{"id":7365,"date":"2020-09-14T16:25:25","date_gmt":"2020-09-14T14:25:25","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7365"},"modified":"2020-09-14T16:26:48","modified_gmt":"2020-09-14T14:26:48","slug":"formatus-pruebas-del-silogismo-hipotetico-p-%e2%86%92-q-q-%e2%86%92-r-%e2%8a%a2-p-%e2%86%92-r","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-del-silogismo-hipotetico-p-%e2%86%92-q-q-%e2%86%92-r-%e2%8a%a2-p-%e2%86%92-r\/","title":{"rendered":"ForMatUS: Pruebas del silogismo hipot\u00e9tico: P \u2192 Q, Q \u2192 R \u22a2 P \u2192 R"},"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\/V7aGZdevLzY\">Pruebas del silogismo hipot\u00e9tico<\/a> en el que se se comentan 11 pruebas en Lean del silogismo hipot\u00e9tico<\/p>\n<blockquote><p>\n  P \u2192 Q, Q \u2192 R \u22a2 P \u2192 R.\n<\/p><\/blockquote>\n<p>Se comienza con pruebas declarativas, con razonamiento hacia adelante, que se reducen a funcionales; a continuaci\u00f3n, se hacen pruebas aplicativas, con razonamiento hacia atr\u00e1s, que tambi\u00e9n se reducen a funcionales y, finalmente, se buscan las pruebas autom\u00e1ticas.<\/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\/xOBStCZ8F2g\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>El c\u00f3digo es<\/p>\n<pre lang=\"lean\">\n-- Pruebas del silogismo hipot\u00e9tico\n-- --------------------------------\n\nimport tactic\n\nvariables (P Q R : Prop)\n\n-- Ej. 1. Demostrar que\n--    P \u2192 Q, Q \u2192 R \u22a2 P \u2192 R\n\n-- 1\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nassume h : P,\nhave h3 : Q,\n  from h1 h,\nshow R, \n  from h2 h3\n\n-- 2\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nassume h : P,\nhave h3 : Q := h1 h,\nshow R, \n  from h2 h3\n\n-- 3\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nassume h : P,\nshow R, \n  from h2 (h1 h)\n\n-- 4\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nassume h : P, h2 (h1 h)\n\n-- 5\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\n\u03bb h, h2 (h1 h)\n\n-- 6\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nh2 \u2218 h1\n\n-- 7\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nbegin\n  intro h,\n  apply h2, \n  apply h1,\n  exact h,\nend\n\n-- 8\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nbegin\n  intro h,\n  apply h2, \n  exact h1 h,\nend\n\n-- 9\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nbegin\n  intro h,\n  exact h2 (h1 h),\nend\n\n-- 10\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\n\u03bb h, h2 (h1 h)\n\n-- 11\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nh2 \u2218 h1\n\n-- 12\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nby tauto\n\n-- 13\u00ba demostraci\u00f3n\nexample \n  (h1 : P \u2192 Q)\n  (h2 : Q \u2192 R)\n  : P \u2192 R :=\nby finish\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista L\u00f3gica con Lean el v\u00eddeo Pruebas del silogismo hipot\u00e9tico en el que se se comentan 11 pruebas en Lean del silogismo hipot\u00e9tico P \u2192 Q, Q \u2192 R \u22a2 P \u2192 R. Se comienza con pruebas declarativas, con razonamiento hacia adelante, que se reducen a funcionales; a continuaci\u00f3n, se hacen&#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\/7365"}],"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=7365"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7365\/revisions"}],"predecessor-version":[{"id":7368,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7365\/revisions\/7368"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7365"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7365"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}