{"id":1458,"date":"2023-08-15T06:00:28","date_gmt":"2023-08-15T04:00:28","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=1458"},"modified":"2023-07-30T18:24:49","modified_gmt":"2023-07-30T16:24:49","slug":"15-ago-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/15-ago-23\/","title":{"rendered":"En los anillos, 1 + 1 = 2"},"content":{"rendered":"<p>Demostrar con Lean4 que En los anillos, \\(1 + 1 = 2\\)<\/p>\n<p>Para ello, completar la siguiente teor\u00eda de Lean4:<\/p>\n<pre lang=\"lean\">\r\nimport Mathlib.Algebra.Ring.Defs\r\nimport Mathlib.Tactic\r\nvariable {R : Type _} [Ring R]\r\n\r\nexample : 1 + 1 = (2 : R) :=\r\nsorry\r\n<\/pre>\n<p><!--more--><\/p>\n<p><b>Demostraci\u00f3n en lenguaje natural<\/b><\/p>\n<p><br \/>\nPor c\u00e1lculo.<\/p>\n<p><b>Demostraciones con Lean4<\/b><\/p>\n<pre lang=\"lean\">\r\nimport Mathlib.Algebra.Ring.Defs\r\nimport Mathlib.Tactic\r\nvariable {R : Type _} [Ring R]\r\n\r\n-- Demostraciones con Lean4\r\n-- ========================\r\n\r\n-- 1\u00aa demostraci\u00f3n\r\nexample : 1 + 1 = (2 : R) :=\r\nby norm_num\r\n\r\n-- 2\u00aa demostraci\u00f3n\r\nexample : 1 + 1 = (2 : R) :=\r\none_add_one_eq_two\r\n<\/pre>\n<p><b>Demostraciones interactivas<\/b><\/p>\n<p>Se puede interactuar con las demostraciones anteriores en <a href=\"https:\/\/lean.math.hhu.de\/#url=https:\/\/raw.githubusercontent.com\/jaalonso\/Calculemus2\/main\/src\/Uno_mas_uno_es_dos.lean\" rel=\"noopener noreferrer\" target=\"_blank\">Lean 4 Web<\/a>.<\/p>\n<p><b>Referencias<\/b><\/p>\n<ul>\n<li> J. Avigad y P. Massot. <a href=\"https:\/\/bit.ly\/3U4UjBk\">Mathematics in Lean<\/a>, p. 12.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar con Lean4 que En los anillos, \\(1 + 1 = 2\\) Para ello, completar la siguiente teor\u00eda de Lean4: import Mathlib.Algebra.Ring.Defs import Mathlib.Tactic variable {R : Type _} [Ring R] example : 1 + 1 = (2 : R) := sorry<\/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":"","_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,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[284,297],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1458"}],"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=1458"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1458\/revisions"}],"predecessor-version":[{"id":1459,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1458\/revisions\/1459"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=1458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=1458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=1458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}