{"id":968,"date":"2022-08-23T06:00:12","date_gmt":"2022-08-23T04:00:12","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=968"},"modified":"2022-09-11T13:37:10","modified_gmt":"2022-09-11T11:37:10","slug":"identidad-condicional-en-los-reales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/identidad-condicional-en-los-reales\/","title":{"rendered":"Si a, b, c, d, e y f son n\u00fameros reales tales que a * b = c * d y  e = f entonces, a * (b * e) = c * (d * f)"},"content":{"rendered":"<p>Demostrar que si a, b, c, d, e y f son n\u00fameros reales tales que<\/p>\n<pre lang=\"text\">\n   a * b = c * d\n   e = f\n<\/pre>\n<p>Entonces,<\/p>\n<pre lang=\"text\">\n   a * (b * e) = c * (d * f)\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 d e f : \u211d\n\nexample\n  (h1 : a * b = c * d)\n  (h2 : e = f)\n  : a * (b * e) = c * (d * f) :=\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 d e f : \u211d\n\n-- 1\u00aa demostraci\u00f3n\nexample\n  (h1 : a * b = c * d)\n  (h2 : e = f)\n  : a * (b * e) = c * (d * f) :=\nbegin\n  rw h2,\n  rw \u2190mul_assoc,\n  rw h1,\n  rw mul_assoc,\nend\n\n-- 2\u00aa demostraci\u00f3n\nexample\n  (h1 : a * b = c * d)\n  (h2 : e = f)\n  : a * (b * e) = c * (d * f) :=\ncalc a * (b * e)\n     = a * (b * f) : by rw h2\n ... = (a * b) * f : by rw \u2190mul_assoc\n ... = (c * d) * f : by rw h1\n ... = c * (d * f) : by rw mul_assoc\n\n-- 3\u00aa demostraci\u00f3n\nexample\n  (h1 : a * b = c * d)\n  (h2 : e = f)\n  : a * (b * e) = c * (d * f) :=\ncalc a * (b * e)\n     = a * (b * f) : by rw h2\n ... = (a * b) * f : by ring\n ... = (c * d) * f : by rw h1\n ... = c * (d * f) : by ring\n\n-- 4\u00aa demostraci\u00f3n\nexample\n  (h1 : a * b = c * d)\n  (h2 : e = f)\n  : a * (b * e) = c * (d * f) :=\nby finish\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\/Identidad_condicional_en_los_reales.lean\" rel=\"noopener noreferrer\" target=\"_blank\">esta sesi\u00f3n con Lean<\/a>.<br \/>\n<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. 6.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar que si a, b, c, d, e y f son n\u00fameros reales tales que a * b = c * d e = f Entonces, a * (b * e) = c * (d * f) Para ello, completar la siguiente teor\u00eda de Lean: import data.real.basic variables a b c d e f : \u211d example (h1 : a * b = c * d) (h2 : e = f) : a * (b * e) = c * (d * f) :=<\/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\/968"}],"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=968"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/968\/revisions"}],"predecessor-version":[{"id":1070,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/968\/revisions\/1070"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}