src/HOL/Groebner_Basis.thy
 changeset 29667 53103fc8ffa3 parent 29233 ce6d35a0bed6 child 30027 ab40c5e007e0 child 30240 5b25fee0362c
```     1.1 --- a/src/HOL/Groebner_Basis.thy	Sun Jan 18 13:58:17 2009 +0100
1.2 +++ b/src/HOL/Groebner_Basis.thy	Wed Jan 28 16:29:16 2009 +0100
1.3 @@ -165,7 +165,7 @@
1.4
1.5  interpretation class_semiring!: gb_semiring
1.6      "op +" "op *" "op ^" "0::'a::{comm_semiring_1, recpower}" "1"
1.7 -  proof qed (auto simp add: ring_simps power_Suc)
1.8 +  proof qed (auto simp add: algebra_simps power_Suc)
1.9
1.10  lemmas nat_arith =
1.12 @@ -345,13 +345,13 @@
1.13
1.14  interpretation class_ringb!: ringb
1.15    "op +" "op *" "op ^" "0::'a::{idom,recpower,number_ring}" "1" "op -" "uminus"
1.16 -proof(unfold_locales, simp add: ring_simps power_Suc, auto)
1.17 +proof(unfold_locales, simp add: algebra_simps power_Suc, auto)
1.18    fix w x y z ::"'a::{idom,recpower,number_ring}"
1.19    assume p: "w * y + x * z = w * z + x * y" and ynz: "y \<noteq> z"
1.20    hence ynz': "y - z \<noteq> 0" by simp
1.21    from p have "w * y + x* z - w*z - x*y = 0" by simp
1.22 -  hence "w* (y - z) - x * (y - z) = 0" by (simp add: ring_simps)
1.23 -  hence "(y - z) * (w - x) = 0" by (simp add: ring_simps)
1.24 +  hence "w* (y - z) - x * (y - z) = 0" by (simp add: algebra_simps)
1.25 +  hence "(y - z) * (w - x) = 0" by (simp add: algebra_simps)
1.26    with  no_zero_divirors_neq0 [OF ynz']
1.27    have "w - x = 0" by blast
1.28    thus "w = x"  by simp
1.29 @@ -361,20 +361,20 @@
1.30
1.31  interpretation natgb!: semiringb
1.32    "op +" "op *" "op ^" "0::nat" "1"
1.33 -proof (unfold_locales, simp add: ring_simps power_Suc)
1.34 +proof (unfold_locales, simp add: algebra_simps power_Suc)
1.35    fix w x y z ::"nat"
1.36    { assume p: "w * y + x * z = w * z + x * y" and ynz: "y \<noteq> z"
1.37      hence "y < z \<or> y > z" by arith
1.38      moreover {
1.39        assume lt:"y <z" hence "\<exists>k. z = y + k \<and> k > 0" by (rule_tac x="z - y" in exI, auto)
1.40        then obtain k where kp: "k>0" and yz:"z = y + k" by blast
1.41 -      from p have "(w * y + x *y) + x*k = (w * y + x*y) + w*k" by (simp add: yz ring_simps)
1.42 +      from p have "(w * y + x *y) + x*k = (w * y + x*y) + w*k" by (simp add: yz algebra_simps)
1.43        hence "x*k = w*k" by simp
1.44        hence "w = x" using kp by (simp add: mult_cancel2) }
1.45      moreover {
1.46        assume lt: "y >z" hence "\<exists>k. y = z + k \<and> k>0" by (rule_tac x="y - z" in exI, auto)
1.47        then obtain k where kp: "k>0" and yz:"y = z + k" by blast
1.48 -      from p have "(w * z + x *z) + w*k = (w * z + x*z) + x*k" by (simp add: yz ring_simps)
1.49 +      from p have "(w * z + x *z) + w*k = (w * z + x*z) + x*k" by (simp add: yz algebra_simps)
1.50        hence "w*k = x*k" by simp
1.51        hence "w = x" using kp by (simp add: mult_cancel2)}
1.52      ultimately have "w=x" by blast }
```