{"id":1220,"date":"2022-11-25T18:04:36","date_gmt":"2022-11-25T16:04:36","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/?p=1220"},"modified":"2022-11-25T18:04:36","modified_gmt":"2022-11-25T16:04:36","slug":"25-nov-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/25-nov-22\/","title":{"rendered":"\u2203 x \u2208 \u211d, 2 < x < 3"},"content":{"rendered":"<p>Demostrar que \u2203 x \u2208 \u211d, 2 &lt; x &lt; 3<\/p>\n<p>Para ello, completar la siguiente teor\u00eda de Lean:<\/p>\n<pre lang=\"lean\">\nimport data.real.basic\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nsorry\n<\/pre>\n<p><!--more--><\/p>\n<p><b>Soluciones con Lean<\/b><\/p>\n<pre lang=\"lean\">\nimport data.real.basic\n\n-- 1\u00aa demostraci\u00f3n\n-- ===============\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nbegin\n  have h : 2 < (5 : \u211d) \/ 2 \u2227 (5 : \u211d) \/ 2 < 3,\n    by norm_num,\n  show \u2203 x : \u211d, 2 < x \u2227 x < 3,\n    by exact Exists.intro (5 \/ 2) h,\nend\n\n-- 2\u00aa demostraci\u00f3n\n-- ===============\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nbegin\n  have h : 2 < (5 : \u211d) \/ 2 \u2227 (5 : \u211d) \/ 2 < 3,\n    by norm_num,\n  show \u2203 x : \u211d, 2 < x \u2227 x < 3,\n    by exact \u27e85 \/ 2, h\u27e9,\nend\n\n-- 3\u00aa demostraci\u00f3n\n-- ===============\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\nbegin\n  use 5 \/ 2,\n  norm_num\nend\n\n-- 4\u00aa demostraci\u00f3n\n-- ===============\n\nexample : \u2203 x : \u211d, 2 < x \u2227 x < 3 :=\n\u27e85 \/ 2, by norm_num\u27e9\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\/Existencia_de_valor_intermedio.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. 30.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Demostrar que \u2203 x \u2208 \u211d, 2 &lt; x &lt; 3 Para ello, completar la siguiente teor\u00eda de Lean: import data.real.basic example : \u2203 x : \u211d, 2 < x \u2227 x < 3 := sorry\n<\/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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1220"}],"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=1220"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1220\/revisions"}],"predecessor-version":[{"id":1221,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/posts\/1220\/revisions\/1221"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/media?parent=1220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/categories?post=1220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/calculemus\/wp-json\/wp\/v2\/tags?post=1220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}