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


DEBUG:Going to execute:
lazymatch goal with
           | id':=?v:_
             |- context [ id ] =>
                 generalize (eq_refl : v = id'); clearbody id'; simpl in id';
                  cont id id' id v
           | id':=?v:_
             |- _ =>
                 let id'1 := fresh id' in
                 let id'2 := fresh id' in
                 set (id'2 := pr2 id'); set (id'1 := pr1 id') in id'2;
                  hnf in (value of id'1), (value of id'2);
                  try red in (type of id'2);
                  match goal with
                  | id'1:=?t:_
                    |- _ =>
                        generalize (eq_refl : t = id'1); clearbody id'2 id'1;
                         clear id' id; try unfold signature in id'2;
                         hnf in id'2; simpl in id'2; rename id'2 into id;
                         cont id id id'1 t
                  end
           end