Goal:
  
  A : Type
  B : Type
  C : Type
  P : A → B → C → Type
  p0 : A × B
  c : C
  l : list ((A × B) × C)
  p : let '(a, b) := p0 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
  ============================
   (P (p0, c).1.1 (p0, c).1.2 (p0, c).2)


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 ]