{"id":7312,"date":"2020-08-31T11:40:55","date_gmt":"2020-08-31T09:40:55","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7312"},"modified":"2020-08-31T17:07:02","modified_gmt":"2020-08-31T15:07:02","slug":"formatus-el-maximo-comun-divisor-de-m-y-n-es-igual-a-m-si-y-solo-si-m-divide-a-n-en-lean","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-el-maximo-comun-divisor-de-m-y-n-es-igual-a-m-si-y-solo-si-m-divide-a-n-en-lean\/","title":{"rendered":"ForMatUS: El m\u00e1ximo com\u00fan divisor de m y n es igual a m si, y s\u00f3lo si, m divide a n (en Lean)"},"content":{"rendered":"<p>He a\u00f1adido a la lista <a href=\"https:\/\/bit.ly\/2QwnT30\">DAO (Demostraci\u00f3n Asistida por Ordenador) con Lean<\/a> el v\u00eddeo <a href=\"https:\/\/youtu.be\/8x5EfZx7TsY\">El m\u00e1ximo com\u00fan divisor de m y n es igual a m si, y s\u00f3lo si, m divide a n (en Lean)<\/a> en el que se comenta la prueba en Lean de la siguiente propiedad de los n\u00fameros naturales: el m\u00e1ximo com\u00fan divisor de a y b es igual a a si, y s\u00f3lo si, a divide a b. M\u00e1s concretamente,<\/p>\n<blockquote><p>\n  Sean m y n son n\u00fameros naturales. Entonces, son equivalentes<\/p>\n<ol>\n<li>mcd(m,n) = n <\/li>\n<li>m divide a n<\/li>\n<\/ol>\n<\/blockquote>\n<p>Su enunciado en Lean es<\/p>\n<pre lang=\"lean\">\nimport data.nat.gcd\n\nopen nat\n\nvariables (a b : \u2115)\n\nexample : a \u2223 b \u2194 gcd a b = a :=\nsorry\n<\/pre>\n<p>En la demostraci\u00f3n se utilizan los siguientes propiedades de los n\u00fameros naturales:<\/p>\n<pre lang=\"lean\">\ndvd_refl:      a \u2223 a\ndvd_antisymm : a \u2223 b \u2192 b \u2223 a \u2192 a = b \ndvd_gcd_iff :  c \u2223 gcd a b \u2194 c \u2223 a \u2227 c \u2223 b\ngcd_dvd :      gcd a b \u2223 a \u2227 gcd a b \u2223 b\n<\/pre>\n<p>Los enlaces correspondientes son:<\/p>\n<ul>\n<li>a la <a href=\"https:\/\/bit.ly\/2YOSsWh\">sesi\u00f3n en Lean Web<\/a>, <\/li>\n<li>al <a href=\"https:\/\/bit.ly\/32JUp7g\">c\u00f3digo<\/a>,<\/li>\n<li>al <a href=\"https:\/\/bit.ly\/32AyBuQ\">libro &#8220;DAO con Lean&#8221;<\/a> y<\/li>\n<li>al <a href=\"https:\/\/bit.ly\/34LaHzI\">repositorio en GitHub &#8220;DAO con Lean&#8221;<\/a>.<\/li>\n<\/ul>\n<p>A continuaci\u00f3n, se muestra el v\u00eddeo<\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/8x5EfZx7TsY\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista DAO (Demostraci\u00f3n Asistida por Ordenador) con Lean el v\u00eddeo El m\u00e1ximo com\u00fan divisor de m y n es igual a m si, y s\u00f3lo si, m divide a n (en Lean) en el que se comenta la prueba en Lean de la siguiente propiedad de los n\u00fameros naturales: el m\u00e1ximo&#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":[],"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\/7312"}],"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=7312"}],"version-history":[{"count":24,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7312\/revisions"}],"predecessor-version":[{"id":7336,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7312\/revisions\/7336"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}