reserve a,b,c,k,l,m,n for Nat,
  i,j,x,y for Integer;

theorem Th13:
  c divides a*b & a,c are_coprime implies c divides b
proof
  assume that
A1: c divides a*b and
A2: a,c are_coprime;
A3: c divides c*b by NAT_D:9;
  a gcd c = 1 by A2,INT_2:def 3;
  then (a*b gcd c*b) = b by Th5;
  hence thesis by A1,A3,NEWTON:50;
end;
