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 Th13:
  F is t-periodic implies for x st x in dom F holds F.x=F.(x-t)
proof
  assume
A1: F is t-periodic;
    let x;
    assume x in dom F; then
    x+t in dom F & x-t in dom F by A1,Th1;
    then F.(x-t)=F.(x-t+t) by A1
                       .=F.x;
    hence thesis;
end;
