{"id":7419,"date":"2020-09-29T13:38:20","date_gmt":"2020-09-29T11:38:20","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7419"},"modified":"2020-12-20T13:39:26","modified_gmt":"2020-12-20T12:39:26","slug":"formatus-pruebas-en-lean-de-la-regla-de-reduccion-al-absurdo","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-la-regla-de-reduccion-al-absurdo\/","title":{"rendered":"ForMatUS: Pruebas en Lean de la regla de reducci\u00f3n al absurdo"},"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\/3HLxFpKjld8\">v\u00eddeo<\/a> en el que se comentan 6 pruebas en Lean de la regla de reducci\u00f3n al absurdo 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\/3HLxFpKjld8\" 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\/Prueba_de_la_regla_de_reduccion_al_absurdo.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">import tactic\n\nvariable (P : Prop)\n\n-- ----------------------------------------------------\n-- Ej. 1 (p. 22) Demostrar que\n--    \u00acP \u2192 false \u22a2 P\n-- ----------------------------------------------------\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 false)\n  : P :=\nhave h2 : \u00ac\u00acP, from\n  assume h3 : \u00acP,\n  show false, from h1 h3,\nshow P, from not_not.mp h2\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 false)\n  : P :=\nbegin\n  apply not_not.mp,\n  intro h2,\n  exact h1 h2,\nend\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 false)\n  : P :=\nbegin\n  apply not_not.mp,\n  exact \u03bb h2, h1 h2,\nend\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 false)\n  : P :=\nnot_not.mp (\u03bb h2, h1 h2)\n\n-- #print axioms not_not\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 false)\n  : P :=\n-- by library_search\nby_contra h1\n\n-- #print axioms by_contra\n\n-- 6\u00aa demostraci\u00f3n\nlemma RAA\n  (h1 : \u00acP \u2192 false)\n  : P :=\n-- by hint\nby finish\n\n-- #print axioms RAA\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 6 pruebas en Lean de la regla de reducci\u00f3n al absurdo 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 import tactic variable (P : Prop) &#8212; &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-&#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\/7419"}],"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=7419"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7419\/revisions"}],"predecessor-version":[{"id":7421,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7419\/revisions\/7421"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}