t_rect = 
fun (P : t -> Type) (f : let x := t in forall x0 : x, P x0 -> P (k x0)) =>
fix F (t : t) : P t :=
  match t as t0 return (P t0) with
  | @k _ x0 => f x0 (F x0)
  end
     : forall P : t -> Type,
       (let x := t in forall x0 : x, P x0 -> P (k x0)) -> forall t : t, P t

Argument scopes are [function_scope function_scope _]
     = fun d : TT => match d with
                     | @CTT _ _ b => b
                     end
     : TT -> 0 = 0
     = fun d : TT => match d with
                     | @CTT _ _ b => b
                     end
     : TT -> 0 = 0
proj = 
fun (x y : nat) (P : nat -> Type) (def : P x) (prf : P y) =>
match Nat.eq_dec x y with
| left eqprf => match eqprf in (_ = z) return (P z) with
                | eq_refl => def
                end
| right _ => prf
end
     : forall (x y : nat) (P : nat -> Type), P x -> P y -> P y

Argument scopes are [nat_scope nat_scope function_scope _ _]
foo = 
fix foo (A : Type) (l : list A) {struct l} : option A :=
  match l with
  | nil => None
  | x0 :: nil => Some x0
  | x0 :: (_ :: _) as l0 => foo A l0
  end
     : forall A : Type, list A -> option A

Argument scopes are [type_scope list_scope]
uncast = 
fun (A : Type) (x : I A) => match x with
                            | x0 <: _ => x0
                            end
     : forall A : Type, I A -> A

Argument scopes are [type_scope _]
foo' = if A 0 then true else false
     : bool
f = 
fun H : B =>
match H with
| AC x =>
    let b0 := b in
    (if b0 as b return (P b -> True)
     then fun _ : P true => Logic.I
     else fun _ : P false => Logic.I) x
end
     : B -> True
The command has indeed failed with message:
Non exhaustive pattern-matching: no clause found for pattern 
gadtTy _ _
The command has indeed failed with message:
In environment
texpDenote : forall t : type, texp t -> typeDenote t
t : type
e : texp t
t1 : type
t2 : type
t0 : type
b : tbinop t1 t2 t0
e1 : texp t1
e2 : texp t2
The term "0" has type "nat" while it is expected to have type
 "typeDenote t0".
