{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [L:a:A fp-> B[a] List].
[x:A].
([f:a:A fp-> B[a]]. (
(L)(x) = f(x)) supposing ((
x 
dom(f)) and (f L)))\000C supposing
((f,gL. x:A. (
((x dom(f)) 
(x dom(g))))) and
(x dom((L)))) }
{ Proof }
Definitions occuring in Statement :
fpf-join-list: (L),
fpf-ap: f(x),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
assert: b,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: x:A. B[x],
not: A,
and: P Q,
function: x:A B[x],
list: type List,
universe: Type,
equal: s = t,
l_member: (x l),
deq: EqDecider(T),
pairwise: (x,yL. P[x; y])
Definitions :
nil: [],
cand: A c B,
implies: P 
Q,
pair: <a, b>,
bool: 
,
subtype: S 
T,
lambda: 
x.A[x],
strong-subtype: strong-subtype(A;B),
void: Void,
false: False,
l_exists: (
xL. P[x]),
exists: x:A. B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
set: {x:A| B[x]} ,
le: A 
B,
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
top: Top,
fpf-dom: x dom(f),
axiom: Ax,
fpf-join-list: (L),
fpf-ap: f(x),
member: t T,
deq: EqDecider(T),
list: type List,
uall: [x:A]. B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
equal: s = t,
l_member: (x l),
so_lambda: 
x.t[x],
so_apply: x[s],
apply: f a,
pairwise: (x,yL. P[x; y]),
so_lambda: x y.t[x; y],
all: x:A. B[x],
function: x:A B[x],
not: A,
and: P Q,
product: x:A 
B[x],
assert: b,
prop: 
,
universe: Type,
fpf: a:A fp-> B[a],
limited-type: LimitedType,
nat: 
,
int: 
,
real: 
,
grp_car: |g|,
select: l[i],
union: left + right,
or: P 
Q,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_all: (xL.P[x]),
infix_ap: x f y,
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
l_disjoint: l_disjoint(T;l1;l2),
fset-closed: (s closed under fs),
decidable: Dec(P),
btrue: tt,
true: True,
lelt: i j < k,
int_seg: {i..j
},
natural_number: $n,
length: ||as||,
sq_type: SQType(T),
sqequal: s ~ t,
it: 
,
guard: {T}
Lemmas :
nat_wf,
set_subtype_base,
int_subtype_base,
select_wf,
subtype_base_sq,
product_subtype_base,
list_subtype_base,
squash_wf,
bool_wf,
length_wf_nat,
assert_elim,
true_wf,
ifthenelse_wf,
false_wf,
le_wf,
length_wf1,
decidable__lt,
fpf_wf,
top_wf,
member_wf,
fpf-dom_wf,
assert_wf,
not_wf,
pairwise_wf,
l_member_wf,
fpf-trivial-subtype-top,
subtype_rel_wf,
deq_wf,
uall_wf,
fpf-join-list-ap,
fpf-join-list_wf,
fpf-ap_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[L:a:A fp-> B[a] List]. \mforall{}[x:A].
(\mforall{}[f:a:A fp-> B[a]]. (\moplus{}(L)(x) = f(x)) supposing ((\muparrow{}x \mmember{} dom(f)) and (f \mmember{} L))) supposing
((\mforall{}f,g\mmember{}L. \mforall{}x:A. (\mneg{}((\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}x \mmember{} dom(g))))) and
(\muparrow{}x \mmember{} dom(\moplus{}(L))))
Date html generated:
2011_08_10-AM-08_01_28
Last ObjectModification:
2011_06_18-AM-08_19_58
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