Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  a : C
  ls1 : list C
  IH : ∀ (ls2 : list A) (ls3 : list B),
         All2 (λ (x : A) (y : B), All (P x y) ls1) ls2 ls3
         → All (λ z : C, All2 (λ (x : A) (y : B), P x y z) ls2 ls3) ls1
  a0 : A
  ls2 : list A
  b : B
  ls3 : list B
  X1 : All2 (λ (x : A) (y : B), All (P x y) (a :: ls1)) ls2 ls3
  X : P a0 b a
  X2 : All (P a0 b) ls1
  ============================
   (All (λ z : C, All2 (λ (x : A) (y : B), P x y z) (a0 :: ls2) (b :: ls3))
      ls1)


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congruence
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No applicable tactic.