Goal:
  
  A : Type
  B : Type
  C : Type
  R : A → B → C → Type
  b : All3 R [] [] []
  b0 : 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 := b |} =
    b0
    → 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:
<coq-core.plugins.ltac::rename@0> $1