{"id":7514,"date":"2020-10-31T16:47:23","date_gmt":"2020-10-31T15:47:23","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7514"},"modified":"2020-12-21T16:48:04","modified_gmt":"2020-12-21T15:48:04","slug":"formatus-pruebas-en-lean-de-que-las-partes-simetricas-son-simetricas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-que-las-partes-simetricas-son-simetricas\/","title":{"rendered":"ForMatUS: Pruebas en Lean de que las partes sim\u00e9tricas son sim\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\/-B9CkdlvS2s\">v\u00eddeo<\/a> en el que se comentan 6 pruebas en Lean de la siguiente propiedad: &#8220;Si R es una relaci\u00f3n, entonces su parte sim\u00e9trica (es decir, la relaci\u00f3n S definida por S x y := R x y \u2227 R y x) es sim\u00e9trica&#8221;, 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\/-B9CkdlvS2s\" 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_partes_simetricas_son_simetricas.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. La parte sim\u00e9trica de una relaci\u00f3n R es la\n-- relaci\u00f3n S definida por\n--    S x y := R x y \u2227 R y x\n--\n-- Demostrar que la parte sim\u00e9trica de cualquier\n-- relaci\u00f3n es sim\u00e9trica.\n-- ----------------------------------------------------\n\nsection\nparameter A : Type\nparameter R : A \u2192 A \u2192 Prop\n\ndef S (x y : A) := R x y \u2227 R y x\n\n-- 1\u00aa demostraci\u00f3n\nexample : symmetric S :=\nbegin\n  intros x y h,\n  split,\n  { exact h.right, },\n  { exact h.left, },\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample : symmetric S :=\nbegin\n  intros x y h,\n  exact \u27e8h.right, h.left\u27e9,\nend\n\n-- 3\u00aa demostraci\u00f3n\nexample : symmetric S :=\n\u03bb x y h, \u27e8h.right, h.left\u27e9\n\n-- 4\u00aa demostraci\u00f3n\nexample : symmetric S :=\nassume x y,\nassume h : S x y,\nhave h1 : R x y, from h.left,\nhave h2 : R y x, from h.right,\nshow S y x, from \u27e8h2, h1\u27e9\n\n-- 5\u00aa demostraci\u00f3n\nexample : symmetric S :=\nassume x y,\nassume h : S x y,\nshow S y x, from \u27e8h.right, h.left\u27e9\n\n-- 6\u00aa demostraci\u00f3n\nexample : symmetric S :=\n\u03bb x y h, \u27e8h.right, h.left\u27e9\n\nend\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 6 pruebas en Lean de la siguiente propiedad: &#8220;Si R es una relaci\u00f3n, entonces su parte sim\u00e9trica (es decir, la relaci\u00f3n S definida por S x y := R x y \u2227 R y x) es sim\u00e9trica&#8221;, usando los estilos&#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\/7514"}],"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=7514"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7514\/revisions"}],"predecessor-version":[{"id":7515,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7514\/revisions\/7515"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7514"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7514"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7514"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}