diff options
Diffstat (limited to 'hott/Nat.thy')
| -rw-r--r-- | hott/Nat.thy | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/hott/Nat.thy b/hott/Nat.thy index 50b7996..4abd315 100644 --- a/hott/Nat.thy +++ b/hott/Nat.thy @@ -20,13 +20,13 @@ where c\<^sub>0: C 0; \<And>k rec. \<lbrakk>k: Nat; rec: C k\<rbrakk> \<Longrightarrow> f k rec: C (suc k); \<And>n. n: Nat \<Longrightarrow> C n: U i - \<rbrakk> \<Longrightarrow> NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) n: C n" and + \<rbrakk> \<Longrightarrow> NatInd (fn n. C n) c\<^sub>0 (fn k rec. f k rec) n: C n" and Nat_comp_zero: "\<lbrakk> c\<^sub>0: C 0; \<And>k rec. \<lbrakk>k: Nat; rec: C k\<rbrakk> \<Longrightarrow> f k rec: C (suc k); \<And>n. n: Nat \<Longrightarrow> C n: U i - \<rbrakk> \<Longrightarrow> NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) 0 \<equiv> c\<^sub>0" and + \<rbrakk> \<Longrightarrow> NatInd (fn n. C n) c\<^sub>0 (fn k rec. f k rec) 0 \<equiv> c\<^sub>0" and Nat_comp_suc: "\<lbrakk> n: Nat; @@ -34,15 +34,15 @@ where \<And>k rec. \<lbrakk>k: Nat; rec: C k\<rbrakk> \<Longrightarrow> f k rec: C (suc k); \<And>n. n: Nat \<Longrightarrow> C n: U i \<rbrakk> \<Longrightarrow> - NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) (suc n) \<equiv> - f n (NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) n)" + NatInd (fn n. C n) c\<^sub>0 (fn k rec. f k rec) (suc n) \<equiv> + f n (NatInd (fn n. C n) c\<^sub>0 (fn k rec. f k rec) n)" lemmas [intros] = NatF Nat_zero Nat_suc and [elims "?n"] = NatE and [comps] = Nat_comp_zero Nat_comp_suc -abbreviation "NatRec C \<equiv> NatInd (\<lambda>_. C)" +abbreviation "NatRec C \<equiv> NatInd (fn _. C)" abbreviation one ("1") where "1 \<equiv> suc 0" abbreviation two ("2") where "2 \<equiv> suc 1" |