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;

theorem Th22:
  add_inverse(G) is_an_inverseOp_wrt the addF of G
proof
  let h be Element of G;
  thus (the addF of G).(h,add_inverse(G).h) = h + -h by Def6
    .= 0_G by Def5
    .= the_unity_wrt the addF of G by Th21;
  thus (the addF of G).(add_inverse(G).h,h) = -h + h by Def6
    .= 0_G by Def5
    .= the_unity_wrt the addF of G by Th21;
end;
