--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/agda-term3.agda.replaced	Tue Sep 08 18:38:08 2020 +0900
@@ -0,0 +1,12 @@
++-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) @$\equiv$@@$\langle$@ sym (+-suc {y} {x}) @$\rangle$@
+  y + suc x @$\blacksquare$@
+
+-- +-suc : {x y : @$\mathbb{N}$@} @$\rightarrow$@ x + suc y @$\equiv$@ suc (x + y)
+-- +-suc {zero} {y} = refl
+-- +-suc {suc x} {y} = cong suc (+-suc {x} {y})