reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve p for Prime;
reserve a,b,c,d for Element of GF(p);
reserve K for Ring;
reserve a1,a2,a3,a4,a5,a6 for Element of K;

theorem Th13:
  K is commutative implies
  (a1*a2*a3) |^n = (a1 |^n)*(a2 |^n)*(a3 |^n)
  proof
    assume
A1: K is commutative;
    hence (a1*a2*a3) |^n = ((a1*a2) |^n)*(a3 |^n) by BINOM:9
    .= (a1 |^n)*(a2 |^n)*(a3 |^n) by A1,BINOM:9;
  end;
