{"id":7437,"date":"2020-10-01T17:12:23","date_gmt":"2020-10-01T15:12:23","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7437"},"modified":"2020-12-20T17:13:24","modified_gmt":"2020-12-20T16:13:24","slug":"formatus-regla-de-introduccion-del-cuantificador-universal-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-regla-de-introduccion-del-cuantificador-universal-en-lean\/","title":{"rendered":"ForMatUS: Regla de introducci\u00f3n del cuantificador universal 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\/MDpiS1BwNaU\">v\u00eddeo<\/a> en el que se comentan pruebas en Lean de la propiedad<\/p>\n<pre lang=\"lean\">\u2200x [P(x) \u2192 \u00acQ(x)], \u2200x P(x) \u22a2 \u2200x \u00acQ(x)\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\/MDpiS1BwNaU\" 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\/2_LPO\/Regla_de_introduccion_del_cuantificador_universal.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- Ej. 1. Demostrar\n--    \u2200x [P(x) \u2192 \u00acQ(x)], \u2200x P(x) \u22a2 \u2200x \u00acQ(x)\n\nimport tactic\n\nvariable  U : Type\nvariables P Q : U \u2192 Prop\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nassume x\u2080,\nhave h4 : P x\u2080 \u2192 \u00acQ x\u2080, from h1 x\u2080,\nhave h5 : P x\u2080,         from h2 x\u2080,\nshow \u00acQ x\u2080,             from h4 h5\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nassume x\u2080, (h1 x\u2080) (h2 x\u2080)\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\n\u03bb x\u2080, (h1 x\u2080) (h2 x\u2080)\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nbegin\n  intro x\u2080,\n  apply h1,\n  apply h2,\nend\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nbegin\n  intro x\u2080,\n  specialize h1 x\u2080,\n  specialize h2 x\u2080,\n  apply h1,\n  exact h2,\nend\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nbegin\n  intro x\u2080,\n  specialize h1 x\u2080,\n  specialize h2 x\u2080,\n  exact h1 h2,\nend\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\n-- by hint\nby tauto\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h1 : \u2200x, P x \u2192 \u00acQ x)\n  (h2 : \u2200x, P x)\n  : \u2200x, \u00acQ x :=\nby finish\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 pruebas en Lean de la propiedad \u2200x [P(x) \u2192 \u00acQ(x)], \u2200x P(x) \u22a2 \u2200x \u00acQ(x) 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; 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":[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\/7437"}],"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=7437"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7437\/revisions"}],"predecessor-version":[{"id":7438,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7437\/revisions\/7438"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}