anchor.diff:   	   :use ((:instance split-phi-2n+1)
   		 (:instance delta-<-0)
   		 (:instance except-for-delta-<-0)))))
  -
  -(defthm phi-2n+1-<-0-inductive-corollary
  -  (implies (basic-params (- i 1) 3 v0 dv g1 phi0
  -			 (< (phi-2n-1 (- i 1) phi0 v0 dv g1) 0))
  -	   (< (phi-2n-1 i phi0 v0 dv g1) 0))
  -  :hints (("Goal"
  -	   :use ((:instance phi-2n+1-<-0-inductive
  -			    (n (- i 1)))))))
  -
  -(defthm phi-2n+1-<-0-inductive-corollary-2
  -  (implies (basic-params (- i 1) 3 v0 dv g1 phi0
  -			 (< (phi-2n-1 (- i 1) phi0 v0 dv g1) 0))
  -	   (< (+ (A i phi0 v0 dv g1)
  -		 (* (B-expt i)
  -		    (B-sum 1 (- i 2) v0 dv g1))) 0))
  -  :hints (("Goal"
  -	   :use ((:instance phi-2n+1-<-0-inductive-corollary)))))
  -
   
   (defthm phi-2n+1-<-0-base-lemma
     (IMPLIES (AND (RATIONALP V0)
  
positive.code: 	   (< (phi-2n-1 n phi0 v0 dv g1) 0))
    :hints (("Goal"
  	   :use ((:instance phi-2n+1-<-0
  			    (i n))))))
  )
  
negative.code:            :use ((:instance phi-2n+1-<-0-base-lemma))))
    )
  
  (skip-proofs
   (defthm phi-2n+1-<-0-lemma
    (implies (and (implies (basic-params n 3 v0 dv g1 phi0
                                         (< (phi-2n-1 n phi0 v0 dv g1) 0))
                           (< (phi-2n-1 (1+ n) phi0 v0 dv g1) 0))
                  (implies (basic-params-equal n 2 v0 dv g1 phi0)
                           (< (phi-2n-1 (1+ n) phi0 v0 dv g1) 0)))
             (implies (basic-params n 2 v0 dv g1 phi0)
                      (< (phi-2n-1 (1+ n) phi0 v0 dv g1) 0))))
   )
  
  (defthm phi-2n+1-<-0
    (implies (basic-params n 2 v0 dv g1 phi0)
  	   (< (phi-2n-1 (1+ n) phi0 v0 dv g1) 0))
    :hints (("Goal"
             :do-not '(simplify)
             :use ((:instance phi-2n+1-<-0-lemma)
                   (:instance phi-2n+1-<-0-base)
                   (:instance phi-2n+1-<-0-inductive))
  	   ))
    )
  
  