https://jaalonso.github.io/calculemus/esContents © 2026 <a href="mailto:">José A. Alonso</a> <a rel="license" href="https://creativecommons.org/licenses/by-nc-sa/4.0/"> <img alt="Creative Commons License BY-NC-SA" style="border-width:0; margin-bottom:12px;" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png"></a>Wed, 14 Oct 2026 18:49:44 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rsshttps://jaalonso.github.io/calculemus/es/posts/2020/04/08-las_reflexivas_circulares_son_simetricases/José A. Alonso<div><hr> <p>Se dice que la relación binaria \(R\) es</p> <ul> <li>reflexiva si \((∀x)R(x, x)\)</li> <li>circular si \((∀x, y, z)[R(x, y) ∧ R(y, z) ⟶ R(z, x)]\)</li> <li>simétrica si \((∀x, y)[R(x, y) ⟶ R(y, x)]\)</li> </ul> <p>Demostrar que las relaciones reflexivas y circulares son simétricas. Para ello, completar la siguiente teoría de Isabelle/HOL:</p> <div class="code"><pre class="code literal-block"><span class="k">theory</span><span class="w"> </span><span class="n">Las_reflexivas_circulares_son_simetricas</span> <span class="kp">imports</span><span class="w"> </span><span class="n">Main</span> <span class="k">begin</span> <span class="kn">lemma</span> <span class="w"> </span><span class="kp">assumes</span><span class="w"> </span><span class="s">"∀x. R(x, x)"</span> <span class="w"> </span><span class="s">"∀x y z. R(x, y) ∧ R(y, z) ⟶ R(z, x)"</span> <span class="w"> </span><span class="kp">shows</span><span class="w"> </span><span class="s">"∀x y. R(x, y) ⟶ R(y, x)"</span> <span class="w"> </span><span class="gr">oops</span> <span class="k">end</span> </pre></div> <hr> <p><a href="https://jaalonso.github.io/calculemus/es/posts/2020/04/08-las_reflexivas_circulares_son_simetricases/">Leer más…</a> (quedan 1 minutos de lectura)</p></div>https://jaalonso.github.io/calculemus/es/posts/2020/04/08-las_reflexivas_circulares_son_simetricases/Wed, 08 Apr 2020 04:00:00 GMT