reserve G for Abelian add-associative right_complementable right_zeroed
  non empty addLoopStr;
reserve GS for non empty addLoopStr;
reserve F for Field;

theorem
  0.F is_a_unity_wrt the addF of F
proof
  now
    let x be Element of F;
    thus (the addF of F).(0.F,x) = x+(0.F) by RLVECT_1:2
      .= x by RLVECT_1:4;
    thus (the addF of F).(x,0.F) = x+(0.F) .= x by RLVECT_1:4;
  end;
  hence thesis by BINOP_1:3;
end;
