theorem
  F is associative & F is having_a_unity & F is having_an_inverseOp
  implies (F*(id D,the_inverseOp_wrt F)).(d,the_unity_wrt F) = d
proof
  assume that
A1: F is associative and
A2: F is having_a_unity and
A3: F is having_an_inverseOp;
  set u = the_inverseOp_wrt F, e = the_unity_wrt F;
  thus (F*(id D,u)).(d,e) = F.(d,u.e) by Th81
    .= F.(d,e) by A1,A2,A3,Th61
    .= d by A2,SETWISEO:15;
end;
