There is also a quick proof, by Morris Hirsch (indeed by Elon Lages Lima), based on the impossibility of a differentiable retraction.
Lima | Lima Region | Miraflores District, Lima | Elon University | Lima District | Elon Musk | Lima, Ohio | Adriana Lima | Ponte de Lima | Lima Province | Kevin Lima | Alianza Lima | Jesús María District, Lima | Elon, North Carolina | Santa Rosa de Lima | Rafael Lima (boxer) | Rafael Lima | Marina Lima | La Victoria District, Lima | Elon | Anthony Lima | Santa Rosa de Lima, La Unión | Rose of Lima | Ponte de Lima (North) | Nova Lima | Mordechai Elon | María Martha Serra Lima | La Lima | Gusttavo Lima | Edson Luís de Lima Souto |