{"id":7378,"date":"2020-09-17T16:48:57","date_gmt":"2020-09-17T14:48:57","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7378"},"modified":"2020-09-17T16:48:57","modified_gmt":"2020-09-17T14:48:57","slug":"formatus-pruebas-en-lean-de-p-%e2%86%92-q-%e2%86%92-r-p-%c2%acr-%e2%8a%a2-%c2%acq","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-p-%e2%86%92-q-%e2%86%92-r-p-%c2%acr-%e2%8a%a2-%c2%acq\/","title":{"rendered":"ForMatUS: Pruebas en Lean de P \u2192 (Q \u2192 R), P, \u00acR \u22a2 \u00acQ"},"content":{"rendered":"<p>He a\u00f1adido a la lista <a href=\"https:\/\/bit.ly\/2FcUrwQ\">L\u00f3gica con Lean<\/a> un <a href=\"https:\/\/youtu.be\/VEyvycuVmdI\">v\u00eddeo<\/a> en el que se se comentan 9 prueba en Lean de<\/p>\n<blockquote><p>\n  P \u2192 (Q \u2192 R), P, \u00acR \u22a2 \u00acQ\n<\/p><\/blockquote>\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><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/VEyvycuVmdI\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>y el c\u00f3digo de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">\n-- Pruebas de P \u2192 (Q \u2192 R), P, \u00acR \u22a2 \u00acQ\n-- ==================================\n\n-- Ej. 1. Demostrar\n--    Pruebas de P \u2192 (Q \u2192 R), P, \u00acR \u22a2 \u00acQ \n\nimport tactic\n\nvariables (P Q R : Prop)\n\n-- 1\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nhave h4 : Q \u2192 R,\n  from h1 h2,\nshow \u00acQ,\n  from mt h4 h3  \n\n-- 2\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nhave h4 : Q \u2192 R := h1 h2,\nshow \u00acQ,\n  from mt h4 h3  \n\n-- 3\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nshow \u00acQ,\n  from mt (h1 h2) h3  \n\n-- 4\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nmt (h1 h2) h3\n\n-- 5\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nbegin\n  intro h4,\n  apply h3,\n  apply (h1 h2),\n  exact h4,\nend\n\n-- 6\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nbegin\n  intro h4,\n  apply h3,\n  exact (h1 h2) h4,\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nbegin\n  intro h4,\n  exact h3 ((h1 h2) h4),\nend\n\n-- 8\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\n\u03bb h4, h3 ((h1 h2) h4)\n\n-- 9\u00aa demostraci\u00f3n\nexample \n  (h1 : P \u2192 (Q \u2192 R)) \n  (h2 : P)\n  (h3 : \u00acR)\n  : \u00acQ :=\nby finish\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista L\u00f3gica con Lean un v\u00eddeo en el que se se comentan 9 prueba en Lean de P \u2192 (Q \u2192 R), P, \u00acR \u22a2 \u00acQ 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; Pruebas de P&#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\/7378"}],"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=7378"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7378\/revisions"}],"predecessor-version":[{"id":7379,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7378\/revisions\/7379"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7378"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}