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


DEBUG:Going to execute:
<coq-core.plugins.ltac::eauto@0> $1 $2 $3

Goals:

DEBUG:Going to execute:
edestruct IH as [IH'| IH']

Goals:

DEBUG:Going to execute:
try (apply IH'; clear IH')

Goals:

DEBUG:Going to execute:
clear IH