compose S
     : (nat -> nat) -> nat -> nat
ex_intro (P:=fun _ : nat => True) (x:=0) I
     : ex (fun _ : nat => True)
d2 = fun x : nat => d1 (y:=x)
     : forall x x0 : nat, x0 = x -> x0 = x

Arguments d2 [x x]%nat_scope _
map id (1 :: nil)
     : list nat
map id' (1 :: nil)
     : list nat
map (id'' (A:=nat)) (1 :: nil)
     : list nat
fix f (x : nat) : option nat := match x with
                                | 0 => None
                                | S _ => x
                                end
     : nat -> option nat
fun x : False => let y := False_rect (A:=bool) x in y
     : False -> bool
fun x : False => let y : True := False_rect x in y
     : False -> True