import data.vector
open nat
universes u v
set_option pp.all true

set_option trace.eqn_compiler.wf_rec true
set_option trace.debug.eqn_compiler.wf_rec true
set_option trace.debug.eqn_compiler.mutual true
set_option trace.eqn_compiler.elim_match true


mutual def even, odd
with even : nat → bool
| 0     := tt
| (a+1) := odd a
with odd : nat → bool
| 0     := ff
| (a+1) := even a


mutual def f, g {α : Type u} {β : Type v} (f : α → β) (p : α × β)
with f : Π n : nat, vector (α × β) n
| 0        := vector.nil
| (succ n) := vector.cons p $ (g n p.1).map (λ b, (p.1, b))
with g : Π n : nat, α → vector β n
| 0        a := vector.nil
| (succ n) a := vector.cons p.2 $ (f n).map (λ p, p.2)