{ 
[T:Type]. [eq:EqDecider(T)]. [a,b,c:T List].
l_disjoint(T;a;l_intersection(eq;b;c))
supposing l_disjoint(T;a;b) 
l_disjoint(T;a;c) }
{ Proof }
Definitions occuring in Statement :
l_intersection: l_intersection(eq;L1;L2),
uimplies: b supposing a,
uall: [x:A]. B[x],
or: P Q,
list: type List,
universe: Type,
l_disjoint: l_disjoint(T;l1;l2),
deq: EqDecider(T)
Definitions :
guard: {T},
rev_implies: P 
Q,
iff: P 
Q,
l_intersection: l_intersection(eq;L1;L2),
strong-subtype: strong-subtype(A;B),
equal: s = t,
le: A 
B,
ge: i 
j ,
less_than: a < b,
uiff: uiff(P;Q),
assert: 
b,
set: {x:A| B[x]} ,
subtype_rel: A 
r B,
l_member: (x 
l),
product: x:A 
B[x],
and: P 
Q,
lambda: 
x.A[x],
prop: 
,
universe: Type,
l_disjoint: l_disjoint(T;l1;l2),
all: x:A. B[x],
not: 
A,
implies: P Q,
function: x:A 
B[x],
false: False,
void: Void,
deq: EqDecider(T),
uall: [x:A]. B[x],
list: type List,
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t T,
or: P Q,
union: left + right,
ParallelOp: Error :ParallelOp,
THENM: Error :THENM,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
not_wf,
l_member_wf,
deq_wf,
iff_weakening_uiff,
l_intersection_wf,
l_disjoint_intersection,
l_disjoint_wf,
l_disjoint-symmetry
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a,b,c:T List].
l\_disjoint(T;a;l\_intersection(eq;b;c)) supposing l\_disjoint(T;a;b) \mvee{} l\_disjoint(T;a;c)
Date html generated:
2011_08_10-AM-07_49_04
Last ObjectModification:
2011_06_18-AM-08_13_22
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