theorem
  0c*z = 0c n
proof
A1: rng z c= COMPLEX;
  thus 0c*z = multcomplex[;](0c,(id COMPLEX)*z) by FUNCOP_1:34
    .= multcomplex[;](0c,z) by A1,RELAT_1:53
    .= 0c n by Th51,Th54,BINOP_2:1,FINSEQOP:76;
end;
