reserve f,f1,f2,g for PartFunc of REAL,REAL;
reserve A for non empty closed_interval Subset of REAL;
reserve p,r,x,x0 for Real;
reserve n for Element of NAT;
reserve Z for open Subset of REAL;

theorem Th1:
  sin(x + 2 * n * PI) = sin x
proof
  sin.x = sin.(2*PI*n + x) by SIN_COS2:10;
  hence thesis;
end;
