theorem Th65:
  F is having_a_unity & F is associative & F is having_an_inverseOp &
  (F.(d1,d2) = d2 or F.(d2,d1) = d2) implies d1 = the_unity_wrt F
proof
  assume that
A1: F is having_a_unity and
A2: F is associative & F is having_an_inverseOp;
  set e = the_unity_wrt F;
  assume F.(d1,d2) = d2 or F.(d2,d1) = d2;
  then F.(d1,d2) = F.(e,d2) or F.(d2,d1) = F.(d2,e) by A1,SETWISEO:15;
  hence thesis by A1,A2,Th64;
end;
