generalize some lemmas from field to division_ring
authorhuffman
Thu May 17 08:53:57 2007 +0200 (2007-05-17)
changeset 22988f6b8184f5b4a
parent 22987 550709aa8e66
child 22989 3bcbe6187027
generalize some lemmas from field to division_ring
src/HOL/Power.thy
     1.1 --- a/src/HOL/Power.thy	Thu May 17 08:42:51 2007 +0200
     1.2 +++ b/src/HOL/Power.thy	Thu May 17 08:53:57 2007 +0200
     1.3 @@ -147,18 +147,18 @@
     1.4  done
     1.5  
     1.6  lemma field_power_eq_0_iff [simp]:
     1.7 -     "(a^n = 0) = (a = (0::'a::{field,recpower}) & 0<n)"
     1.8 +     "(a^n = 0) = (a = (0::'a::{division_ring,recpower}) & 0<n)"
     1.9  apply (induct "n")
    1.10  apply (auto simp add: power_Suc field_mult_eq_0_iff zero_neq_one[THEN not_sym])
    1.11  done
    1.12  
    1.13 -lemma field_power_not_zero: "a \<noteq> (0::'a::{field,recpower}) ==> a^n \<noteq> 0"
    1.14 +lemma field_power_not_zero: "a \<noteq> (0::'a::{division_ring,recpower}) ==> a^n \<noteq> 0"
    1.15  by force
    1.16  
    1.17  lemma nonzero_power_inverse:
    1.18 -  "a \<noteq> 0 ==> inverse ((a::'a::{field,recpower}) ^ n) = (inverse a) ^ n"
    1.19 +  "a \<noteq> 0 ==> inverse ((a::'a::{division_ring,recpower}) ^ n) = (inverse a) ^ n"
    1.20  apply (induct "n")
    1.21 -apply (auto simp add: power_Suc nonzero_inverse_mult_distrib mult_commute)
    1.22 +apply (auto simp add: power_Suc nonzero_inverse_mult_distrib power_commutes)
    1.23  done
    1.24  
    1.25  text{*Perhaps these should be simprules.*}