1 files changed, 0 insertions, 56 deletions
diff --git a/Sum.thy b/Sum.thy
deleted file mode 100644
index a1c0d34..0000000
--- a/Sum.thy
+++ /dev/null
@@ -1,56 +0,0 @@
-(********
-Isabelle/HoTT: Dependent sum (dependent pair)
-Feb 2019
-
-********)
-
-theory Sum
-imports HoTT_Base
-
-begin
-
-axiomatization
-  Sum    :: "[t, t \<Rightarrow> t] \<Rightarrow> t" and
-  pair   :: "[t, t] \<Rightarrow> t"  ("(2<_,/ _>)") and
-  indSum :: "[t \<Rightarrow> t, [t, t] \<Rightarrow> t, t] \<Rightarrow> t"
-
-syntax
-  "_Sum"  :: "[idt, t, t] \<Rightarrow> t"  ("(2\<Sum>'(_: _')./ _)" 20)
-  "_Sum'" :: "[idt, t, t] \<Rightarrow> t"  ("(2\<Sum>_: _./ _)" 20)
-translations
-  "\<Sum>(x: A). B" \<rightleftharpoons> "(CONST Sum) A (\<lambda>x. B)"
-  "\<Sum>x: A. B" \<rightleftharpoons> "(CONST Sum) A (\<lambda>x. B)"
-
-abbreviation Pair :: "[t, t] \<Rightarrow> t"  (infixr "\<times>" 50)
-  where "A \<times> B \<equiv> \<Sum>_: A. B"
-
-axiomatization where
-\<comment> \<open>Type rules\<close>
-
-  Sum_form: "\<lbrakk>A: U i; \<And>x. x: A \<Longrightarrow> B x: U i\<rbrakk> \<Longrightarrow> \<Sum>x: A. B x: U i" and
-
-  Sum_intro: "\<lbrakk>\<And>x. x: A \<Longrightarrow> B x: U i; a: A; b: B a\<rbrakk> \<Longrightarrow> <a, b>: \<Sum>x: A. B x" and
-
-  Sum_elim: "\<lbrakk>
-    p: \<Sum>x: A. B x;
-    C: \<Sum>x: A. B x \<leadsto> U i;
-    \<And>x y. \<lbrakk>x: A; y: B x\<rbrakk> \<Longrightarrow> f x y: C <x,y> \<rbrakk> \<Longrightarrow> indSum C f p: C p" and
-
-  Sum_cmp: "\<lbrakk>
-    a: A;
-    b: B a;
-    B: A \<leadsto> U i;
-    C: \<Sum>x: A. B x \<leadsto> U i;
-    \<And>x y. \<lbrakk>x: A; y: B x\<rbrakk> \<Longrightarrow> f x y: C <x,y> \<rbrakk> \<Longrightarrow> indSum C f <a, b> \<equiv> f a b" and
-
-\<comment> \<open>Congruence rules\<close>
-
-  Sum_form_eq: "\<lbrakk>A: U i; B: A \<leadsto> U i; C: A \<leadsto> U i; \<And>x. x: A \<Longrightarrow> B x \<equiv> C x\<rbrakk>
-    \<Longrightarrow> \<Sum>x: A. B x \<equiv> \<Sum>x: A. C x"
-
-lemmas Sum_form [form]
-lemmas Sum_routine [intro] = Sum_form Sum_intro Sum_elim
-lemmas Sum_comp [comp] = Sum_cmp
-lemmas Sum_cong [cong] = Sum_form_eq
-
-end