{"id":7455,"date":"2020-10-18T19:07:16","date_gmt":"2020-10-18T17:07:16","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7455"},"modified":"2020-12-20T19:08:06","modified_gmt":"2020-12-20T18:08:06","slug":"formatus-pruebas-en-lean-de-la-transitividad-de-la-igualdad","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-la-transitividad-de-la-igualdad\/","title":{"rendered":"ForMatUS: Pruebas en Lean de la transitividad de la igualdad"},"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\/DHWM7yy88oc\">v\u00eddeo<\/a> en el que se comentan pruebas en Lean de la transitividad de la igualdad 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\/DHWM7yy88oc\" 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_la_transitividad_de_la_igualdad.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">import tactic\n\nvariable  (U : Type)\nvariables (x y z : U)\n\n-- ----------------------------------------------------\n-- Ej. 1. Demostrar que\n--    x = y, y = z \u22a2 x = z\n-- ----------------------------------------------------\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\neq.subst h2 h1\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nh2 \u25b8 h1\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\neq.substr h1 h2\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\neq.trans h1 h2\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nbegin\n  rw h1,\n  exact h2,\nend\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nbegin\n  rw h1,\n  assumption,\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nbegin\n  rwa h1,\nend\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nby rwa h1\n\n-- 9\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nbegin\n  rwa \u2190h2,\nend\n\n-- 10\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nbegin\n  rwa h2 at h1,\nend\n\n-- 11\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\nby simp *\n\n-- 12\u00aa demostraci\u00f3n\nexample\n  (h1 : x = y)\n  (h2 : y = z)\n  : x = z :=\n-- by hint\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 pruebas en Lean de la transitividad de la igualdad 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 (U : Type) variables (x y z&#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\/7455"}],"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=7455"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7455\/revisions"}],"predecessor-version":[{"id":7456,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7455\/revisions\/7456"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}