{"id":7485,"date":"2020-10-29T13:43:52","date_gmt":"2020-10-29T12:43:52","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7485"},"modified":"2020-12-21T13:45:04","modified_gmt":"2020-12-21T12:45:04","slug":"formatus-pruebas-en-lean-de-a-%e2%88%a9-b%e1%b6%9c-%e2%88%aa-b-a-%e2%88%aa-b","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-a-%e2%88%a9-b%e1%b6%9c-%e2%88%aa-b-a-%e2%88%aa-b\/","title":{"rendered":"ForMatUS: Pruebas en Lean de (A \u2229 B\u1d9c) \u222a B = A \u222a B"},"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\/Co3dEzqLVzM\">v\u00eddeo<\/a> en el que se comentan 4 pruebas en Lean de la propiedad<\/p>\n<pre lang=\"lean\">(A \u2229 B\u1d9c) \u222a B = A \u222a B\n<\/pre>\n<p>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\/Co3dEzqLVzM\" 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\/Prueba_de_(A%E2%88%A9B%E1%B6%9C)%E2%88%AAB_igual_A%E2%88%AAB.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    (A \u2229 B\u1d9c) \u222a B = A \u222a B\n-- ----------------------------------------------------\n\nimport data.set\n\nopen set\n\nvariable  U : Type\nvariables A B C : set U\n\n-- 1\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (A \u2229 B\u1d9c) \u222a B = A \u222a B :=\ncalc\n  (A \u2229 B\u1d9c) \u222a B = (A \u222a B) \u2229 (B\u1d9c \u222a B) : by rw union_distrib_right\n           ... = (A \u222a B) \u2229 univ     : by rw compl_union_self\n           ... = A \u222a B              : by rw inter_univ\n\nexample : (A \u2229 B) \u222a C = (A \u222a C) \u2229 (B \u222a C) :=\n-- by library_search\nunion_distrib_right A B C\n\nexample : B\u1d9c \u222a B = univ :=\n-- by library_search\ncompl_union_self B\n\nexample : A \u2229 univ = A :=\n-- by library_search\ninter_univ A\n\n-- 2\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (A \u2229 B\u1d9c) \u222a B = A \u222a B :=\nbegin\n  rw union_distrib_right,\n  rw compl_union_self,\n  rw inter_univ,\nend\n\n-- 3\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (A \u2229 B\u1d9c) \u222a B = A \u222a B :=\nby rw [union_distrib_right, compl_union_self, inter_univ]\n\n-- 4\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (A \u2229 B\u1d9c) \u222a B = A \u222a B :=\nby simp [union_distrib_right]\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 la propiedad (A \u2229 B\u1d9c) \u222a B = A \u222a B 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;- &#8211;&#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\/7485"}],"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=7485"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7485\/revisions"}],"predecessor-version":[{"id":7487,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7485\/revisions\/7487"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}