src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy
 changeset 41814 3848eb635eab parent 41813 4eb43410d2fa child 41815 9a0cacbcd825
```     1.1 --- a/src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy	Mon Feb 21 23:14:36 2011 +0100
1.2 +++ b/src/HOL/Decision_Procs/Reflected_Multivariate_Polynomial.thy	Mon Feb 21 23:14:36 2011 +0100
1.3 @@ -107,12 +107,6 @@
1.4  subsection{* Operations for normalization *}
1.5
1.6
1.7 -consts
1.8 -  polysub :: "poly\<times>poly \<Rightarrow> poly"
1.9 -
1.10 -abbreviation poly_sub :: "poly \<Rightarrow> poly \<Rightarrow> poly" (infixl "-\<^sub>p" 60)
1.11 -  where "a -\<^sub>p b \<equiv> polysub (a,b)"
1.12 -
1.13  declare if_cong[fundef_cong del]
1.14  declare let_cong[fundef_cong del]
1.15
1.16 @@ -136,8 +130,9 @@
1.17  | "polyneg (CN c n p) = CN (polyneg c) n (polyneg p)"
1.18  | "polyneg a = Neg a"
1.19
1.20 -defs polysub_def[code]: "polysub \<equiv> \<lambda> (p,q). polyadd p (polyneg q)"
1.21 -
1.22 +definition polysub :: "poly \<Rightarrow> poly \<Rightarrow> poly" (infixl "-\<^sub>p" 60)
1.23 +where
1.24 +  "p -\<^sub>p q = polyadd p (polyneg q)"
1.25
1.26  fun polymul :: "poly \<Rightarrow> poly \<Rightarrow> poly" (infixl "*\<^sub>p" 60)
1.27  where
1.28 @@ -592,15 +587,15 @@
1.29
1.30  text{* polysub is a substraction and preserves normal forms *}
1.31
1.32 -lemma polysub[simp]: "Ipoly bs (polysub (p,q)) = (Ipoly bs p) - (Ipoly bs q)"
1.33 +lemma polysub[simp]: "Ipoly bs (polysub p q) = (Ipoly bs p) - (Ipoly bs q)"
1.35 -lemma polysub_normh: "\<And> n0 n1. \<lbrakk> isnpolyh p n0 ; isnpolyh q n1\<rbrakk> \<Longrightarrow> isnpolyh (polysub(p,q)) (min n0 n1)"
1.36 +lemma polysub_normh: "\<And> n0 n1. \<lbrakk> isnpolyh p n0 ; isnpolyh q n1\<rbrakk> \<Longrightarrow> isnpolyh (polysub p q) (min n0 n1)"