{"id":7439,"date":"2020-10-02T17:17:10","date_gmt":"2020-10-02T15:17:10","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7439"},"modified":"2020-12-20T17:18:29","modified_gmt":"2020-12-20T16:18:29","slug":"formatus-regla-de-introduccion-del-cuantificador-existencial-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-regla-de-introduccion-del-cuantificador-existencial-en-lean\/","title":{"rendered":"ForMatUS: Regla de introducci\u00f3n del cuantificador existencial 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\/vUHLphX4Aco\">v\u00eddeo<\/a> en el que se comentan pruebas en Lean de a propiedad<\/p>\n<pre lang=\"lean\">\u2200x P(x) \u22a2 \u2203x P(x)\n<\/pre>\n<p>usando los estilos 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\/vUHLphX4Aco\" 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\/2_LPO\/Regla_de_introduccion_del_cuantificador_existencial.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- Ej. 1. Demostrar\n--    \u2200x P(x) \u22a2 \u2203x P(x)\n\nimport tactic\n\nvariable U : Type\nvariable c : U\nvariable P : U -&gt; Prop\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nhave h2 : P c, from h1 c,\nshow \u2203x, P x,  from exists.intro c h2\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nshow \u2203x, P x,  from exists.intro c (h1 c)\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nexists.intro c (h1 c)\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\n\u27e8c, h1 c\u27e9\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (a : U)\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nbegin\n  use a,\n  apply h1,\nend\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (a : U)\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nbegin\n  constructor,\n  apply h1 a,\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  [inhabited U]\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nbegin\n  constructor,\n  apply h1 (default U),\nend\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h : nonempty U)\n  (h1 : \u2200x, P x)\n  : \u2203x, P x :=\nbegin\n  use (classical.choice h),\n  apply h1,\nend\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 comentan pruebas en Lean de a propiedad \u2200x P(x) \u22a2 \u2203x P(x) usando los estilos declarativos, aplicativos, funcional y autom\u00e1tico. A continuaci\u00f3n, se muestra el v\u00eddeo y el c\u00f3digo de la teor\u00eda utilizada &#8212; Ej. 1. Demostrar &#8212; \u2200x P(x) \u22a2&#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":[336],"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\/7439"}],"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=7439"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7439\/revisions"}],"predecessor-version":[{"id":7440,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7439\/revisions\/7440"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7439"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7439"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7439"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}