theory demo imports Main begin

section ‹Inductive predicates for lists›

datatype ‘a list = Nil (“[]”) | Cons ’a “‘a list” (“_ # _”)

fun length

“‘a list ⇒ nat” where

"length [] = 0" | "length (x # xs) = 1 + length xs"
inductive ζ

“‘a list ⇒ nat ⇒ bool” where

Nil: “ζ [] 0” | Cons: “ζ xs l ⟹ ζ (x # xs) (1 + l)”

(* Not the answer? *) lemma “ζ xs 42”

oops