Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  x : (A × B) × C
  l : list ((A × B) × C)
  p : let '(a, b, c) := x in P a b c
  X : All (λ '(a, b, c), P a b c) l
  IHX : All (λ abc : (A × B) × C, P abc.1.1 abc.1.2 abc.2) l
  ============================
   (All (λ abc : (A × B) × C, P abc.1.1 abc.1.2 abc.2) l)


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

Goals:

DEBUG:Going to execute:
hnf

Goals:

DEBUG:Going to execute:
intros

Goals:

DEBUG:Going to execute:
solve
[ do
![ solve
 [ trivial | apply : eq_sym ; trivial ]
 | discriminate
 | contradiction
 | Ltac.split ]
| case not_locked_false_eq_true; Ltac.assumption
| match goal with
  | H:¬ _ |- _ => solve [ case H; trivial ]
  end ]