reserve r,r1,r2, s,x for Real,
  i for Integer;

theorem Th104:
  -1 <= r & r <= 1 implies sin arccos r = sqrt(1-r^2)
proof
  set s = sqrt(1-r^2);
  assume -1 <= r & r <= 1;
  then r^2+0 <= 1^2 by SQUARE_1:49;
  then 0 <= 1-r^2 by XREAL_1:19;
  then 0 <= s & r^2 + s^2 = r^2 + (1-r^2) by SQUARE_1:def 2;
  hence thesis by Th102;
end;
