reserve x1,x2,z for set;
reserve A,B for non empty set;
reserve f,g,h for Element of Funcs(A,REAL);
reserve a,b for Real;

theorem
  RRing(A) is commutative Ring
proof
A1: RRing A is Abelian by Th25;
A2: RRing A is add-associative by Th25;
A3: RRing A is right_complementable
  proof
    let x be Element of RRing A;
    consider t being Element of RRing A such that
A4: x+t = 0.RRing(A) by Th25;
    take t;
    thus thesis by A4;
  end;
A5: RRing A is right_zeroed by Th25;
A6: RRing A is distributive by Th25;
A7: RRing A is well-unital by Th25;
A8: RRing A is associative by Th25;
  RRing A is commutative by Th25;
  hence thesis by A1,A2,A5,A3,A8,A7,A6;
end;
