{"id":965,"date":"2022-08-22T06:30:36","date_gmt":"2022-08-22T04:30:36","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=965"},"modified":"2022-09-11T13:34:21","modified_gmt":"2022-09-11T11:34:21","slug":"asociativa-conmutativa-de-los-reales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/asociativa-conmutativa-de-los-reales\/","title":{"rendered":"Si a, b y c son n\u00fameros reales, entonces (a * b) * c = b * (a * c)"},"content":{"rendered":"<p>Demostrar que los n\u00fameros reales tienen la siguiente propiedad<\/p>\n<pre lang=\"text\">\n(a * b) * c = b * (a * c)\n<\/pre>\n<p>Para ello, completar la siguiente teor\u00eda de Lean:<\/p>\n<pre lang=\"lean\">\nimport data.real.basic\n\nvariables a b c : \u211d\n\nexample : (a * b) * c = b * (a * c) :=\nsorry\n<\/pre>\n<p><!--more--><\/p>\n<p><b>Soluciones con Lean<\/b><\/p>\n<pre lang=\"lean\">\nimport data.real.basic\n\nvariables a b c : \u211d\n\n-- 1\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (a * b) * c = b * (a * c) :=\nbegin\n  rw mul_comm a b,\n  rw mul_assoc b a c,\nend\n\n-- 2\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (a * b) * c = b * (a * c) :=\ncalc (a * b) * c\n     = (b * a) * c : by rw mul_comm a b\n ... = b * (a * c) : by rw mul_assoc b a c\n\n-- 3\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (a * b) * c = b * (a * c) :=\ncalc (a * b) * c\n     = (b * a) * c : by ring\n ... = b * (a * c) : by ring\n\n-- 4\u00aa demostraci\u00f3n\n-- ===============\n\nexample : (a * b) * c = b * (a * c) :=\nby ring\n<\/pre>\n<p>Se puede interactuar con la prueba anterior en <a href=\"https:\/\/leanprover-community.github.io\/lean-web-editor\/#url=https:\/\/raw.githubusercontent.com\/jaalonso\/Calculemus\/main\/src\/Asociativa_conmutativa_de_los_reales.lean\" rel=\"noopener noreferrer\" target=\"_blank\">esta sesi\u00f3n con Lean<\/a>.<\/p>\n<p><b>Referencias<\/b><\/p>\n<ul>\n<li>J. Avigad, K. Buzzard, R.Y. Lewis y P. Massot. <a href=\"https:\/\/bit.ly\/3U4UjBk\">Mathematics in Lean<\/a>, p. 5.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar que los n\u00fameros reales tienen la siguiente propiedad (a * b) * c = b * (a * c) Para ello, completar la siguiente teor\u00eda de Lean: import data.real.basic variables a b c : \u211d example : (a * b) * c = b * (a * c) := 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":[286],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/965"}],"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=965"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/965\/revisions"}],"predecessor-version":[{"id":1069,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/965\/revisions\/1069"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}