diff options
Diffstat (limited to '')
-rw-r--r-- | Equal.thy | 20 |
1 files changed, 10 insertions, 10 deletions
@@ -28,11 +28,11 @@ translations section \<open>Type rules\<close> axiomatization where - Equal_form: "\<And>i A a b. \<lbrakk>A: U(i); a: A; b: A\<rbrakk> \<Longrightarrow> a =\<^sub>A b : U(i)" + Equal_form: "\<lbrakk>A: U(i); a: A; b: A\<rbrakk> \<Longrightarrow> a =\<^sub>A b : U(i)" and - Equal_intro: "\<And>A a. a : A \<Longrightarrow> refl(a): a =\<^sub>A a" + Equal_intro: "a : A \<Longrightarrow> refl(a): a =\<^sub>A a" and - Equal_elim: "\<And>i A C f a b p. \<lbrakk> + Equal_elim: "\<lbrakk> \<And>x y. \<lbrakk>x: A; y: A\<rbrakk> \<Longrightarrow> C(x)(y): x =\<^sub>A y \<longrightarrow> U(i); \<And>x. x: A \<Longrightarrow> f(x) : C(x)(x)(refl x); a: A; @@ -40,23 +40,23 @@ and p: a =\<^sub>A b \<rbrakk> \<Longrightarrow> ind\<^sub>=(f)(a)(b)(p) : C(a)(b)(p)" and - Equal_comp: "\<And>i A C f a. \<lbrakk> + Equal_comp: "\<lbrakk> \<And>x y. \<lbrakk>x: A; y: A\<rbrakk> \<Longrightarrow> C(x)(y): x =\<^sub>A y \<longrightarrow> U(i); \<And>x. x: A \<Longrightarrow> f(x) : C(x)(x)(refl x); a: A \<rbrakk> \<Longrightarrow> ind\<^sub>=(f)(a)(a)(refl(a)) \<equiv> f(a)" text "Admissible inference rules for equality type formation:" - +(* axiomatization where - Equal_form_cond1: "\<And>i A a b. a =\<^sub>A b: U(i) \<Longrightarrow> A: U(i)" + Equal_form_cond1: "a =\<^sub>A b: U(i) \<Longrightarrow> A: U(i)" and - Equal_form_cond2: "\<And>i A a b. a =\<^sub>A b: U(i) \<Longrightarrow> a: A" + Equal_form_cond2: "a =\<^sub>A b: U(i) \<Longrightarrow> a: A" and - Equal_form_cond3: "\<And>i A a b. a =\<^sub>A b: U(i) \<Longrightarrow> b: A" - + Equal_form_cond3: "a =\<^sub>A b: U(i) \<Longrightarrow> b: A" +*) lemmas Equal_rules [intro] = Equal_form Equal_intro Equal_elim Equal_comp -lemmas Equal_form_conds [intro] = Equal_form_cond1 Equal_form_cond2 Equal_form_cond3 +(*lemmas Equal_form_conds [intro] = Equal_form_cond1 Equal_form_cond2 Equal_form_cond3*) lemmas Equal_comps [comp] = Equal_comp |