A1:
dom f = A
by FUNCT_2:def 1;

rng f c= COMPLEX by NUMBERS:11;

then f is Function of A,COMPLEX by A1, FUNCT_2:2;

hence - f is finite-support ; :: thesis: verum

rng f c= COMPLEX by NUMBERS:11;

then f is Function of A,COMPLEX by A1, FUNCT_2:2;

hence - f is finite-support ; :: thesis: verum