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

theorem Th5:
  1_F is_a_unity_wrt the multF of F
proof
  now
    let x be Element of F;
    thus (the multF of F).(1_F,x) = (1_F)*x .= x;
    thus (the multF of F).(x,1_F) = x*(1_F) .= x;
  end;
  hence thesis by BINOP_1:3;
end;
