diff -r 2f337bf81085 -r eb2ba30c2981 src/HOL/ex/Lagrange.ML --- a/src/HOL/ex/Lagrange.ML Fri Nov 29 15:07:27 1996 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,18 +0,0 @@ -(* Title: HOL/ex/Lagrange.ML - ID: $Id$ - Author: Tobias Nipkow - Copyright 1996 TU Muenchen - - -The following lemma schows that all composite natural numbers are sums of -fours squares, provided all prime numbers are. -*) - -goalw Lagrange.thy [Lagrange.sq_def] "!!x1::'a::cring. \ -\ (sq x1 + sq x2 + sq x3 + sq x4) * (sq y1 + sq y2 + sq y3 + sq y4) = \ -\ sq(x1*y1 - x2*y2 - x3*y3 - x4*y4) + \ -\ sq(x1*y2 + x2*y1 + x3*y4 - x4*y3) + \ -\ sq(x1*y3 - x2*y4 + x3*y1 + x4*y2) + \ -\ sq(x1*y4 + x2*y3 - x3*y2 + x4*y1)"; -by(cring_simp 1); -qed "Lagrange_lemma";