{"id":7432,"date":"2020-09-30T14:03:05","date_gmt":"2020-09-30T12:03:05","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7432"},"modified":"2020-12-20T14:03:48","modified_gmt":"2020-12-20T13:03:48","slug":"formatus-pruebas-en-lean-de-%c2%acp-%e2%86%92-q-%c2%acq-%e2%8a%a2-p","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-%c2%acp-%e2%86%92-q-%c2%acq-%e2%8a%a2-p\/","title":{"rendered":"ForMatUS: Pruebas en Lean de \u00acP \u2192 Q, \u00acQ \u22a2 P"},"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\/WBN8Ml17uyM\">v\u00eddeo<\/a> en el que se comentan pruebas en Lean de<\/p>\n<pre lang=\"lean\">\u00acP \u2192 Q, \u00acQ \u22a2 P\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\/WBN8Ml17uyM\" 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\/Pruebas_de_%C2%ACP%E2%86%92Q,%C2%ACQ%E2%8A%A2P.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. (p. 7) Demostrar\n--    \u00acP \u2192 Q, \u00acQ \u22a2 P\n-- ----------------------------------------------------\n\nimport tactic\n\nvariables (P Q : Prop)\n\nopen_locale classical\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nhave h3 : \u00ac\u00acP, from mt h1 h2,\nshow P,        from not_not.mp h3\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nnot_not.mp (mt h1 h2)\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nbegin\n  by_contra h3,\n  apply h2,\n  exact h1 h3,\nend\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nbegin\n  by_contra h3,\n  exact h2 (h1 h3),\nend\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nby_contra (\u03bb h3, h2 (h1 h3))\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nby_contra (\u03bb h3, (h2 \u2218 h1) h3)\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\nby_contra (h2 \u2218 h1)\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\n-- by library_search\nnot_not.mp (mt h1 h2)\n\n-- 9\u00aa demostraci\u00f3n\nexample\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\n-- by hint\nby tauto\n\n-- 10\u00aa demostraci\u00f3n\nlemma aux\n  (h1 : \u00acP \u2192 Q)\n  (h2 : \u00acQ)\n  : P :=\n-- by hint\nby finish\n\n-- #print axioms aux\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 \u00acP \u2192 Q, \u00acQ \u22a2 P 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; &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;- &#8212; Ej. 1. (p. 7) Demostrar &#8211;&#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\/7432"}],"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=7432"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7432\/revisions"}],"predecessor-version":[{"id":7433,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7432\/revisions\/7433"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}