{ 
[A:Type]. [eq:EqDecider(A)]. [f,g:a:A fp-> Top]. [L:A List].
uiff(l_disjoint(A;fst(f 
g);L);l_disjoint(A;fst(f);L)
l_disjoint(A;fst(g);L)) }
{ Proof }
Definitions occuring in Statement :
fpf-join: f g,
fpf: a:A fp-> B[a],
uiff: uiff(P;Q),
uall: [x:A]. B[x],
top: Top,
pi1: fst(t),
and: P Q,
list: type List,
universe: Type,
l_disjoint: l_disjoint(T;l1;l2),
deq: EqDecider(T)
Definitions :
l_intersection: l_intersection(eq;L1;L2),
append: as @ bs,
cons: [car / cdr],
nil: [],
cand: A c B,
apply: f a,
so_apply: x[s],
union: left + right,
or: P 
Q,
rev_implies: P 
Q,
fpf-join: f g,
subtype: S 
T,
guard: {T},
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
less_than: a < b,
subtype_rel: A r B,
pi1: fst(t),
iff: P 
Q,
l_member: (x 
l),
prop: 
,
pair: <a, b>,
void: Void,
false: False,
implies: P Q,
not: 
A,
l_disjoint: l_disjoint(T;l1;l2),
uimplies: b supposing a,
and: P Q,
uiff: uiff(P;Q),
list: type List,
product: x:A 
B[x],
lambda: 
x.A[x],
set: {x:A| B[x]} ,
assert: 
b,
all: x:A. B[x],
function: x:A 
B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
so_lambda: 
x.t[x],
top: Top,
universe: Type,
member: t T,
deq: EqDecider(T),
equal: s = t,
tactic: Error :tactic,
btrue: tt,
sq_type: SQType(T),
bool: 
,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
fpf-dom: x dom(f),
tag-by: zT,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
b-union: A 
B,
fpf-sub: f g,
fpf-cap: f(x)?z
Lemmas :
false_wf,
ifthenelse_wf,
true_wf,
fpf-join-dom,
subtype_base_sq,
bool_subtype_base,
bool_wf,
assert_elim,
assert_wf,
fpf-dom_wf,
l_disjoint-fpf-dom,
member_wf,
top_wf,
fpf_wf,
fpf-trivial-subtype-top,
subtype_rel_wf,
l_member_wf,
pi1_wf_top,
l_disjoint_wf,
uiff_wf,
deq_wf,
fpf-join_wf,
not_wf,
rev_implies_wf,
iff_wf,
uiff_inversion
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Top]. \mforall{}[L:A List].
uiff(l\_disjoint(A;fst(f \moplus{} g);L);l\_disjoint(A;fst(f);L) \mwedge{} l\_disjoint(A;fst(g);L))
Date html generated:
2011_08_10-AM-08_11_25
Last ObjectModification:
2011_06_18-AM-08_26_50
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