+-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