Require Import List.
Set Implicit Arguments.
Fixpoint tile_concat ln lt : (list bool) * list bool:=
match ln with
| nil => (nil,nil)
| x::ln => match nth x lt (nil,nil), tile_concat ln lt with
| (th,tl), (hh,ll) => (hh++th,ll++tl)
end
end.
Definition tiles_solvable lt :=
exists ln, ln <> nil
/\ Forall (fun x => x < length lt) ln
/\ let (hh,ll) := tile_concat ln lt in hh = ll.