diff options
Diffstat (limited to 'Prod.thy')
-rw-r--r-- | Prod.thy | 8 |
1 files changed, 4 insertions, 4 deletions
@@ -37,13 +37,13 @@ translations section \<open>Type rules\<close> axiomatization where - Prod_form: "\<And>A B. \<lbrakk>A : U; B: A \<rightarrow> U\<rbrakk> \<Longrightarrow> \<Prod>x:A. B x : U" + Prod_form: "\<And>i A B. \<lbrakk>A : U(i); B: A \<longrightarrow> U(i)\<rbrakk> \<Longrightarrow> \<Prod>x:A. B x : U(i)" and - Prod_form_cond1: "\<And>A B. (\<Prod>x:A. B x : U) \<Longrightarrow> A : U" + Prod_form_cond1: "\<And>i A B. (\<Prod>x:A. B x : U(i)) \<Longrightarrow> A : U(i)" and - Prod_form_cond2: "\<And>A B. (\<Prod>x:A. B x : U) \<Longrightarrow> B: A \<rightarrow> U" + Prod_form_cond2: "\<And>i A B. (\<Prod>x:A. B x : U(i)) \<Longrightarrow> B: A \<longrightarrow> U(i)" and - Prod_intro: "\<And>A B b. \<lbrakk>A : U; \<And>x. x : A \<Longrightarrow> b x : B x\<rbrakk> \<Longrightarrow> \<^bold>\<lambda>x:A. b x : \<Prod>x:A. B x" + Prod_intro: "\<And>i A B b. (\<And>x. x : A \<Longrightarrow> b x : B x) \<Longrightarrow> \<^bold>\<lambda>x:A. b x : \<Prod>x:A. B x" and Prod_elim: "\<And>A B f a. \<lbrakk>f : \<Prod>x:A. B x; a : A\<rbrakk> \<Longrightarrow> f`a : B a" and |