reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th14:
  for f,g being complex-valued Function holds support(f(#)g) c= support f
  proof
    let f,g be complex-valued Function;
    let x be object;
    assume
A1: x in support(f(#)g);
    (f(#)g).x = f.x * g.x by VALUED_1:5;
    then f.x <> 0 by A1,PRE_POLY:def 7;
    hence thesis by PRE_POLY:def 7;
  end;
