/-! # Basic section variable tests -/

/-! Directly referenced variables should be included. -/
variable {n : Nat} in
theorem t1 : n = n := by induction n <;> rfl

/-! Variables mentioned only in the body should not be included. -/
variable {n : Nat} in
/-- error: unknown identifier 'n' -/
#guard_msgs in
theorem t2 : ∃ (n : Nat), n = n := by exists n

/-! Variables transitively mentioned should be included. -/
variable {n : Nat} (h : n = n) in
theorem t3 : h = h := rfl

/-! Instance variables mentioning only included variables should be included. -/
variable {α : Type} [ToString α] in
theorem t4 (a : α) : a = a := let _ := toString a; rfl

/-! Instance variables not mentioning only included variables should not be included. -/
variable {α β : Type} [Coe α β] in
/--
error: don't know how to synthesize placeholder
context:
α : Type
a : α
⊢ a = a
-/
#guard_msgs in
theorem t5 (a : α) : a = a := _

/-! Accidentally included variables should be warned for. -/
variable {α : Type} [ToString α] in
/-- warning: included section variable '[ToString α]' is not used in 't6', consider excluding it -/
#guard_msgs in
theorem t6 (a : α) : a = a := rfl

/-! `include` should always include. -/
variable {n : Nat} in
include n in
theorem t7 : ∃ (n : Nat), n = n := by exists n

/-! traversal order bug broke instance inclusion -/
variable {M N : Type} (r : N → N → Prop)
class IsTrans (N : Type) (r : N → N → Prop) : Prop
variable [IsTrans N r] {a b c d : N}
/--
warning: included section variable '[IsTrans N r]' is not used in 'act_rel_of_rel_of_act_rel', consider excluding it
-/
#guard_msgs in
theorem act_rel_of_rel_of_act_rel (ab : r a b) : r a b := ab

/-! More complex include case, instance should be included via `f`. -/
class EquivLike (F : Type) (α β : Type) : Type
variable {F : Type} [EquivLike F α β] (f : F) in
include f in
theorem MulEquiv.decompositionMonoid (_b : β) : α = α :=
  let _ : EquivLike F α β := inferInstance; let _ := f; rfl
/-- info: MulEquiv.decompositionMonoid {α β F : Type} [EquivLike F α β] (f : F) (_b : β) : α = α -/
#guard_msgs in
#check MulEquiv.decompositionMonoid