
theorem Th1:
  for r,s being Real holds 0 <= r & s*s < r*r implies s < r
proof
  let r,s be Real;
  assume that
A1: 0<=r and
A2: s*s<r*r;
  assume s>=r;
  then r*s<=s*s & r*r<=s*r by A1,XREAL_1:64;
  hence contradiction by A2,XXREAL_0:2;
end;
