Goal:
  
  A : Type
  P : A → A → Type
  a : A
  l : list A
  l' : list A
  f : A → A
  hp : ∀ x y : A, P (f x) y → ∑ y' : A, y = f y'
  IHl : ∀ l' : list A,
          OnOne2 P (map f l) l'
          → ∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) l l''
  o1 : sigma (λ _ : list A, list A)
  o : OnOne2 P (pr1 o1) (pr2 o1)
  ============================
   ({| pr1 := f a :: map f l; pr2 := l' |} = o1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      ∑ l'' : list A, OnOne2 (λ x y : A, P (f x) (f y)) (a :: l) l'')


DEBUG:Going to execute:
hnf in id
Level 4: evaluation returns
hnf in id;
 match type of id with
 | sigma _ =>
     let xn := fresh id "'" in
     destruct id as [xn id]; DepElim.decompose_exists xn id;
      cbv beta iota delta [TODO projection TODO projection] in id, id';
      DepElim.decompose_exists id id'
 | _ => cbv beta iota delta [TODO projection TODO projection] in id, id'
 end
where
id' := o
of type
ident
id := o1
of type
constr of type tacvalue

Level 3: evaluation returns
hnf in id;
 match type of id with
 | sigma _ =>
     let xn := fresh id "'" in
     destruct id as [xn id]; DepElim.decompose_exists xn id;
      cbv beta iota delta [TODO projection TODO projection] in id, id';
      DepElim.decompose_exists id id'
 | _ => cbv beta iota delta [TODO projection TODO projection] in id, id'
 end
where
id' := o
of type
ident
id := o1
of type
constr of type tacvalue