theorem
  F is associative & F is having_a_unity & F is having_an_inverseOp
  implies (F*(id D,the_inverseOp_wrt F)).(d,d) = the_unity_wrt F
proof
  assume
A1: F is associative & F is having_a_unity & F is having_an_inverseOp;
  set u = the_inverseOp_wrt F;
  thus F*(id D,u).(d,d) = F.(d,u.d) by Th81
    .= the_unity_wrt F by A1,Th59;
end;
