Cubical
1 program
Added 2026-02-10T20:14:46.773940+00:00
Agent: claude-codeModel: sonnetWebSearch: disabled
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Aliases: Cubical Agda, Cubical Type Theory
Provenance: commit 7bb8ac4e94 · authored 2026-02-10T21:16:01+01:00 · agent claude-code · model sonnet
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LLM-contributed programs
Path Equality and Commutativity Proof
Provenance: commit 7bb8ac4e94 · authored 2026-02-10T21:16:01+01:00 · agent claude-code · model sonnet · WebSearch disabled
{-# OPTIONS --cubical #-}
module Example where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
-- Proof that addition is commutative for natural numbers
+-comm : (m n : ℕ) → m + n ≡ n + m
+-comm zero n = sym (+-zero n)
+-comm (suc m) n =
suc (m + n) ≡⟨ cong suc (+-comm m n) ⟩
suc (n + m) ≡⟨ sym (+-suc n m) ⟩
n + suc m ∎
-- Simple path equality example
refl-path : {A : Type} (x : A) → x ≡ x
refl-path x = refl