case mp
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
⊢ WellFounded r → IsEmpty ((fun x x_1 => x > x_1) ↪r r)

case mpr
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
⊢ IsEmpty ((fun x x_1 => x > x_1) ↪r r) → WellFounded r
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
⊢ WellFounded r ↔ IsEmpty ((fun x x_1 => x > x_1) ↪r r)
constructor
case mp.intro
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
h : ∀ (a : α), Acc r a
⊢ IsEmpty ((fun x x_1 => x > x_1) ↪r r)
case mp
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
⊢ WellFounded r → IsEmpty ((fun x x_1 => x > x_1) ↪r r)
rintro ⟨h⟩
no goals
case mp.intro
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
h : ∀ (a : α), Acc r a
⊢ IsEmpty ((fun x x_1 => x > x_1) ↪r r)
exact ⟨fun f => not_acc_of_decreasing_seq f 0 (h _)⟩
case mpr
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
h : IsEmpty ((fun x x_1 => x > x_1) ↪r r)
⊢ WellFounded r
case mpr
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
⊢ IsEmpty ((fun x x_1 => x > x_1) ↪r r) → WellFounded r
intro h
no goals
case mpr
α : Type u_1
r : α → α → Prop
inst✝ : IsStrictOrder α r
h : IsEmpty ((fun x x_1 => x > x_1) ↪r r)
⊢ WellFounded r
exact ⟨fun x => acc_iff_no_decreasing_seq.2 inferInstance⟩