Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  a : A
  b : B
  c : C
  l : list ((A × B) × C)
  p : 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
  ============================
   (P (a, b, c).1.1 (a, b, c).1.2 (a, b, c).2)


DEBUG:Going to execute:
trivial; hnf; intros; (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 ])