{"id":2021,"date":"2024-01-31T06:00:05","date_gmt":"2024-01-31T04:00:05","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=2021"},"modified":"2024-02-17T09:30:03","modified_gmt":"2024-02-17T07:30:03","slug":"31-ene-24","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/31-ene-24\/","title":{"rendered":"En \u211d, |a| = |a &#8211; b + b|"},"content":{"rendered":"\n<p>Demostrar con Lean4 que en &#92;(\u211d&#92;), &#92;(|a| = |a &#8211; b + b|&#92;)<\/p>\n<p>Para ello, completar la siguiente teor\u00eda de Lean4:<\/p>\n<pre lang=\"lean\">\nimport Mathlib.Data.Real.Basic\nvariable (a b : \u211d)\n\nexample\n  : |a| = |a - b + b| :=\nby sorry\n<\/pre>\n<p><!--more--><\/p>\n<h2>Demostraciones con Lean4<\/h2>\n<pre lang=\"lean\">\nimport Mathlib.Data.Real.Basic\nvariable (a b : \u211d)\n\n-- 1\u00aa demostraci\u00f3n\n-- ===============\n\nexample\n  : |a| = |a - b + b| :=\nby\n  congr\n  -- a = a - b + b\n  ring\n\n-- Comentario: La t\u00e1ctica congr sustituye una conclusi\u00f3n de la forma\n-- A = B por las igualdades de sus subt\u00e9rminos que no no iguales por\n-- definici\u00f3n. Por ejemplo, sustituye la conclusi\u00f3n (x * f y = g w * f z)\n-- por las conclusiones (x = g w) y (y = z).\n\n-- 2\u00aa demostraci\u00f3n\n-- ===============\n\nexample\n  (a b : \u211d)\n  : |a| = |a - b + b| :=\nby { congr ; ring }\n\n-- 3\u00aa demostraci\u00f3n\n-- ===============\n\nexample\n  (a b : \u211d)\n  : |a| = |a - b + b| :=\nby ring_nf\n<\/pre>\n<p>Se puede interactuar con las demostraciones anteriores en <a href=\"https:\/\/live.lean-lang.org\/#url=https:\/\/raw.githubusercontent.com\/jaalonso\/Calculemus2\/main\/src\/Demostracion_por_congruencia.lean\" rel=\"noopener noreferrer\" target=\"_blank\">Lean 4 Web<\/a>.<\/p>\n<h3>Referencias<\/h3>\n<ul>\n<li> J. Avigad y P. Massot. <a href=\"https:\/\/bit.ly\/3U4UjBk\">Mathematics in Lean<\/a>, p. 41.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar con Lean4 que en \u211d, |a| = |a &#8211; b + b|.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"default","_kad_post_title":"default","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"default","_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,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[24],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/2021"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/comments?post=2021"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/2021\/revisions"}],"predecessor-version":[{"id":2070,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/2021\/revisions\/2070"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=2021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=2021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=2021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}