 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;
 reserve u for UnOp of G;

theorem
  g * h = h * g implies g * (h |^ i) = h |^ i * g
proof
  assume
A1: g * h = h * g;
  thus g * (h |^ i) = g |^ 1 * (h |^ i) by Th25
    .= h |^ i * (g |^ 1) by A1,Th38
    .= h |^ i * g by Th25;
end;
