diff options
author | Josh Chen | 2018-08-13 10:37:20 +0200 |
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committer | Josh Chen | 2018-08-13 10:37:20 +0200 |
commit | 962fc96123039b53b9c6946796e909fb50ec9004 (patch) | |
tree | 16f7d456fef26b6eb549200515a274e8ed3fc388 /Equal.thy | |
parent | 7a89ec1e72f61179767c6488177c6d12e69388c5 (diff) |
rcompose done
Diffstat (limited to 'Equal.thy')
-rw-r--r-- | Equal.thy | 12 |
1 files changed, 6 insertions, 6 deletions
@@ -15,7 +15,7 @@ section \<open>Constants and syntax\<close> axiomatization Equal :: "[Term, Term, Term] \<Rightarrow> Term" and refl :: "Term \<Rightarrow> Term" and - indEqual :: "[Term \<Rightarrow> Term, Term, Term, Term] \<Rightarrow> Term" ("(1ind\<^sub>=)") + indEqual :: "[Term \<Rightarrow> Term, Term] \<Rightarrow> Term" ("(1ind\<^sub>=)") syntax "_EQUAL" :: "[Term, Term, Term] \<Rightarrow> Term" ("(3_ =\<^sub>_/ _)" [101, 0, 101] 100) @@ -35,16 +35,16 @@ and 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; - b: A; + x: A; + y: A; p: a =\<^sub>A b - \<rbrakk> \<Longrightarrow> ind\<^sub>=(f)(a)(b)(p) : C(a)(b)(p)" + \<rbrakk> \<Longrightarrow> ind\<^sub>=(f)(p) : C(x)(y)(p)" and 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)" + \<rbrakk> \<Longrightarrow> ind\<^sub>=(f)(refl(a)) \<equiv> f(a)" text "Admissible inference rules for equality type formation:" (* @@ -56,7 +56,7 @@ and 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_wellform [intro] = Equal_form_cond1 Equal_form_cond2 Equal_form_cond3*) lemmas Equal_comps [comp] = Equal_comp |