 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem Canonical: ::: squarefree-decompose
  for n being non zero Nat holds
    n = (SquarefreePart n) * (SqF n) ^2
  proof
    let n be non zero Nat;
    (SqF n) |^ 2 divides n by Skup; then
    TSqF n divides n by Cosik; then
    n = (TSqF n) * (n div TSqF n) by NAT_D:3
     .= ((SqF n) |^2) * (n div TSqF n) by Cosik
     .= ((SqF n) ^2) * (n div TSqF n) by NEWTON:81;
    hence thesis;
  end;
