{"id":7636,"date":"2021-12-29T10:11:34","date_gmt":"2021-12-29T09:11:34","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7636"},"modified":"2021-12-29T10:11:34","modified_gmt":"2021-12-29T09:11:34","slug":"resena-a-machine-checked-direct-proof-of-the-steiner-lehmus-theorem","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-a-machine-checked-direct-proof-of-the-steiner-lehmus-theorem\/","title":{"rendered":"Rese\u00f1a: A machine-checked direct proof of the Steiner-Lehmus theorem"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nuprl\">Nuprl<\/a> sobre geometr\u00eda titulado <a href=\"https:\/\/arxiv.org\/pdf\/2112.11182.pdf\">A machine-checked direct proof of the Steiner-Lehmus theorem<\/a>.<\/p>\n<p>Su autora es <a href=\"https:\/\/ak-2485.github.io\/\">Ariel Kellison<\/a> (de Cornell University).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>A direct proof of the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Steiner%E2%80%93Lehmus_theorem\">Steiner-Lehmus theorem<\/a> has eluded geometers for over 170 years. The challenge has been that a proof is only considered direct if it does not rely on reductio ad absurdum. Thus, any proof that claims to be direct must show, going back to the axioms, that all of the auxiliary theorems used are also proved directly. In this paper, we give a proof of the Steiner-Lehmus theorem that is guaranteed to be direct. The evidence for this claim is derived from our methodology: we have formalized <a href=\"http:\/\/www.nuprl.org\/LibrarySnapshots\/Published\/Version2\/Mathematics\/euclidean!plane!geometry\/index.html\">a constructive axiom set for Euclidean plane geometry in a proof assistant<\/a> that implements a constructive logic and have built the <a href=\"http:\/\/www.nuprl.org\/LibrarySnapshots\/Published\/Version2\/Mathematics\/euclidean!plane!geometry\/Steiner-LehmusTheorem.html\">proof of the Steiner-Lehmus theorem<\/a> on this constructive foundation.<\/p><\/blockquote>\n<p>El trabajo se presentar\u00e1 en el <a href=\"https:\/\/popl22.sigplan.org\/home\/CPP-2022\">Certified Programs and Proofs (CPP) 2022<\/a> el 18 de enero de 2022.<\/p>\n<p>El c\u00f3digo de las correspondientes teor\u00edas se encuentra <a href=\"http:\/\/www.nuprl.org\/LibrarySnapshots\/Published\/Version2\/Mathematics\/euclidean!plane!geometry\/Steiner-LehmusTheorem.html\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Nuprl sobre geometr\u00eda titulado A machine-checked direct proof of the Steiner-Lehmus theorem. Su autora es Ariel Kellison (de Cornell University). Su resumen es A direct proof of the Steiner-Lehmus theorem has eluded geometers for over 170 years. The challenge has been that a proof is only&#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":[100],"tags":[166,224,285],"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\/7636"}],"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=7636"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7636\/revisions"}],"predecessor-version":[{"id":7637,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7636\/revisions\/7637"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}