reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem
  m <> 0 & p|^m divides a*b implies p divides a or p divides b
  proof
    assume that
A1: m <> 0 and
A2: p|^m divides a*b;
    p divides p|^m by A1,NAT_3:3;
    then p divides a*b by A2,INT_2:9;
    hence thesis by INT_5:7;
  end;
