consider r2 being Element of REAL such that
A7: for c being Element of C st c in dom f2 holds
f2 . c = r2 by PARTFUN2:def 1;
consider r1 being Element of REAL such that
A8: for c being Element of C st c in dom f1 holds
f1 . c = r1 by PARTFUN2:def 1;

now :: thesis: for c being Element of C st c in dom (f1 - f2) holds
(f1 - f2) . c = r1 - r2

let c be Element of C; :: thesis: ( c in dom (f1 - f2) implies (f1 - f2) . c = r1 - r2 )
assume A9: c in dom (f1 - f2) ; :: thesis: (f1 - f2) . c = r1 - r2
then A10: c in (dom f1) /\ (dom f2) by VALUED_1:12;
then A11: c in dom f1 by XBOOLE_0:def 4;
A12: c in dom f2 by A10, XBOOLE_0:def 4;
thus (f1 - f2) . c = (f1 . c) - (f2 . c) by A9, VALUED_1:13
.= (f1 . c) - r2 by A7, A12
.= r1 - r2 by A8, A11 ; :: thesis: verum

end;

hence f1 - f2 is constant by PARTFUN2:def 1; :: thesis: verum