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 Th77:
  a divides k*(a*n+1) iff a divides k
  proof
    a divides k*(a*n+1) implies a divides k
    proof
      assume a divides k*(a*n+1); then
      A1: a divides k*a*n + k*1;
      a divides a*(k*n);
      hence thesis by A1,INT_2:1;
    end;
    hence thesis by INT_2:2;
  end;
