added a thm
authornipkow
Wed Aug 04 19:12:15 2004 +0200 (2004-08-04)
changeset 151126f0772a94299
parent 15111 c108189645f8
child 15113 fafcd72b9d4b
added a thm
src/HOL/Relation_Power.thy
     1.1 --- a/src/HOL/Relation_Power.thy	Wed Aug 04 19:11:02 2004 +0200
     1.2 +++ b/src/HOL/Relation_Power.thy	Wed Aug 04 19:12:15 2004 +0200
     1.3 @@ -12,10 +12,10 @@
     1.4  Examples: range(f^n) = A and Range(R^n) = B need constraints.
     1.5  *)
     1.6  
     1.7 -Relation_Power = Nat +
     1.8 +theory Relation_Power = Nat:
     1.9  
    1.10  instance
    1.11 -  set :: (type) power   (* only ('a * 'a) set should be in power! *)
    1.12 +  set :: (type) power ..  (* only ('a * 'a) set should be in power! *)
    1.13  
    1.14  primrec (relpow)
    1.15    "R^0 = Id"
    1.16 @@ -23,10 +23,13 @@
    1.17  
    1.18  
    1.19  instance
    1.20 -  fun :: (type, type) power   (* only 'a => 'a should be in power! *)
    1.21 +  fun :: (type, type) power ..  (* only 'a => 'a should be in power! *)
    1.22  
    1.23  primrec (funpow)
    1.24    "f^0 = id"
    1.25    "f^(Suc n) = f o (f^n)"
    1.26  
    1.27 +lemma funpow_add: "f ^ (m+n) = f^m o f^n"
    1.28 +by(induct m) simp_all
    1.29 +
    1.30  end