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


DEBUG:Going to execute:
hnf in id
Level 5: evaluation returns
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
where
id' := b
of type
constr
id := b
of type
constr of type tacvalue

Level 4: evaluation returns
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
where
id' := b
of type
constr
id := b
of type
constr of type tacvalue