reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;
reserve A for Abelian addGroup;
reserve a,b for Element of A;
reserve x for object;
reserve y,y1,y2,Y,Z for set;
reserve k for Nat;
reserve G for addGroup;
reserve a,g,h for Element of G;
reserve A for Subset of G;

theorem
  -([#](the carrier of G)) = the carrier of G
proof
  thus -([#](the carrier of G)) c= the carrier of G;
  let x be object;
  assume x in the carrier of G;
  then reconsider a = x as Element of G;
  - -a in ([#](the carrier of G));
  hence thesis;
end;
