view paper/src/agda-term2.agda.replaced @ 19:046b2b20d6c7 default tip

fix
author ryokka
date Mon, 09 Mar 2020 11:25:49 +0900
parents 8ef64db63497
children
line wrap: on
line source

+-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