reserve x,t,t1,t2,r,a,b for Real;
reserve F,G for real-valued Function;
reserve k for Nat;
reserve i for non zero Integer;

theorem
  F is t1-periodic & F is t2-periodic & t1+t2<>0 implies F is (t1+t2)-periodic
proof
  assume
A1:F is t1-periodic & F is t2-periodic & t1+t2<>0;
   for x st x in dom F holds (x+(t1+t2) in dom F & x-(t1+t2) in dom F)
     & F.x=F.(x+(t1+t2))
      proof
       let x;
       assume
A2:    x in dom F; then
       x+t1 in dom F & x-t1 in dom F by A1,Th1;
       then x+t1+t2 in dom F & x-t1-t2 in dom F
       & F.(x+t1)=F.((x+t1)+t2) by A1,Th1;
       hence thesis by A1,A2;
      end;
   hence thesis by A1,Th1;
end;
