{"id":1118,"date":"2022-10-05T06:00:06","date_gmt":"2022-10-05T04:00:06","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=1118"},"modified":"2022-09-26T17:08:43","modified_gmt":"2022-09-26T15:08:43","slug":"si-a-b-%e2%88%88-%e2%84%9d-entonces-a-b-%e2%89%a4-a-b","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/si-a-b-%e2%88%88-%e2%84%9d-entonces-a-b-%e2%89%a4-a-b\/","title":{"rendered":"Si a, b \u2208 \u211d, entonces |a| &#8211; |b| \u2264 |a &#8211; b|"},"content":{"rendered":"<p>Sean a y b n\u00fameros reales. Demostrar que<\/p>\n<pre lang=\"text\">\n   |a| - |b| \u2264 |a - b|\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 : \u211d\n\nexample : |a| - |b| \u2264 |a - b| :=\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 : \u211d\n\nexample : |a| - |b| \u2264 |a - b| :=\ncalc |a| - |b|\n     = |a - b + b| - |b|     : by simp\n ... \u2264 (|a - b| + |b|) - |b| : sub_le_sub_right (abs_add (a - b) b) (|b|)\n ... = |a - b|               : add_sub_cancel (|a - b|) (|b|)\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\/absoluto_resta.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. 20.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Sean a y b n\u00fameros reales. Demostrar que |a| &#8211; |b| \u2264 |a &#8211; b| Para ello, completar la siguiente teor\u00eda de Lean: import data.real.basic variables a b : \u211d example : |a| &#8211; |b| \u2264 |a &#8211; b| := 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\/1118"}],"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=1118"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1118\/revisions"}],"predecessor-version":[{"id":1119,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1118\/revisions\/1119"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=1118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=1118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=1118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}