{"id":7429,"date":"2020-09-30T13:58:45","date_gmt":"2020-09-30T11:58:45","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7429"},"modified":"2020-12-20T13:59:42","modified_gmt":"2020-12-20T12:59:42","slug":"formatus-pruebas-en-lean-de-p-%c2%ac%c2%acq-%e2%88%a7-r-%e2%8a%a2-%c2%ac%c2%acp-%e2%88%a7-r","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-p-%c2%ac%c2%acq-%e2%88%a7-r-%e2%8a%a2-%c2%ac%c2%acp-%e2%88%a7-r\/","title":{"rendered":"ForMatUS: Pruebas en Lean de P, \u00ac\u00ac(Q \u2227 R) \u22a2 \u00ac\u00acP \u2227 R"},"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\/Ky8hmE_qCGM\">v\u00eddeo<\/a> en el que se comentan 8 pruebas en Lean de la propiedad en Lean de<\/p>\n<pre lang=\"lean\">P, \u00ac\u00ac(Q \u2227 R) \u22a2 \u00ac\u00acP \u2227 R\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\/Ky8hmE_qCGM\" 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_P,%C2%AC%C2%AC(Q%E2%88%A7R)%E2%8A%A2%C2%AC%C2%ACP%E2%88%A7R.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. (p. 5) Demostrar\n--    P, \u00ac\u00ac(Q \u2227 R) \u22a2 \u00ac\u00acP \u2227 R\n-- ----------------------------------------------------\n\nimport tactic\n\nvariables (P Q R : Prop)\n\nopen_locale classical\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\nhave h3 : \u00ac\u00acP,   from not_not_intro h1,\nhave h4 : Q \u2227 R, from not_not.mp h2,\nhave h5 : R,     from and.elim_right h4,\nshow \u00ac\u00acP \u2227 R,    from and.intro h3 h5\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\nhave h3 : \u00ac\u00acP,   from not_not_intro h1,\nhave h4 : Q \u2227 R, from not_not.mp h2,\nhave h5 : R,     from and.elim_right h4,\nand.intro h3 h5\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\nhave h3 : \u00ac\u00acP,   from not_not_intro h1,\nhave h4 : Q \u2227 R, from not_not.mp h2,\nhave h5 : R,     from h4.2,\nand.intro h3 h5\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\nand.intro (not_not_intro h1) (not_not.mp h2).2\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\nbegin\n  split,\n  { exact not_not_intro h1, },\n  { push_neg at h2,\n    exact h2.2, },\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\n-- by hint\nby tauto\n\n-- 8\u00aa demostraci\u00f3n\nlemma aux\n  (h1 : P)\n  (h2 : \u00ac\u00ac(Q \u2227 R))\n  : \u00ac\u00acP \u2227 R :=\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 8 pruebas en Lean de la propiedad en Lean de P, \u00ac\u00ac(Q \u2227 R) \u22a2 \u00ac\u00acP \u2227 R 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 &#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\/7429"}],"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=7429"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7429\/revisions"}],"predecessor-version":[{"id":7431,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7429\/revisions\/7431"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}