Mercurial > hg > Papers > 2020 > soto-midterm
view src/agda-term.agda @ 1:73127e0ab57c
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author | soto@cr.ie.u-ryukyu.ac.jp |
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date | Tue, 08 Sep 2020 18:38:08 +0900 |
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module agda-term where open import Data.Nat.Base open import Relation.Binary.PropositionalEquality +zero : {y : ℕ} → y + zero ≡ y +zero {zero} = refl +zero {suc y} = cong (λ yy → suc yy) (+zero {y}) +-suc : {x y : ℕ} → x + suc y ≡ suc (x + y) +-suc {zero} {y} = refl +-suc {suc x} {y} = cong suc (+-suc {x} {y}) +-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 ∎ +-come : (x y : ℕ) → x + y ≡ y + x +-come zero y rewrite (+zero {y}) = refl +-come (suc x) y rewrite (cong suc (+-come x y)) | sym (+-suc {y} {x}) = refl