--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/prepaper/src/agda-term2.agda.replaced	Tue Dec 08 19:06:49 2020 +0900
@@ -0,0 +1,11 @@
++-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x
++-comm zero y rewrite (+zero {y}) = refl
++-comm (suc x) y = let open @$\equiv$@-Reasoning in
+  begin
+  (suc x) + y @$\equiv$@@$\langle$@@$\rangle$@
+  suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@
+  suc (y + x) @$\equiv$@@$\langle$@ ?0 @$\rangle$@
+  ?1 @$\blacksquare$@
+
+-- ?0 : suc (y + x) @$\equiv$@ y + suc x
+-- ?1 : y + suc x