Mercurial > hg > Papers > 2020 > soto-midterm

comparison src/agda-term2.agda @ 1:73127e0ab57c

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author soto@cr.ie.u-ryukyu.ac.jp
date Tue, 08 Sep 2020 18:38:08 +0900
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0:b919985837a3 1:73127e0ab57c
1 +-comm : (x y : ℕ) → x + y ≡ y + x
2 +-comm zero y rewrite (+zero {y}) = refl
3 +-comm (suc x) y = let open ≡-Reasoning in
4 begin
5 (suc x) + y ≡⟨⟩
6 suc (x + y) ≡⟨ cong suc (+-comm x y) ⟩
7 suc (y + x) ≡⟨ ?0 ⟩
8 ?1 ∎
9
10 -- ?0 : suc (y + x) ≡ y + suc x
11 -- ?1 : y + suc x