src/HOL/Library/Countable.thy
 changeset 37715 44b27ea94a16 parent 37678 0040bafffdef child 39198 f967a16dfcdd
```     1.1 --- a/src/HOL/Library/Countable.thy	Mon Jul 05 15:12:20 2010 +0200
1.2 +++ b/src/HOL/Library/Countable.thy	Mon Jul 05 15:12:20 2010 +0200
1.3 @@ -110,26 +110,20 @@
1.4    "to_nat_typerep (Typerep.Typerep c ts) = to_nat (to_nat c, to_nat (map to_nat_typerep ts))"
1.5
1.6  instance proof (rule countable_classI)
1.7 -  fix t t' :: typerep and ts
1.8 -  have "(\<forall>t'. to_nat_typerep t = to_nat_typerep t' \<longrightarrow> t = t')
1.9 -    \<and> (\<forall>ts'. map to_nat_typerep ts = map to_nat_typerep ts' \<longrightarrow> ts = ts')"
1.10 -  proof (induct rule: typerep.induct)
1.11 -    case (Typerep c ts) show ?case
1.12 -    proof (rule allI, rule impI)
1.13 -      fix t'
1.14 -      assume hyp: "to_nat_typerep (Typerep.Typerep c ts) = to_nat_typerep t'"
1.15 -      then obtain c' ts' where t': "t' = (Typerep.Typerep c' ts')"
1.16 -        by (cases t') auto
1.17 -      with Typerep hyp have "c = c'" and "ts = ts'" by simp_all
1.18 -      with t' show "Typerep.Typerep c ts = t'" by simp
1.19 -    qed
1.20 +  fix t t' :: typerep and ts ts' :: "typerep list"
1.21 +  assume "to_nat_typerep t = to_nat_typerep t'"
1.22 +  moreover have "to_nat_typerep t = to_nat_typerep t' \<Longrightarrow> t = t'"
1.23 +    and "map to_nat_typerep ts = map to_nat_typerep ts' \<Longrightarrow> ts = ts'"
1.24 +  proof (induct t and ts arbitrary: t' and ts' rule: typerep.inducts)
1.25 +    case (Typerep c ts t')
1.26 +    then obtain c' ts' where t': "t' = Typerep.Typerep c' ts'" by (cases t') auto
1.27 +    with Typerep have "c = c'" and "ts = ts'" by simp_all
1.28 +    with t' show "Typerep.Typerep c ts = t'" by simp
1.29    next
1.30      case Nil_typerep then show ?case by simp
1.31    next
1.32      case (Cons_typerep t ts) then show ?case by auto
1.33    qed
1.34 -  then have "to_nat_typerep t = to_nat_typerep t' \<Longrightarrow> t = t'" by auto
1.35 -  moreover assume "to_nat_typerep t = to_nat_typerep t'"
1.36    ultimately show "t = t'" by simp
1.37  qed
1.38
```