{"id":7374,"date":"2020-09-15T18:36:32","date_gmt":"2020-09-15T16:36:32","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7374"},"modified":"2020-09-15T18:36:32","modified_gmt":"2020-09-15T16:36:32","slug":"formatus-pruebas-en-lean-de-p-%e2%86%92-q-%e2%8a%a2-%c2%acq-%e2%86%92-%c2%acp","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-p-%e2%86%92-q-%e2%8a%a2-%c2%acq-%e2%86%92-%c2%acp\/","title":{"rendered":"ForMatUS: Pruebas en Lean de P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP"},"content":{"rendered":"<p>He a\u00f1adido a la lista <a href=\"https:\/\/bit.ly\/2FcUrwQ\">L\u00f3gica con Lean<\/a> el v\u00eddeo <a href=\"https:\/\/youtu.be\/i-FV1lKxCfc\">Pruebas en Lean de P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP<\/a> en el que se comentan 12 pruebas en Lean de la propiedad<\/p>\n<blockquote><p>\n  P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP\n<\/p><\/blockquote>\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\/i-FV1lKxCfc\" 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 \u22a2 \u00acQ \u2192 \u00acP\n-- ==========================\n\n-- Ej. 1. Demostrar\n--    P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP\n\nimport tactic\n\nvariables (P Q : Prop)\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nassume h2 : \u00acQ,\nshow \u00acP,\n  from mt h1 h2\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nassume h2 : \u00acQ, mt h1 h2\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\n\u03bb h2, mt h1 h2\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nmt h1\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nbegin\n  intro h2,\n  exact mt h1 h2,\nend\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nbegin\n  intro h2,\n  intro h3,\n  apply h2,\n  apply h1,\n  exact h3,\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nbegin\n  intro h2,\n  intro h3,\n  apply h2,\n  exact h1 h3,\nend\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nbegin\n  intro h2,\n  intro h3,\n  exact h2 (h1 h3),\nend\n\n-- 9\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nbegin\n  intros h2 h3,\n  exact h2 (h1 h3),\nend\n\n-- 10\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\n\u03bb h2 h3, h2 (h1 h3)\n\n-- 11\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nby tauto\n\n-- 12\u00aa demostraci\u00f3n\nexample\n  (h1 : P \u2192 Q)\n  : \u00acQ \u2192 \u00acP :=\nby finish\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista L\u00f3gica con Lean el v\u00eddeo Pruebas en Lean de P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP en el que se comentan 12 pruebas en Lean de la propiedad P \u2192 Q \u22a2 \u00acQ \u2192 \u00acP A continuaci\u00f3n, se muestra el v\u00eddeo y el c\u00f3digo de la teor\u00eda utilizada &#8212; Pruebas&#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\/7374"}],"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=7374"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7374\/revisions"}],"predecessor-version":[{"id":7375,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7374\/revisions\/7375"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}