ex/natsum.ML

Reorganized/optimized datatype definitions.

(*  Title: 	HOL/ex/natsum.ML
    ID:         $Id$
    Author: 	Tobias Nipkow
    Copyright   1994 TU Muenchen

Summing natural numbers, squares and cubes. Could be continued...
*)

val natsum_ss = arith_ss addsimps
  ([NatSum.sum_0,NatSum.sum_Suc] @ add_ac);

goal NatSum.thy "Suc(Suc(0))*sum(%i.i,Suc(n)) = n*Suc(n)";
by (simp_tac natsum_ss 1);
by (nat_ind_tac "n" 1);
by (simp_tac natsum_ss 1);
by (asm_simp_tac natsum_ss 1);
result();

goal NatSum.thy
  "Suc(Suc(Suc(Suc(Suc(Suc(0))))))*sum(%i.i*i,Suc(n)) = \
\  n*Suc(n)*Suc(Suc(Suc(0))*n)";
by (simp_tac natsum_ss 1);
by (nat_ind_tac "n" 1);
by (simp_tac natsum_ss 1);
by (asm_simp_tac natsum_ss 1);
result();

goal NatSum.thy
  "Suc(Suc(Suc(Suc(0))))*sum(%i.i*i*i,Suc(n)) = n*n*Suc(n)*Suc(n)";
by (simp_tac natsum_ss 1);
by (nat_ind_tac "n" 1);
by (simp_tac natsum_ss 1);
by (asm_simp_tac natsum_ss 1);
result();