reserve a,b,c,x,y,z for Real;

theorem Th26:
  0 <= x & x <= y implies sqrt x <= sqrt y
proof
  per cases;
  suppose
    x = y;
    hence thesis;
  end;
  suppose
A1: x <> y;
    assume
A2: 0 <= x;
    assume x <= y;
    then x < y by A1,XXREAL_0:1;
    hence thesis by A2,Lm3;
  end;
end;
