{"id":7465,"date":"2020-10-22T11:28:14","date_gmt":"2020-10-22T09:28:14","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7465"},"modified":"2020-12-21T11:29:13","modified_gmt":"2020-12-21T10:29:13","slug":"formatus-pruebas-en-lean-de-la-antisimetria-de-la-inclusion-de-conjuntos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-la-antisimetria-de-la-inclusion-de-conjuntos\/","title":{"rendered":"ForMatUS: Pruebas en Lean de la antisimetr\u00eda de la inclusi\u00f3n de conjuntos"},"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\/t8dxr4jjvMM\">v\u00eddeo<\/a> en el que se comentan 7 pruebas en Lean de la propiedad antisim\u00e9trica de la inclusi\u00f3n de conjuntos 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\/t8dxr4jjvMM\" 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\/3_Conjuntos\/Pruebas_de_la_antisimetria_de_la_inclusion_de_conjuntos.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    A \u2286 B, B \u2286 A \u22a2 A = B\n-- ----------------------------------------------------\n\nimport data.set\n\nvariable  U : Type\nvariables A B : set U\n\nopen set\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\nbegin\n  ext,\n  split,\n  { intro h,\n    exact h1 h, },\n  { intro h,\n    exact h2 h, },\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\next\n( assume x,\n  iff.intro\n  ( assume h : x \u2208 A,\n    show x \u2208 B, from h1 h)\n  ( assume h : x \u2208 B,\n    show x \u2208 A, from h2 h))\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\next\n(\u03bb x,\n iff.intro\n (\u03bb h, h1 h)\n (\u03bb h, h2 h))\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\neq_of_subset_of_subset\n  ( assume x,\n    assume h : x \u2208 A,\n    show x \u2208 B, from h1 h)\n  ( assume x,\n    assume h : x \u2208 B,\n    show x \u2208 A, from h2 h)\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\neq_of_subset_of_subset h1 h2\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : A \u2286 B)\n  (h2 : B \u2286 A)\n  : A = B :=\n-- by library_search\nsubset.antisymm h1 h2\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 7 pruebas en Lean de la propiedad antisim\u00e9trica de la inclusi\u00f3n de conjuntos 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\/7465"}],"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=7465"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7465\/revisions"}],"predecessor-version":[{"id":7466,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7465\/revisions\/7466"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}