Question

Isabelle中是否存在以下等式：

setprod f (UNIV :: 'n∷finite set) = setprod (λx. x) (f ` (UNIV :: 'n∷finite set))

如果是，我该如何证明？

(* tested with Isabelle2013-2 *)
theory Notepad
imports
  Main
  "~~/src/HOL/Library/Polynomial"
begin

notepad
begin{
fix f :: "'n∷finite ⇒ ('a::comm_ring_1 poly)"

have "finite (UNIV :: 'n∷finite set)" by simp
from this have "setprod f (UNIV :: 'n∷finite set) = setprod (λx. x) (f ` (UNIV :: 'n∷finite set))" 
sorry (* can this be proven ? *)

Answer 1

只有当您添加inj f假设f是单射的假设时，引理才会成立。然后从文库引理setprod_reindex_id得到引理，可以使用命令find_theorems setprod image找到它。

setprod_reindex_id [unfolded id_def]为您提供了您要求的引理的通用版本。

Isabelle：setprod的问题

1 个答案: