Goal:
  
  G : t
  invG : invariants G
  acG : acyclic_no_loop G
  x : V.t
  y : V.t
  hx : VSet.In x (V G)
  hy : VSet.In y (V G)
  nxy : Z
  hxy : (lsp G x y <= Some nxy)%nbar
  k : nat
  _p_ : positive
  H : 0 <= Z.pos _p_
  ============================
   ((Pos.to_nat _p_ + k)%nat =
    match
      match Z.of_nat k with
      | 0 => Z.pos _p_
      | Z.pos y' => Z.pos (_p_ + y')
      | Z.neg y' => Z.pos_sub _p_ y'
      end
    with
    | Z.pos p => Pos.to_nat p
    | _ => 0%nat
    end)


DEBUG:Going to execute:
case not_locked_false_eq_true; Ltac.assumption
Level 1: Backtrace:

In environment
G : t
invG : invariants G
acG : acyclic_no_loop G
x, y : V.t
hx : VSet.In x (V G)
hy : VSet.In y (V G)
nxy : Z
hxy : (lsp G x y <= Some nxy)%nbar
k : nat
_p_ : positive
H : 0 <= Z.pos _p_
Unable to unify
 "match
    match Z.of_nat k with
    | 0 => Z.pos _p_
    | Z.pos y' => Z.pos (_p_ + y')
    | Z.neg y' => Z.pos_sub _p_ y'
    end
  with
  | Z.pos p => Pos.to_nat p
  | _ => 0%nat
  end"
with "(Pos.to_nat _p_ + k)%nat".
Level 0: Backtrace:

In environment
G : t
invG : invariants G
acG : acyclic_no_loop G
x, y : V.t
hx : VSet.In x (V G)
hy : VSet.In y (V G)
nxy : Z
hxy : (lsp G x y <= Some nxy)%nbar
k : nat
_p_ : positive
H : 0 <= Z.pos _p_
Unable to unify
 "match
    match Z.of_nat k with
    | 0 => Z.pos _p_
    | Z.pos y' => Z.pos (_p_ + y')
    | Z.neg y' => Z.pos_sub _p_ y'
    end
  with
  | Z.pos p => Pos.to_nat p
  | _ => 0%nat
  end"
with "(Pos.to_nat _p_ + k)%nat".
Level 0: Backtrace:

No applicable tactic.
Level 0: Backtrace:

No applicable tactic.