{"id":7516,"date":"2020-11-01T19:02:03","date_gmt":"2020-11-01T18:02:03","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7516"},"modified":"2020-12-21T19:02:53","modified_gmt":"2020-12-21T18:02:53","slug":"formatus-pruebas-en-lean-de-una-desigualdad-entre-numeros-naturales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-una-desigualdad-entre-numeros-naturales\/","title":{"rendered":"ForMatUS: Pruebas en Lean de una desigualdad entre n\u00fameros naturales"},"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\/rV_seI6Zlac\">v\u00eddeo<\/a> en el que se comentan 8 pruebas en Lean de una desigualdad entre n\u00fameros naturales, 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\/rV_seI6Zlac\" 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\/4_Relaciones\/Pruebas_de_desigualdad_entre_naturales.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar que si n y m son n\u00fameros naturales\n-- tales que n + 1 \u2264 m, entonces n &lt; m + 1.\n-- ----------------------------------------------------\n\nimport tactic\n\nvariables n m : \u2115\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\ncalc\n  n   &lt; n + 1 : lt_add_one n\n  ... \u2264 m     : h\n  ... &lt; m + 1 : lt_add_one m\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\nhave h1 : n &lt; n + 1, from lt_add_one n,\nhave h2 : n &lt; m,     from lt_of_lt_of_le h1 h,\nhave h3 : m &lt; m + 1, from lt_add_one m,\nshow n &lt; m + 1,      from lt.trans h2 h3\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\nbegin\n  apply lt_trans (lt_add_one n),\n  apply lt_of_le_of_lt h (lt_add_one m),\nend\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\nlt_trans (lt_add_one n) (lt_of_le_of_lt h (lt_add_one m))\n\n-- 5\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\n-- by suggest\nnat.lt.step h\n\n-- 6\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\n-- by hint\nby omega\n\n-- 7\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\nby linarith\n\n-- 8\u00aa demostraci\u00f3n\nexample\n  (h : n + 1 \u2264 m)\n  : n &lt; m + 1 :=\nby nlinarith\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 8 pruebas en Lean de una desigualdad entre n\u00fameros naturales, 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 que si n&#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\/7516"}],"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=7516"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7516\/revisions"}],"predecessor-version":[{"id":7517,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7516\/revisions\/7517"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7516"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}