reserve x1,x2,z for set;
reserve A,B for non empty set;
reserve f,g,h for Element of Funcs(A,COMPLEX);
reserve a,b for Complex;
reserve C for strict non empty CLSStruct,
        u,v,w for Element of C;

theorem
  CRing(A) is commutative Ring
proof
  for x,y,z being Element of CRing(A) holds x+y = y+x & (x+y)+z = x+(y+z)
& x+(0.CRing(A)) = x & x is right_complementable & x*y = y*x & (x*y)*z = x*(y*z
) & x*(1.CRing(A)) = x & (1.CRing(A))*x = x & x*(y+z) = x*y + x*z & (y+z)*x = y
  *x + z*x by Th24;
  hence thesis by ALGSTR_0:def 16,GROUP_1:def 3,def 12,RLVECT_1:def 2,def 3
,def 4,VECTSP_1:def 6,def 7;
end;
