<s>
In	O
mathematical	O
logic	O
,	O
the	O
Scott	B-Application
–	I-Application
Curry	I-Application
theorem	I-Application
is	O
a	O
result	O
in	O
lambda	B-Language
calculus	I-Language
stating	O
that	O
if	O
two	O
non-empty	O
sets	O
of	O
lambda	O
terms	O
A	O
and	O
B	O
are	O
closed	O
under	O
beta-convertibility	O
then	O
they	O
are	O
recursively	O
inseparable	O
.	O
</s>
<s>
The	O
Scott	B-Application
–	I-Application
Curry	I-Application
theorem	I-Application
applies	O
equally	O
to	O
sets	O
of	O
terms	O
in	O
combinatory	B-Application
logic	I-Application
with	O
weak	O
equality	O
.	O
</s>
<s>
The	O
proof	O
is	O
adapted	O
from	O
Barendregt	O
in	O
The	O
Lambda	B-Language
Calculus	I-Language
.	O
</s>
