Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  H1 : sigma (λ _ : list A, list B)
  H : All2 Q (pr1 H1) (pr2 H1)
  ============================
   ({| pr1 := []; pr2 := [] |} = H1
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in All2 (Trel_conj P Q) [] [])


DEBUG:Going to execute:
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