{"id":7396,"date":"2020-09-20T12:17:23","date_gmt":"2020-09-20T10:17:23","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7396"},"modified":"2020-12-20T12:18:18","modified_gmt":"2020-12-20T11:18:18","slug":"formatus-regla-de-eliminacion-de-la-disyuncion-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-regla-de-eliminacion-de-la-disyuncion-en-lean\/","title":{"rendered":"ForMatUS: Regla de eliminaci\u00f3n de la disyunci\u00f3n en Lean"},"content":{"rendered":"<p>He a\u00f1adido a la lista <a href=\"https:\/\/bit.ly\/2FcUrwQ\">L\u00f3gica con Lean<\/a> el <a href=\"https:\/\/youtu.be\/dpjRLUgJGK0\">v\u00eddeo<\/a> en el que se comenta la regla de eliminaci\u00f3n de la disyunci\u00f3n en Lean usando ejemplos con distintos estilos de prueba: declarativos, aplicativos, funcional y autom\u00e1tico.<\/p>\n<p>A continuaci\u00f3n, se muestra el v\u00eddeo<\/p>\n<p><center><\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/dpjRLUgJGK0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><\/iframe><\/p>\n<p><\/center>y el <a href=\"https:\/\/github.com\/jaalonso\/Logica_con_Lean\/blob\/master\/src\/1_Proposicional\/Regla_de_eliminacion_de_la_disyuncion.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">import tactic\n\nvariables (P Q R : Prop)\n\n-- ----------------------------------------------------\n-- Ej. 1. (p. 11) Demostrar\n--    P \u2228 Q, P \u2192 R, Q \u2192 R \u22a2 R\n-- ----------------------------------------------------\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\nor.elim h1 h2 h3\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\nh1.elim h2 h3\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\n-- by library_search\nor.rec h2 h3 h1\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\nbegin\n  cases h1 with hP hQ,\n  { exact h2 hP, },\n  { exact h3 hQ, },\nend\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\n-- by hint\nby tauto\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2228 Q)\n  (h2 : P \u2192 R)\n  (h3 : Q \u2192 R)\n  : R :=\nby finish\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista L\u00f3gica con Lean el v\u00eddeo en el que se comenta la regla de eliminaci\u00f3n de la disyunci\u00f3n en Lean usando ejemplos con distintos estilos de prueba: declarativos, aplicativos, funcional y autom\u00e1tico. A continuaci\u00f3n, se muestra el v\u00eddeo y el c\u00f3digo de la teor\u00eda utilizada import tactic variables (P Q R&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[335],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7396"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=7396"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7396\/revisions"}],"predecessor-version":[{"id":7397,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7396\/revisions\/7397"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}