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chore: use IsDirected in Filter.isBounded_sup (#6511)
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urkud authored and semorrison committed Aug 14, 2023
1 parent 6e3d836 commit e54ce68
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions Mathlib/Order/LiminfLimsup.lean
Original file line number Diff line number Diff line change
Expand Up @@ -82,10 +82,10 @@ theorem isBounded_principal (s : Set α) : IsBounded r (𝓟 s) ↔ ∃ t, ∀ x
simp [IsBounded, subset_def]
#align filter.is_bounded_principal Filter.isBounded_principal

theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r b₂ b) :
theorem isBounded_sup [IsTrans α r] [IsDirected α r] :
IsBounded r f → IsBounded r g → IsBounded r (f ⊔ g)
| ⟨b₁, h₁⟩, ⟨b₂, h₂⟩ =>
let ⟨b, rb₁b, rb₂b⟩ := hr b₁ b₂
let ⟨b, rb₁b, rb₂b⟩ := directed_of r b₁ b₂
⟨b, eventually_sup.mpr
⟨h₁.mono fun _ h => _root_.trans h rb₁b, h₂.mono fun _ h => _root_.trans h rb₂b⟩⟩
#align filter.is_bounded_sup Filter.isBounded_sup
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