reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th14:
  for i,j,k being Integer st
  i divides j & i,j are_coprime holds i = 1 or i = -1
  proof
    let i,j,k be Integer;
    assume i divides j;
    then
A1: |.i.| divides |.j.| by INT_2:16;
    assume i,j are_coprime;
    then |.i.|,|.j.| are_coprime by INT_2:34;
    then
A2: |.i.| = 1 by A1,PYTHTRIP:def 1;
    |.i.| = i or |.i.| = -i by COMPLEX1:71;
    hence i = 1 or i = -1 by A2;
  end;
