(NATP-FC-1)
(NATP-FC-2)
(POSP-FC-1)
(POSP-FC-2)
(NATP-RW)
(POSP-RW)
(NATP-POSP)
(|(posp (+ c x))|
 (6 1 (:REWRITE NATP-POSP))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NATP-RW))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 )
(|(natp (+ c x))|
 (6 5 (:REWRITE DEFAULT-+-2))
 (6 1 (:REWRITE NATP-POSP))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE |(posp (+ c x))|))
 )
(|(natp (* x y))|
 (29 5 (:REWRITE NATP-RW))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:REWRITE DEFAULT-*-1))
 )
(|(natp (* x y)) backchaining|)
(|(posp (* x y))|
 (75 5 (:REWRITE NATP-POSP))
 (35 35 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE DEFAULT-<-1))
 (32 6 (:DEFINITION NATP))
 (30 6 (:REWRITE NATP-RW))
 (29 5 (:REWRITE POSP-RW))
 (28 2 (:REWRITE <-*-0))
 (12 4 (:REWRITE <-MINUS-ZERO))
 (8 1 (:REWRITE |(natp (* x y)) backchaining|))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE |(natp (* x y))|))
 )
(|(posp (* x y)) backchaining|)
(|x < y  =>  0 < -x+y|
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE |(posp (+ c x))|))
 (1 1 (:REWRITE |(natp (+ c x))|))
 )
(|x < y  =>  0 < y-x|
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(|x < y  =>  0 <= -x+y|
 (24 24 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE |(natp (+ c x))|))
 )
(|x < y  =>  0 <= y-x|
 (20 20 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
