reserve a,b,d,n,k,i,j,x,s for Nat;

theorem Th8:
  Fib(n+2) >= n
proof
  defpred P[Nat] means Fib($1+2) >= $1;
A1: P[0];
A2: for n st P[n] holds P[n+1]
  proof
    let n such that A3:P[n];
    n+2 > 1+0 by XREAL_1:8;
    then Fib(n+2+1)>= Fib(n+2)+1 >= n+1 by A3,FIB_NUM2:44,NAT_1:13,XREAL_1:7;
    hence thesis by XXREAL_0:2;
  end;
  for n holds P[n] from NAT_1:sch 2(A1,A2);
  hence thesis;
end;
