 reserve m,n for Nat;
 reserve i,j for Integer;
 reserve S for non empty multMagma;
 reserve r,r1,r2,s,s1,s2,t for Element of S;
 reserve G for Group-like non empty multMagma;
 reserve e,h for Element of G;
 reserve G for Group;
 reserve f,g,h for Element of G;

theorem Th16:
  (h * g)" = g" * h"
proof
  (g" * h") * (h * g) = g" * h" * h * g by Def3
    .= g" * (h" * h) * g by Def3
    .= g" * 1_G * g by Def5
    .= g" * g by Def4
    .= 1_G by Def5;
  hence thesis by Th11;
end;
