reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th59:
  i <> 1 & i <> -1 implies for m being Multiple of i st m is prime holds
  m = i or m = -i
  proof
    assume that
A1: i <> 1 and
A2: i <> -1;
    let m be Multiple of i such that
A3: m is prime;
    per cases;
    suppose i >= 0;
      then i in NAT by INT_1:3;
      hence thesis by A1,A3,Def15;
    end;
    suppose i < 0;
      then
A4:   -i in NAT by INT_1:3;
      -i divides m by Def15,INT_2:10;
      then -i = 1 or -i = m by A3,A4;
      hence thesis by A2;
    end;
  end;
