 reserve i,j,k,m,n,m1,n1 for Nat;
 reserve a,r,r1,r2 for Real;
 reserve m0,cn,cd for Integer;
 reserve x1,x2,o for object;

theorem Th13:
  r is irrational implies
    (c_d(r).(n+1)*(c_d(r).(n+1)*rfs(r).(n+2) + c_d(r).n)) > 0
  proof
    assume
A1: r is irrational; then
A2: c_d(r).(n+1) >=1 by Th8;
    (c_d(r).(n+1)*rfs(r).(n+2) + c_d(r).n) > 0 by A1,Th12;
    hence thesis by A2;
  end;
