reserve x for Real;

theorem
  for a being Real st 0 <= a & a < 2*PI & cos(a) = 1 holds a = 0
proof
  let a be Real such that
A1: 0 <= a & a < 2*PI and
A2: cos(a) = 1;
  1*1+(sin a)*(sin a) = 1 by A2,SIN_COS:29;
  then sin a = 0;
  hence thesis by A1,A2,Th17,SIN_COS:77;
end;
