
theorem Th10:
  for a,b,c be Integer st c <>0 & a = b mod c & b,c are_coprime
  holds a,c are_coprime
  proof
    let a,b,c be Integer;
    assume A1: c <>0 & a = b mod c & b,c are_coprime; then
    b gcd c = 1 by INT_2:def 3;
    then
    a gcd c = 1 by A1,Th8,WSIERP_1:43;
    hence thesis by INT_2:def 3;
  end;
