{"id":7499,"date":"2020-10-30T16:21:44","date_gmt":"2020-10-30T15:21:44","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7499"},"modified":"2020-12-21T16:22:33","modified_gmt":"2020-12-21T15:22:33","slug":"formatus-pruebas-en-lean-de-%e2%8b%83i-%e2%8b%82j-a-i-j-%e2%8a%86-%e2%8b%82j-%e2%8b%83i-a-i-j","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-%e2%8b%83i-%e2%8b%82j-a-i-j-%e2%8a%86-%e2%8b%82j-%e2%8b%83i-a-i-j\/","title":{"rendered":"ForMatUS: Pruebas en Lean de (\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j)"},"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\/9vTnKpMSblI\">v\u00eddeo<\/a> en el que se comentan 2 pruebas en Lean de la propiedad<\/p>\n<pre lang=\"lean\">(\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j)\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\/9vTnKpMSblI\" 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\/Uniones_de_intersecciones.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    (\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j)\n-- ----------------------------------------------------\n\nimport data.set\n\nopen set\n\nvariables {I J U : Type}\nvariables (A : I \u2192 J \u2192 set U)\n\n-- 1\u00aa demostraci\u00f3n\nexample : (\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j) :=\nbegin\n  intros x h,\n  rw mem_Union at h,\n  cases h with i hi,\n  rw mem_Inter at hi,\n  apply mem_Inter.mpr,\n  intro j,\n  apply mem_Union.mpr,\n  use i,\n  exact (hi j),\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample : (\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j) :=\nbegin\n  intros x h,\n  simp * at *,\n  cases h with i hi,\n  intro j,\n  use i,\n  exact (hi j),\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 la propiedad (\u22c3i, \u22c2j, A i j) \u2286 (\u22c2j, \u22c3i, A i j) 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 &#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\/7499"}],"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=7499"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7499\/revisions"}],"predecessor-version":[{"id":7500,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7499\/revisions\/7500"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}