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

theorem Th13:
  0 < a & a < 1 implies a^2 < a
proof
  assume that
A1: 0 < a and
A2: a < 1;
  a*a < a*1 by A1,A2,XREAL_1:68;
  hence thesis;
end;
