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

theorem
  a^2 < 1 implies -1 < a & a < 1
proof
  assume a^2<1;
  then a^2-1^2<1^2-1^2 by XREAL_1:9;
  then (a-1)*(a+1)<0;
  hence thesis by XREAL_1:94;
end;
