)',
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_bool: p =b q,
in-eclass: e 
X,
IdLnk: IdLnk,
Id: Id,
rationals: 
,
append: as @ bs,
locl: locl(a),
Knd: Knd,
lt_int: i <z j,
le_int: i 
z j,
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
eq_atom: x =a y,
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'),
eq_atom: eq_atom$n(x;y),
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,
bnot: 
b,
unit: Unit,
bool: 
,
permutation: permutation(T;L1;L2),
list: type List,
apply: f a,
so_apply: x[s],
implies: P Q,
union: left + right,
or: P Q,
guard: {T},
l_member: (x l),
assert: 
b,
quotient: x,y:A//B[x; y],
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
int: 
,
nat: 
,
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
top: Top,
bag: bag(T),
fpf: a:A fp-> B[a],
void: Void,
false: False,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
function: x:A 
B[x],
all: x:A. B[x],
axiom: Ax,
primed-class: Prior(X),
empty-bag: {},
bag-only: only(bs),
pair: <a, b>,
single-bag: {x},
natural_number: $n,
bag-size: bag-size(bs),
eq_int: (i = j),
ifthenelse: if b then t else f fi ,
lambda: x.A[x],
eclass-compose2: eclass-compose2(f;X;Y),
es-interface-pair-prior: X;Y,
product: x:A B[x],
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
so_lambda: 
x y.t[x; y],
prop: 
,
sv-class: Singlevalued(X),
member: t T,
isect: 
x:A. B[x],
Auto: Error :Auto,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
squash: 
T,
eclass-val: X(e),
true: True,
cand: A c B,
es-E-interface: E(X),
rev_implies: P Q,
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
cond-class: [X?Y],
eq_knd: a = b,
fpf-dom: x dom(f),
tactic: Error :tactic,
so_apply: x[s1;s2],
pi1: fst(t)
Lemmas :
es-interface-subtype_rel2,
rev_implies_wf,
is-pair-prior,
iff_weakening_uiff,
iff_functionality_wrt_iff,
true_wf,
eclass-val_wf,
assert_functionality_wrt_uiff,
squash_wf,
primed-class-prior-val,
nat_wf,
bag-size_wf,
eq_int_wf,
ifthenelse_wf,
bag_wf,
eclass-compose2_wf,
primed-class_wf,
es-interface-pair-prior_wf,
es-interface-extensionality,
single-bag_wf,
bag-only_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass_wf,
sv-class_wf,
empty-bag_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
permutation_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
assert_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
le_wf,
in-eclass_wf,
false_wf,
top_wf,
es-base-E_wf,
subtype_rel_self,
es-prior-val_wf,
iff_wf
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
X;Y
= eclass-compose2(\mlambda{}ys,xs.
if (bag-size(ys) =\msubz{} 1)
then if (bag-size(xs) =\msubz{} 1) then \{<only(xs), only(ys)>\} else \{\} fi
else \{\}
fi ;Y;Prior(X))
supposing Singlevalued(X)
Date html generated:
2011_08_16-PM-05_39_34
Last ObjectModification:
2011_06_20-AM-01_29_31
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