Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  x : A
  y : B
  l : list A
  l' : list B
  r : P x y
  X : All2 P l l'
  IHX : All2 Q l l' → All2 (Trel_conj P Q) l l'
  H1' : list A
  H1 : list B
  H : All2 Q (pr1 {| pr1 := H1'; pr2 := H1 |})
        (pr2 {| pr1 := H1'; pr2 := H1 |})
  ============================
   ({| pr1 := x :: l; pr2 := y :: l' |} = {| pr1 := H1'; pr2 := H1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) (x :: l) (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