src/HOL/Integ/Lagrange.ML
author wenzelm
Thu Jan 23 14:19:16 1997 +0100 (1997-01-23)
changeset 2545 d10abc8c11fb
parent 2281 e00c13a29eda
child 3239 6e2ceb50e17b
permissions -rw-r--r--
added AxClasses test;
     1 (*  Title:      HOL/Integ/Lagrange.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1996 TU Muenchen
     5 
     6 
     7 The following lemma essentially shows that all composite natural numbers are
     8 sums of fours squares, provided all prime numbers are. However, this is an
     9 abstract thm about commutative rings and has a priori nothing to do with nat.
    10 *)
    11 
    12 goalw Lagrange.thy [Lagrange.sq_def] "!!x1::'a::cring. \
    13 \  (sq x1 + sq x2 + sq x3 + sq x4) * (sq y1 + sq y2 + sq y3 + sq y4) = \
    14 \  sq(x1*y1 - x2*y2 - x3*y3 - x4*y4)  + \
    15 \  sq(x1*y2 + x2*y1 + x3*y4 - x4*y3)  + \
    16 \  sq(x1*y3 - x2*y4 + x3*y1 + x4*y2)  + \
    17 \  sq(x1*y4 + x2*y3 - x3*y2 + x4*y1)";
    18 by(cring_simp 1);
    19 qed "Lagrange_lemma";