author huffman Thu, 17 May 2007 08:53:57 +0200 changeset 22988 f6b8184f5b4a parent 22987 550709aa8e66 child 22989 3bcbe6187027
generalize some lemmas from field to division_ring
 src/HOL/Power.thy file | annotate | diff | comparison | revisions
```--- a/src/HOL/Power.thy	Thu May 17 08:42:51 2007 +0200
+++ b/src/HOL/Power.thy	Thu May 17 08:53:57 2007 +0200
@@ -147,18 +147,18 @@
done

lemma field_power_eq_0_iff [simp]:
-     "(a^n = 0) = (a = (0::'a::{field,recpower}) & 0<n)"
+     "(a^n = 0) = (a = (0::'a::{division_ring,recpower}) & 0<n)"
apply (induct "n")
apply (auto simp add: power_Suc field_mult_eq_0_iff zero_neq_one[THEN not_sym])
done

-lemma field_power_not_zero: "a \<noteq> (0::'a::{field,recpower}) ==> a^n \<noteq> 0"
+lemma field_power_not_zero: "a \<noteq> (0::'a::{division_ring,recpower}) ==> a^n \<noteq> 0"
by force

lemma nonzero_power_inverse:
-  "a \<noteq> 0 ==> inverse ((a::'a::{field,recpower}) ^ n) = (inverse a) ^ n"
+  "a \<noteq> 0 ==> inverse ((a::'a::{division_ring,recpower}) ^ n) = (inverse a) ^ n"
apply (induct "n")
-apply (auto simp add: power_Suc nonzero_inverse_mult_distrib mult_commute)
+apply (auto simp add: power_Suc nonzero_inverse_mult_distrib power_commutes)
done

text{*Perhaps these should be simprules.*}```