<s>
In	O
mathematical	O
logic	O
,	O
the	O
cut	B-Application
rule	I-Application
is	O
an	O
inference	O
rule	O
of	O
sequent	O
calculus	O
.	O
</s>
<s>
The	O
cut	B-Application
rule	I-Application
is	O
the	O
subject	O
of	O
an	O
important	O
theorem	O
,	O
the	O
cut	O
elimination	O
theorem	O
.	O
</s>
<s>
It	O
states	O
that	O
any	O
judgement	O
that	O
possesses	O
a	O
proof	O
in	O
the	O
sequent	O
calculus	O
that	O
makes	O
use	O
of	O
the	O
cut	B-Application
rule	I-Application
also	O
possesses	O
a	O
cut-free	O
proof	O
,	O
that	O
is	O
,	O
a	O
proof	O
that	O
does	O
not	O
make	O
use	O
of	O
the	O
cut	B-Application
rule	I-Application
.	O
</s>
