1 files changed, 0 insertions, 63 deletions
diff --git a/tests/Subgoal.thy b/tests/Subgoal.thy
deleted file mode 100644
index 82d7e5d..0000000
--- a/tests/Subgoal.thy
+++ /dev/null
@@ -1,63 +0,0 @@
-theory Subgoal
-  imports "../HoTT"
-begin
-
-
-text "
-  Proof of \<open>rpathcomp_type\<close> (see EqualProps.thy) in apply-style.
-  Subgoaling can be used to fix variables and apply the elimination rules.
-"
-
-lemma rpathcomp_type:
-  assumes "A: U(i)"
-  shows "rpathcomp: \<Prod>x:A. \<Prod>y:A. x =\<^sub>A y \<rightarrow> (\<Prod>z:A. y =\<^sub>A z \<rightarrow> x =\<^sub>A z)"
-unfolding rpathcomp_def
-apply standard
-  subgoal premises 1 for x  \<comment> \<open>\<open>subgoal\<close> is the proof script version of \<open>fix-assume-show\<close>.\<close>
-  apply standard
-    subgoal premises 2 for y
-    apply standard
-      subgoal premises 3 for p
-      apply (rule Equal_elim[where ?x=x and ?y=y and ?A=A])
-        \<comment> \<open>specifying \<open>?A=A\<close> is crucial here to prevent the next \<open>subgoal\<close> from binding a schematic ?A which should be instantiated to \<open>A\<close>.\<close>
-      prefer 4
-        apply standard
-          apply (rule Prod_intro)
-            subgoal premises 4 for u z q
-            apply (rule Equal_elim[where ?x=u and ?y=z])
-            apply (routine lems: assms 4)
-            done
-          apply (routine lems: assms 1 2 3)
-      done
-    apply (routine lems: assms 1 2)
-    done
-  apply fact
-  done
-apply fact
-done
-
-
-text "
-  \<open>subgoal\<close> converts schematic variables to fixed free variables, making it unsuitable for use in \<open>schematic_goal\<close> proofs.
-  This is the same thing as being unable to start a ``sub schematic-goal'' inside an ongoing proof.
-
-  This is a problem for syntheses which need to use induction (elimination rules), as these often have to be applied to fixed variables, while keeping any schematic variables intact.
-"
-
-schematic_goal rpathcomp_synthesis:
-  assumes "A: U(i)"
-  shows "?a: \<Prod>x:A. \<Prod>y:A. x =\<^sub>A y \<rightarrow> (\<Prod>z:A. y =\<^sub>A z \<rightarrow> x =\<^sub>A z)"
-
-text "
-  Try (and fail) to synthesize the constant for path composition, following the proof of \<open>rpathcomp_type\<close> below.
-"
-
-apply (rule intros)
-  apply (rule intros)
-    apply (rule intros)
-      subgoal 123 for x y p
-      apply (rule Equal_elim[where ?x=x and ?y=y and ?A=A])
-      oops
-
-
-end