以下等式在伊莎贝尔中是否成立:
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 ? *)
仅当您添加假设时,引理才成立inj f
说明f
是单射的。然后引理来自库引理setprod_reindex_id
,可以使用命令找到find_theorems setprod image
.
setprod_reindex_id [unfolded id_def]
为您提供您所要求的引理的通用版本。
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