Mercurial > hg > Papers > 2021 > soto-thesis
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init-test
author | soto |
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date | Tue, 08 Dec 2020 19:06:49 +0900 (2020-12-08) |
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+-comm : (x y : ℕ) → x + y ≡ y + x +-comm zero y rewrite (+zero {y}) = refl +-comm (suc x) y = let open ≡-Reasoning in begin suc (x + y) ≡⟨⟩ suc (x + y) ≡⟨ cong suc (+-comm x y) ⟩ suc (y + x) ≡⟨ sym (+-suc {y} {x}) ⟩ y + suc x ∎ -- +-suc : {x y : ℕ} → x + suc y ≡ suc (x + y) -- +-suc {zero} {y} = refl -- +-suc {suc x} {y} = cong suc (+-suc {x} {y})