{"id":7508,"date":"2020-10-31T16:39:14","date_gmt":"2020-10-31T15:39:14","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7508"},"modified":"2020-12-21T16:40:08","modified_gmt":"2020-12-21T15:40:08","slug":"formatus-pruebas-en-lean-de-que-las-partes-estrictas-de-los-ordenes-parciales-son-transitivas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-que-las-partes-estrictas-de-los-ordenes-parciales-son-transitivas\/","title":{"rendered":"ForMatUS: Pruebas en Lean de que las partes estrictas de los \u00f3rdenes parciales son transitivas"},"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\/4XBqKYFVjto\">v\u00eddeo<\/a> en el que se comentan 2 pruebas en Lean de que las partes estrictas de los \u00f3rdenes parciales son transitivas usando los estilos aplicativos y declarativos.<\/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\/4XBqKYFVjto\" 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_estrictas_de_los_ordenes_parciales_son_transitivas.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. La parte estricta de una relaci\u00f3n R es la\n-- relaci\u00f3n R' definida por\n--    R' a b := R a b \u2227 a \u2260 b\n--\n-- Demostrar que si R es un orden parcial, entonces su\n-- parte estricta es transitiva.\n-- ----------------------------------------------------\n\nimport tactic\n\nsection\n\nparameter {A : Type}\nparameter (R : A \u2192 A \u2192 Prop)\nparameter (reflR    : reflexive R)\nparameter (transR   : transitive R)\nparameter (antisimR : anti_symmetric R)\nvariables {a b c : A}\n\ndefinition R' (a b : A) : Prop :=\n  R a b \u2227 a \u2260 b\n\ninclude transR\ninclude antisimR\n\n-- 1\u00aa demostraci\u00f3n\nexample : transitive R' :=\nbegin\n  rintros a b c \u27e8h1,h2\u27e9 \u27e8h3,h4\u27e9,\n  split,\n  { apply (transR h1 h3), },\n  { intro h5,\n    apply h4,\n    apply (antisimR h3),\n    rw \u2190h5,\n    exact h1, },\nend\n\n-- 2\u00aa demostraci\u00f3n\n-- ===============\n\nlocal infix \u2264 := R\nlocal infix &lt; := R'\n\nexample : transitive (&lt;) :=\nassume a b c,\nassume h\u2081 : a &lt; b,\nassume h\u2082 : b &lt; c,\nhave a \u2264 b, from and.left h\u2081,\nhave a \u2260 b, from and.right h\u2081,\nhave b \u2264 c, from and.left h\u2082,\nhave b \u2260 c, from and.right h\u2082,\nhave a \u2264 c, from transR \u2039a \u2264 b\u203a \u2039b \u2264 c\u203a,\nhave a \u2260 c, from\n    assume : a = c,\n    have c \u2264 b, from eq.subst \u2039a = c\u203a \u2039a \u2264 b\u203a,\n    have b = c, from antisimR \u2039b \u2264 c\u203a \u2039c \u2264 b\u203a,\n    show false, from \u2039b \u2260 c\u203a \u2039b = c\u203a,\nshow a &lt; c, from and.intro \u2039a \u2264 c\u203a \u2039a \u2260 c\u203a\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 2 pruebas en Lean de que las partes estrictas de los \u00f3rdenes parciales son transitivas usando los estilos aplicativos y declarativos. 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. La&#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\/7508"}],"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=7508"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7508\/revisions"}],"predecessor-version":[{"id":7509,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7508\/revisions\/7509"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}