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 Th73:
  t,z|^n are_coprime & n > 0 implies t,z are_coprime
  proof
    assume
    A1: t,z|^n are_coprime & n > 0; then
    A2: t divides t|^n & z divides z|^n by Th6;
    t gcd z divides t & t gcd z divides z by INT_2:def 2; then
    A3: t gcd z divides t|^n & t gcd z divides z|^n by A2,INT_2:2;
    t|^n, z|^n are_coprime by A1,WSIERP_1:10;
    hence thesis by A3,INT_2:13,22;
  end;
