Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → B → C → Type
  b0 : All3 R [] [] []
  b'' : list A
  b' : sigma (λ _ : list B, list C)
  b : All3 R (pr1 {| pr1 := b''; pr2 := b' |})
        (pr1 (pr2 {| pr1 := b''; pr2 := b' |}))
        (pr2 (pr2 {| pr1 := b''; pr2 := b' |}))
  ============================
   ({|
      pr1 := {| pr1 := []; pr2 := {| pr1 := []; pr2 := [] |} |}; pr2 := b0
    |} = {| pr1 := {| pr1 := b''; pr2 := b' |}; pr2 := b |}
    → ∀ (H := CoreTactics.block) (e : NoConfusionHom_All3 A B C R [] [] []
                                        All3_nil b0),
        let H0 := CoreTactics.block in
        noConfusionHom_All3_obligation_2 A B C R [] [] [] All3_nil b0
          (noConfusionHom_All3_obligation_1 A B C R [] [] [] All3_nil b0 e) =
        e)


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