{"id":7459,"date":"2020-10-19T19:23:31","date_gmt":"2020-10-19T17:23:31","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7459"},"modified":"2020-12-20T19:24:28","modified_gmt":"2020-12-20T18:24:28","slug":"formatus-pruebas-en-lean-de-x-y-z-x-z-y","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-x-y-z-x-z-y\/","title":{"rendered":"ForMatUS: Pruebas en Lean de (x + y) + z = (x + z) + y"},"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\/sI9Krgj0fpA\">v\u00eddeo<\/a> en el que se comentan 10 pruebas en Lean de la peopiedad<\/p>\n<pre lang=\"lean\">(x + y) + z = (x + z) + y\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\/sI9Krgj0fpA\" 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\/2_LPO\/Pruebas_de_(x+y)+zI(x+z)+y.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar que para todo x, y, z en \u2124 se tiene\n--    (x + y) + z = (x + z) + y\n-- ----------------------------------------------------\n\nimport tactic\nimport data.int.basic\n\nvariables (x y z : \u2124)\n\n-- 1\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\ncalc\n   (x + y) + z = x + (y + z) : add_assoc x y z\n           ... = x + (z + y) : eq.subst (add_comm y z) rfl\n           ... = (x + z) + y : eq.symm (add_assoc x z y)\n\n-- 2\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\ncalc\n  (x + y) + z = x + (y + z) : by rw add_assoc\n          ... = x + (z + y) : by rw [add_comm y z]\n          ... = (x + z) + y : by rw add_assoc\n\n-- 3\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nbegin\n  rw add_assoc,\n  rw add_comm y z,\n  rw add_assoc,\nend\n\nexample : (x + y) + z = (x + z) + y :=\nbegin\n  rw [add_assoc, add_comm y z, add_assoc],\nend\n\n-- 4\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nby rw [add_assoc, add_comm y z, add_assoc]\n\n-- 5\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\n-- by library_search\nadd_right_comm x y z\n\n-- 6\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\n-- by hint\nby omega\n\n-- 7\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nby linarith\n\n-- 8\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nby nlinarith\n\n-- 9\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nby ring\n\n-- 10\u00aa demostraci\u00f3n\nexample : (x + y) + z = (x + z) + y :=\nby finish\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 10 pruebas en Lean de la peopiedad (x + y) + z = (x + z) + y 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\/7459"}],"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=7459"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7459\/revisions"}],"predecessor-version":[{"id":7460,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7459\/revisions\/7460"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}