reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;

theorem Th12:
  for n,m,r being Integer holds
  k in divisors(n,m,r) iff k mod m = r & k divides n
proof
  let n,m,r be Integer;
  hereby
    assume k in divisors(n,m,r);
    then ex i be Nat st k=i & i mod m = r & i divides n;
    hence k mod m = r & k divides n;
  end;
  thus thesis;
end;
