reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th4:
  not p divides n implies n,p are_coprime
  proof
    assume
A1: not p divides n;
    assume not n,p are_coprime;
    then consider q being Prime such that
A2: q divides n and
A3: q divides p by PYTHTRIP:def 2;
    q = p or q = 1 by A3,INT_2:def 4;
    hence contradiction by A1,A2,INT_2:def 4;
  end;
