diff options
Diffstat (limited to 'hott/Nat.thy')
| -rw-r--r-- | hott/Nat.thy | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/hott/Nat.thy b/hott/Nat.thy index d54ea7b..c36154e 100644 --- a/hott/Nat.thy +++ b/hott/Nat.thy @@ -44,7 +44,7 @@ lemmas text \<open>Non-dependent recursion\<close> -abbreviation "NatRec C \<equiv> NatInd (K C)" +abbreviation "NatRec C \<equiv> NatInd (\<lambda>_. C)" section \<open>Basic arithmetic\<close> @@ -100,10 +100,10 @@ Lemma (derive) add_comm: shows "m + n = n + m" apply (elim m) \<guillemotright> by (reduce; rule add_zero[symmetric]) - \<guillemotright> prems prms vars m ih + \<guillemotright> prems vars m ih proof reduce have "suc (m + n) = suc (n + m)" by (eq ih) intro - also have "'' = n + suc m" by (rule add_suc[symmetric]) + also have ".. = n + suc m" by (rule add_suc[symmetric]) finally show "suc (m + n) = n + suc m" by this qed done |