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 Th15:
  for f,g being complex-valued Function st
  support(f) = support(g) holds support(f(#)g) = support f
  proof
    let f,g be complex-valued Function such that
A1: support(f) = support g;
    thus support(f(#)g) c= support f by Th14;
    let x be object;
    assume x in support(f);
    then
A2: f.x <> 0 & g.x <> 0 by A1,PRE_POLY:def 7;
    (f(#)g).x = f.x * g.x by VALUED_1:5;
    hence thesis by A2,PRE_POLY:def 7;
   end;
