reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th94:
  i divides p implies i = 1 or i = -1 or i = p or i = -p
  proof
    assume
A1: i divides p;
    per cases;
    suppose i >= 0;
      then i in NAT by INT_1:3;
      hence thesis by A1,INT_2:def 4;
    end;
    suppose i < 0;
      then -i in NAT by INT_1:3;
      then -i = 1 or -i = p by A1,INT_2:10,def 4;
      hence thesis;
    end;
  end;
