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-rw-r--r--hott/Nat.thy14
1 files changed, 7 insertions, 7 deletions
diff --git a/hott/Nat.thy b/hott/Nat.thy
index c36154e..e8657a4 100644
--- a/hott/Nat.thy
+++ b/hott/Nat.thy
@@ -18,24 +18,24 @@ where
NatE: "\<lbrakk>
n: Nat;
c\<^sub>0: C 0;
- \<And>k c. \<lbrakk>k: Nat; c: C k\<rbrakk> \<Longrightarrow> f k c: C (suc k);
+ \<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 c. f k c) n: C n" and
+ \<rbrakk> \<Longrightarrow> NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) n: C n" and
Nat_comp_zero: "\<lbrakk>
c\<^sub>0: C 0;
- \<And>k c. \<lbrakk>k: Nat; c: C k\<rbrakk> \<Longrightarrow> f k c: C (suc k);
+ \<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 c. f k c) 0 \<equiv> c\<^sub>0" and
+ \<rbrakk> \<Longrightarrow> NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k rec. f k rec) 0 \<equiv> c\<^sub>0" and
Nat_comp_suc: "\<lbrakk>
n: Nat;
c\<^sub>0: C 0;
- \<And>k c. \<lbrakk>k: Nat; c: C k\<rbrakk> \<Longrightarrow> f k c: C (suc k);
+ \<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 c. f k c) (suc n) \<equiv>
- f n (NatInd (\<lambda>n. C n) c\<^sub>0 (\<lambda>k c. f k c) n)"
+ 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)"
lemmas
[intros] = NatF Nat_zero Nat_suc and