diff -r b0c81b9a0133 -r e09c53289830 src/HOL/Groebner_Basis.thy --- a/src/HOL/Groebner_Basis.thy Wed Dec 10 17:19:25 2008 +0100 +++ b/src/HOL/Groebner_Basis.thy Thu Dec 11 18:30:26 2008 +0100 @@ -1,5 +1,4 @@ (* Title: HOL/Groebner_Basis.thy - ID: $Id$ Author: Amine Chaieb, TU Muenchen *) @@ -165,7 +164,7 @@ end interpretation class_semiring: gb_semiring - ["op +" "op *" "op ^" "0::'a::{comm_semiring_1, recpower}" "1"] + "op +" "op *" "op ^" "0::'a::{comm_semiring_1, recpower}" "1" proof qed (auto simp add: ring_simps power_Suc) lemmas nat_arith = @@ -242,8 +241,8 @@ end -interpretation class_ring: gb_ring ["op +" "op *" "op ^" - "0::'a::{comm_semiring_1,recpower,number_ring}" 1 "op -" "uminus"] +interpretation class_ring: gb_ring "op +" "op *" "op ^" + "0::'a::{comm_semiring_1,recpower,number_ring}" 1 "op -" "uminus" proof qed simp_all @@ -344,7 +343,7 @@ qed interpretation class_ringb: ringb - ["op +" "op *" "op ^" "0::'a::{idom,recpower,number_ring}" "1" "op -" "uminus"] + "op +" "op *" "op ^" "0::'a::{idom,recpower,number_ring}" "1" "op -" "uminus" proof(unfold_locales, simp add: ring_simps power_Suc, auto) fix w x y z ::"'a::{idom,recpower,number_ring}" assume p: "w * y + x * z = w * z + x * y" and ynz: "y \ z" @@ -360,7 +359,7 @@ declaration {* normalizer_funs @{thm class_ringb.ringb_axioms'} *} interpretation natgb: semiringb - ["op +" "op *" "op ^" "0::nat" "1"] + "op +" "op *" "op ^" "0::nat" "1" proof (unfold_locales, simp add: ring_simps power_Suc) fix w x y z ::"nat" { assume p: "w * y + x * z = w * z + x * y" and ynz: "y \ z" @@ -465,7 +464,7 @@ subsection{* Groebner Bases for fields *} interpretation class_fieldgb: - fieldgb["op +" "op *" "op ^" "0::'a::{field,recpower,number_ring}" "1" "op -" "uminus" "op /" "inverse"] apply (unfold_locales) by (simp_all add: divide_inverse) + fieldgb "op +" "op *" "op ^" "0::'a::{field,recpower,number_ring}" "1" "op -" "uminus" "op /" "inverse" apply (unfold_locales) by (simp_all add: divide_inverse) lemma divide_Numeral1: "(x::'a::{field,number_ring}) / Numeral1 = x" by simp lemma divide_Numeral0: "(x::'a::{field,number_ring, division_by_zero}) / Numeral0 = 0"