(MAJ_SUM_=_SUM_MAJ)
(MAJ_PROD_=_PROD_MAJ
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-*-2))
 (2 2 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (1 1 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 )
(LEMMA1)
(LEMMA2
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (2 2 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 )
(LEMMA3
 (13 12 (:REWRITE DEFAULT-+-2))
 (13 11 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE DEFAULT-+-1))
 (11 11 (:REWRITE DEFAULT-<-2))
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (4 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 )
(INTERMEDIATE_THEOREM
 (136 136 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (7 2 (:LINEAR X*Y>1-POSITIVE))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(FINAL_THEOREM
 (17 13 (:REWRITE DEFAULT-<-1))
 (16 14 (:REWRITE DEFAULT-+-1))
 (15 14 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-*-2))
 (9 9 (:REWRITE DEFAULT-*-1))
 (3 1 (:LINEAR X*Y>1-POSITIVE))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 )
