Goal:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  X : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k 
        (x :: xs) (y :: ys)
  ============================
   (All2i R k (x :: xs) (g x y :: map2 g xs ys))


DEBUG:Going to execute:
PTRDEBUGTACmatch goal with
           | H:¬ _ |- _ => solve [ case H; trivial ]
           end
Level 1: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.
Level 0: Backtrace:

No such assumption.

Goals:
  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  k : nat
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k [] []
  ============================
   (All2i R k [] [])

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  y : B
  ys : list B
  k : nat
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k [] (y :: ys)
  ============================
   (All2i R k [] [])

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  k : nat
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k (x :: xs) []
  ============================
   (All2i R k (x :: xs) [])

  
  A : Type
  B : Type
  C : Type
  R : nat → A → C → Type
  g : A → B → C
  x : A
  xs : list A
  ih : ∀ (l' : list B) (k : nat),
         All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k xs l'
         → All2i R k xs (map2 g xs l')
  y : B
  ys : list B
  k : nat
  z : All2i (λ (i : nat) (x : A) (y : B), R i x (g x y)) k 
        (x :: xs) (y :: ys)
  ============================
   (All2i R k (x :: xs) (g x y :: map2 g xs ys))


DEBUG:Going to execute:
PTRDEBUGTACtry constructor
Level 0: Backtrace:

No matching clauses for match.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.
Level 1: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.