Goal:
  
  A : Type
  B : Type
  C : Type
  D : Type
  E : Type
  P : E → A → Type
  Q : C → A → Type
  R : B → D → Type
  f : B → C → E
  b : B
  l : list B
  l''' : list D
  hb1' : list B
  hb1 : list D
  hb : All2 R (pr1 {| pr1 := hb1'; pr2 := hb1 |})
         (pr2 {| pr1 := hb1'; pr2 := hb1 |})
  ============================
   ({| pr1 := b :: l; pr2 := l''' |} = {| pr1 := hb1'; pr2 := hb1 |}
    → ∀ (H := CoreTactics.block) (x : C) (y : A) (l0 : list C) (l' : list A),
        Q x y
        → All2 Q l0 l'
          → #|l| = #|l0|
            → (∀ (x0 : B) (y0 : C) (z : A) (w : D),
                 R x0 w → Q y0 z → P (f x0 y0) z)
              → (∀ (l : list B) (l''' : list D),
                   All2 R l l''' → #|l| = #|l0| → All2 P (map2 f l l0) l')
                → let H0 := CoreTactics.block in
                  All2 P (map2 f (b :: l) (x :: l0)) (y :: l'))


DEBUG:Going to execute:
fun id id' =>
             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