 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 Th5:
  r is irrational implies 0 < scf(r).(n+1)
  proof
    assume
A1: r is irrational;
A2: rfs(r).(n +1)-1 > 1-1 by A1,Th4,XREAL_1:14;
    rfs(r).(n +1) < scf(r).(n +1) + 1 by A1,Th4; then
    rfs(r).(n +1) -1 < scf(r).(n +1) + 1 -1 by XREAL_1:14;
    hence thesis by A2;
  end;
