{"id":7461,"date":"2020-10-21T19:31:02","date_gmt":"2020-10-21T17:31:02","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7461"},"modified":"2020-12-20T19:31:47","modified_gmt":"2020-12-20T18:31:47","slug":"formatus-pruebas-en-lean-del-desarrollo-de-un-producto-de-dos-sumas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-del-desarrollo-de-un-producto-de-dos-sumas\/","title":{"rendered":"ForMatUS: Pruebas en Lean del desarrollo de un producto de dos sumas"},"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\/78wuVCsvkP8\">v\u00eddeo<\/a> en el que se comentan ??? pruebas en Lean de la propiedad<\/p>\n<pre lang=\"lean\">(a + b) * (c + d) = a * c + b * c + a * d + b * d\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\/78wuVCsvkP8\" 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\/Pruebas_de_desarrollo_de_producto_de_sumas.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ------------------------------------------------------\n-- Ej. 1. Sean a, b, c y d n\u00fameros enteros. Demostrar que\n--    (a + b) * (c + d) = a * c + b * c + a * d + b * d\n-- ------------------------------------------------------\n\nimport tactic\nimport data.int.basic\n\nvariables a b c d : \u2124\n\n-- 1\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\ncalc\n  (a + b) * (c + d)\n      = (a + b) * c + (a + b) * d         : by rw left_distrib\n  ... = (a * c + b * c) + (a + b) * d     : by rw right_distrib\n  ... = (a * c + b * c) + (a * d + b * d) : by rw right_distrib\n  ... = a * c + b * c + a * d + b * d     : by rw \u2190add_assoc\n\n-- 2\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\nby rw [left_distrib, right_distrib, right_distrib, \u2190add_assoc]\n\n-- 3\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\nbegin\n  rw left_distrib,\n  rw right_distrib,\n  rw right_distrib,\n  rw \u2190add_assoc,\nend\n\n-- 4\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\ncalc\n  (a + b) * (c + d)\n      = (a + b) * c + (a + b) * d         : by rw mul_add\n  ... = (a * c + b * c) + (a + b) * d     : by rw add_mul\n  ... = (a * c + b * c) + (a * d + b * d) : by rw add_mul\n  ... = a * c + b * c + a * d + b * d     : by rw \u2190add_assoc\n\n-- 5\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\n-- by hint\nby linarith\n\n-- 6\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\nby nlinarith\n\n-- 7\u00aa demostraci\u00f3n\nexample : (a + b) * (c + d) = a * c + b * c + a * d + b * d :=\nby ring\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 (a + b) * (c + d) = a * c + b * c + a * d + b * d usando los estilos declarativos, aplicativos, funcional y autom\u00e1tico. A continuaci\u00f3n,&#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\/7461"}],"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=7461"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7461\/revisions"}],"predecessor-version":[{"id":7462,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7461\/revisions\/7462"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7461"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7461"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}