src/HOL/Algebra/poly/UnivPoly2.thy
changeset 30240 5b25fee0362c
parent 29667 53103fc8ffa3
child 30968 10fef94f40fc
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30239:179ff9cb160b 30240:5b25fee0362c
     1 (*
     1 (*
     2   Title:     Univariate Polynomials
     2   Title:     Univariate Polynomials
     3   Id:        $Id$
       
     4   Author:    Clemens Ballarin, started 9 December 1996
     3   Author:    Clemens Ballarin, started 9 December 1996
     5   Copyright: Clemens Ballarin
     4   Copyright: Clemens Ballarin
     6 *)
     5 *)
     7 
     6 
     8 header {* Univariate Polynomials *}
     7 header {* Univariate Polynomials *}
   386   fix k
   385   fix k
   387   have "coeff (p * monom a 0) k = coeff (a *s p) k"
   386   have "coeff (p * monom a 0) k = coeff (a *s p) k"
   388   proof (cases k)
   387   proof (cases k)
   389     case 0 then show ?thesis by simp ring
   388     case 0 then show ?thesis by simp ring
   390   next
   389   next
   391     case Suc then show ?thesis by (simp add: algebra_simps) ring
   390     case Suc then show ?thesis by simp (ring, simp)
   392   qed
   391   qed
   393   then show "coeff (monom a 0 * p) k = coeff (a *s p) k" by ring
   392   then show "coeff (monom a 0 * p) k = coeff (a *s p) k" by ring
   394 qed
   393 qed
   395 
   394 
   396 ML {* Addsimprocs [ring_simproc] *}
   395 ML {* Addsimprocs [ring_simproc] *}