reserve i1 for Element of INT;
reserve j1,j2,j3 for Integer;
reserve p,s,k,n for Nat;
reserve x,y,xp,yp for set;
reserve G for Group;
reserve a,b for Element of G;
reserve F for FinSequence of G;
reserve I for FinSequence of INT;

theorem Th16:
  j1 = (@'1) |^ j1
proof
  consider k being Nat such that
A1: j1 = k or j1 = -k by INT_1:2;
  per cases by A1;
  suppose
    j1=k;
    hence thesis by Lm4;
  end;
  suppose
A2: j1=-k;
    reconsider k9=k as Integer;
    reconsider k9 as Element of INT.Group by INT_1:def 2;
    (@'1)|^j1 = ((@'1)|^k)" by A2,GROUP_1:36
      .= (k9)" by Lm4
      .= j1 by A2,Th15;
    hence thesis;
  end;
end;
