Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  a : C
  ls1 : list C
  IH : ∀ (ls2 : list A) (ls3 : list B),
         All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
         → (ls1 = []) + All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
  X1 : All (λ z : C, All2 (λ (x : A) (y : B), P x y z) [] []) ls1
  ============================
   ((a :: ls1 = []) + All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) [] [])%type


DEBUG:Going to execute:
fun x => lazymatch x with
                    | [] => idtac
                    | _ :: _ => idtac
                    end