{"id":7457,"date":"2020-10-19T19:17:40","date_gmt":"2020-10-19T17:17:40","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7457"},"modified":"2020-12-20T19:18:26","modified_gmt":"2020-12-20T18:18:26","slug":"formatus-pruebas-en-lean-de-y-x-%e2%86%92-y-z-%e2%86%92-x-z","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/formatus-pruebas-en-lean-de-y-x-%e2%86%92-y-z-%e2%86%92-x-z\/","title":{"rendered":"ForMatUS: Pruebas en Lean de y = x \u2192 y = z \u2192 x = z"},"content":{"rendered":"<p>He a\u00f1adido a la lista <a href=\"https:\/\/bit.ly\/2FcUrwQ\">L\u00f3gica con Lean<\/a> el <a href=\"https:\/\/youtu.be\/niY1mj3OSbk\">v\u00eddeo<\/a> en el que se comentan 12 pruebas en Lean de la propiedad<\/p>\n<pre lang=\"lean\">y = x \u2192 y = z \u2192 x = z\n<\/pre>\n<p>usando los estilos declarativos, aplicativos, funcional y autom\u00e1tico.<\/p>\n<p>A continuaci\u00f3n, se muestra el v\u00eddeo<\/p>\n<p><center><\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/niY1mj3OSbk\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><\/iframe><\/p>\n<p><\/center>y el <a href=\"https:\/\/github.com\/jaalonso\/Logica_con_Lean\/blob\/master\/src\/2_LPO\/Pruebas_de_yIx%E2%86%92yIz%E2%86%92xIz.lean\">c\u00f3digo<\/a> de la teor\u00eda utilizada<\/p>\n<pre lang=\"lean\">-- ----------------------------------------------------\n-- Ej. 1. Demostrar\n--    y = x \u2192 y = z \u2192 x = z\n-- ----------------------------------------------------\n\nimport tactic\n\nvariables (U : Type)\nvariables (x y z : U)\n\n-- 1\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\nhave h3 : x = y, from eq.symm h1,\nshow x = z,      from eq.trans h3 h2\n\n-- 2\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\nhave h3 : x = y, from eq.symm h1,\neq.trans h3 h2\n\n-- 3\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\neq.trans (eq.symm h1) h2\n\n-- 4\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\n\u03bb h1 h2, eq.trans (eq.symm h1) h2\n\n-- 5\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\n\u03bb h1 h2, eq.trans h1.symm h2\n\n-- 6\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\n-- by library_search\n\u03bb h, h.congr_left.mp\n\n-- 7\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nbegin\n  intros h1 h2,\n  rwa \u2190h1,\nend\n\n-- 8\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nbegin\n  intros h1 h2,\n  rw h1 at h2,\n  assumption,\nend\n\n-- 9\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nbegin\n  intros h1 h2,\n  rwa h1 at h2,\nend\n\n-- 10\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nbegin\n  intros h1 h2,\n  calc x = y : h1.symm\n     ... = z : h2,\nend\n\n-- 11\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\n-- by hint\nby finish\n\n-- 12\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\nshow x = z,\n  begin\n    rw \u2190h1,\n    rw h2\n  end\n\n-- 13\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\nshow x = z,\n  begin\n    rw [\u2190h1, h2]\n  end\n\n-- 14\u00aa demostraci\u00f3n\nexample : y = x \u2192 y = z \u2192 x = z :=\nassume h1 : y = x,\nassume h2 : y = z,\nshow x = z, by rw [\u2190h1, h2]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>He a\u00f1adido a la lista L\u00f3gica con Lean el v\u00eddeo en el que se comentan 12 pruebas en Lean de la propiedad y = x \u2192 y = z \u2192 x = z usando los estilos declarativos, aplicativos, funcional y autom\u00e1tico. A continuaci\u00f3n, se muestra el v\u00eddeo y el c\u00f3digo de la teor\u00eda utilizada &#8211;&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","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,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[335],"tags":[336],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7457"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=7457"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7457\/revisions"}],"predecessor-version":[{"id":7458,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7457\/revisions\/7458"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}