{"id":7471,"date":"2020-10-25T11:43:15","date_gmt":"2020-10-25T10:43:15","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7471"},"modified":"2020-12-21T11:44:08","modified_gmt":"2020-12-21T10:44:08","slug":"formatus-regla-del-conjunto-vacio-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-regla-del-conjunto-vacio-en-lean\/","title":{"rendered":"ForMatUS: Regla del conjunto vac\u00edo en Lean"},"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\/MfoCvy36UP8\">v\u00eddeo<\/a> en el que se comentan 11 pruebas en Lean que ilustran la regla del conjunto vac\u00edo 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\/MfoCvy36UP8\" 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\/Minimimalidad_del_vacio.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    \u2205 \u2286 A\n-- ----------------------------------------------------\n\nimport data.set\n\nvariable  U : Type\nvariables A : set U\nvariable  x : U\n\nopen set\n\n-- #reduce (\u2205 : set U)\n-- #reduce x \u2208 (\u2205 : set U)\n\n-- 1\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nbegin\n  intros x h,\n  simp at h,\n  exfalso,\n  exact h,\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nbegin\n  intros x h,\n  exfalso,\n  exact h,\nend\n\n-- 3\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nassume x,\nassume h : x \u2208 (\u2205 : set U),\nshow x \u2208 A, from false.elim h\n\n-- 4\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\n\u03bb x, \u03bb h, false.elim h\n\n-- 5\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\n\u03bb _, false.elim\n\n-- 6\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\n-- by library_search\nempty_subset A\n\n-- 7\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nassume x,\nassume h : x \u2208 (\u2205 : set U),\nshow x \u2208 A, from absurd h (not_mem_empty x)\n\n-- 8\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\n\u03bb x h, absurd h (not_mem_empty x)\n\n-- 9\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\n-- by hint\nby tauto\n\n-- 10\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nby finish\n\n-- 11\u00aa demostraci\u00f3n\nexample : \u2205 \u2286 A :=\nby simp\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 11 pruebas en Lean que ilustran la regla del conjunto vac\u00edo 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 &#8212; \u2205&#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\/7471"}],"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=7471"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7471\/revisions"}],"predecessor-version":[{"id":7472,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7471\/revisions\/7472"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}