reserve x,x1,x2,x3 for Real;

theorem
  x >= 0 implies sinh x >= 0
proof
  assume
A1: x >= 0;
  per cases by A1,XXREAL_0:1;
  suppose
    x > 0;
    hence thesis by Lm4;
  end;
  suppose
    x = 0;
    hence thesis by SIN_COS2:16,def 2;
  end;
end;
