reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  n > 0 implies (a gcd b) gcd b|^n = a gcd b
  proof
    assume n > 0; then
    A2: n >= 1 by NAT_1:14;
    (a gcd b) gcd b|^n = a gcd (b gcd b|^n) by NEWTON:48
    .= a gcd b|^1 by A2,NEWTON:49,89
    .= a gcd b;
    hence thesis;
  end;
