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

theorem Th3:
  i <> -1 & i <> 1 & i divides j implies not i divides j+1
  proof
    assume
A1: i <> -1 & i <> 1;
    assume i divides j & i divides j+1;
    then i divides j+1-j by INT_5:1;
    hence contradiction by A1,INT_2:13;
  end;
