[isabelle] Stuck with Isabelle type instantiation



Hello,

Could anyone be kind enough to help me with a type instantiation problem?

I defined a simple data type 'kon_nodes' with four constructors (i.e. 'a', 'b', 'c' and 'd'), and I want to show that 'kon_nodes' is of class 'enum'. However, I cannot finish the instance proof. The code is as follows: datatype kon_nodes = a|b|c|d instantiation kon_nodes :: enum begin definition "enum =[a,b,c,d]" definition "enum_all P <-> P a ∧ P b ∧ P c ∧ P d" definition "enum_ex P <-> P a ∨ P b ∨ P c ∨ P d" instance sorry end

Actually, there is a very similar proof in the theory of 'enum' in the library. I copy and paste the exact code to my Isabelle 2013, but, surprisingly, Isabelle does not accept the proof either. The proof from the theory of 'enum' is as follows: datatype finite_4 = a⇣1 | a⇣2 | a⇣3 | a⇣4

notation (output) a⇣1  ("a⇣1")
notation (output) a⇣2  ("a⇣2")
notation (output) a⇣3  ("a⇣3")
notation (output) a⇣4  ("a⇣4")

lemma UNIV_finite_4:
 "UNIV = {a⇣1, a⇣2, a⇣3, a⇣4}"
 by (auto intro: finite_4.exhaust)

instantiation finite_4 :: enum
begin

definition
 "enum = [a⇣1, a⇣2, a⇣3, a⇣4]"

definition
 "enum_all P <-> P a⇣1 ∧ P a⇣2 ∧ P a⇣3 ∧ P a⇣4"

definition
 "enum_ex P <-> P a⇣1 ∨ P a⇣2 ∨ P a⇣3 ∨ P a⇣4"

instance proof qed (simp_all only: enum_finite_4_def enum_all_finite_4_def enum_ex_finite_4_def UNIV_finite_4, simp_all) end

I feel confused. Any help would be greatly appreciated.
Wenda Li




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