{"id":7467,"date":"2020-10-24T11:33:08","date_gmt":"2020-10-24T09:33:08","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7467"},"modified":"2020-12-21T11:33:52","modified_gmt":"2020-12-21T10:33:52","slug":"formatus-regla-de-introduccion-de-la-interseccion-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-regla-de-introduccion-de-la-interseccion-en-lean\/","title":{"rendered":"ForMatUS: Regla de introducci\u00f3n de la intersecci\u00f3n 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\/EWBe22M3ef4\">v\u00eddeo<\/a> en el que se comentan 7 pruebas en Lean de la regla de introducci\u00f3n de la intersecci\u00f3n 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\/EWBe22M3ef4\" 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\/Introduccion_de_la_interseccion.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B\n-- ----------------------------------------------------\n\nimport data.set\n\nvariable  U : Type\nvariables A B : set U\nvariable  x : U\n\nopen set\n\n-- #reduce x \u2208 A \u2229 B\n\n-- 1\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\nbegin\n  intros h1 h2,\n  simp,\n  split,\n  { exact h1, },\n  { exact h2, },\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\nbegin\n  intros h1 h2,\n  split,\n  { exact h1, },\n  { exact h2, },\nend\n\n-- 3\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\nassume h1 : x \u2208 A,\nassume h2 : x \u2208 B,\nshow x \u2208 A \u2229 B, from and.intro h1 h2\n\n-- 4\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\nassume h1 : x \u2208 A,\nassume h2 : x \u2208 B,\nshow x \u2208 A \u2229 B, from \u27e8h1, h2\u27e9\n\n-- 5\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\nassume h1 : x \u2208 A,\nassume h2 : x \u2208 B,\n\u27e8h1, h2\u27e9\n\n-- 6\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\n\u03bb h1 h2, \u27e8h1, h2\u27e9\n\n-- 7\u00aa demostraci\u00f3n\nexample : x \u2208 A \u2192 x \u2208 B \u2192 x \u2208 A \u2229 B :=\n-- by library_search\nmem_inter\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 regla de introducci\u00f3n de la intersecci\u00f3n 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 &#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\/7467"}],"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=7467"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7467\/revisions"}],"predecessor-version":[{"id":7468,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7467\/revisions\/7468"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}