
theorem CoprimeDivides:  :: see WSIERP_1:16
  for a,m,n being Nat st a,m are_coprime & n divides a holds
    n,m are_coprime
  proof
    let a,m,n be Nat;
    assume
A1: a,m are_coprime & n divides a;
    assume not n,m are_coprime; then
    consider k being Nat such that
A2: k divides n & k divides m & k <> 1 by PYTHTRIP:def 1;
    k divides a by A1,A2,INT_2:9; then
    k divides (a gcd m) by A2,INT_2:def 2;
    hence thesis by A2,A1,WSIERP_1:15;
  end;
