Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → Type
  Q : B → C → Type
  R : A → C → Type
  l'' : list C
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : ∀ l'' : list C,
          All2 Q l' l''
          → (∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z) → All2 R l l''
  a1' : list B
  a1 : list C
  a : All2 Q (pr1 {| pr1 := a1'; pr2 := a1 |})
        (pr2 {| pr1 := a1'; pr2 := a1 |})
  ============================
   ({| pr1 := y :: l'; pr2 := l'' |} = {| pr1 := a1'; pr2 := a1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in
      (∀ (x : A) (y : B) (z : C), P x y → Q y z → R x z)
      → All2 R (x :: l) l'')


DEBUG:Going to execute:
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