{"id":7504,"date":"2020-10-31T16:31:54","date_gmt":"2020-10-31T15:31:54","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7504"},"modified":"2020-12-21T16:32:39","modified_gmt":"2020-12-21T15:32:39","slug":"formatus-pruebas-en-lean-de-que-las-relaciones-irreflexivas-y-transitivas-son-asimetricas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-que-las-relaciones-irreflexivas-y-transitivas-son-asimetricas\/","title":{"rendered":"ForMatUS: Pruebas en Lean de que las relaciones irreflexivas y transitivas son asim\u00e9tricas"},"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\/4DLWcRsISdE\">v\u00eddeo<\/a> en el que se comentan 4 pruebas en Lean de que las relaciones irreflexivas y transitivas son asim\u00e9tricas 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\/4DLWcRsISdE\" 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\/4_Relaciones\/Las_irreflexivas_y_transitivas_son_asimetricas.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar que las relaciones irreflexivas y\n-- transitivas son asim\u00e9tricas.\n-- ----------------------------------------------------\n\nvariable A : Type\nvariable R : A \u2192 A \u2192 Prop\n\n-- #reduce irreflexive R\n-- #reduce transitive R\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : irreflexive R)\n  (h2 : transitive R)\n  : \u2200 x y, R x y \u2192 \u00ac R y x :=\nbegin\n  intros x y h3 h4,\n  apply h1 x,\n  apply h2 h3 h4,\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : irreflexive R)\n  (h2 : transitive R)\n  : \u2200 x y, R x y \u2192 \u00ac R y x :=\nbegin\n  intros x y h3 h4,\n  apply (h1 x) (h2 h3 h4),\nend\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : irreflexive R)\n  (h2 : transitive R)\n  : \u2200 x y, R x y \u2192 \u00ac R y x :=\n\u03bb x y h3 h4, (h1 x) (h2 h3 h4)\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : irreflexive R)\n  (h2 : transitive R)\n  : \u2200 x y, R x y \u2192 \u00ac R y x :=\nassume x y,\nassume h3 : R x y,\nassume h4 : R y x,\nhave h5 : R x x, from h2 h3 h4,\nhave h6 : \u00ac R x x, from h1 x,\nshow false, from h6 h5\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 4 pruebas en Lean de que las relaciones irreflexivas y transitivas son asim\u00e9tricas 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. Demostrar&#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":[166,336],"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\/7504"}],"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=7504"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7504\/revisions"}],"predecessor-version":[{"id":7505,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7504\/revisions\/7505"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}