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[Merged by Bors] - feat: add group/field versions of Filter.map_*_atTop_eq_nat #29532

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[Merged by Bors] - feat: add group/field versions of Filter.map_*_atTop_eq_nat #29532

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1e50ff7
feat: add group/field versions of Filter.map_*_atTop_eq_nat
Aaron1011 Sep 9, 2025
28761e8
Move theorems to files with existing imports
Aaron1011 Sep 11, 2025
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9 changes: 9 additions & 0 deletions Mathlib/Order/Filter/AtTopBot/Archimedean.lean
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Expand Up @@ -146,6 +146,15 @@ namespace Filter

variable {l : Filter α} {f : α → R} {r : R}

theorem map_add_atTop_eq [AddCommGroup α] [PartialOrder α] [IsOrderedAddMonoid α]
[IsDirected α (· ≤ ·)] (k : α) : map (fun a => a + k) atTop = atTop :=
map_atTop_eq_of_gc (fun a => a - k) 0 add_left_mono (by simp [le_sub_iff_add_le]) (by simp)

theorem map_sub_atTop_eq [AddCommGroup α] [PartialOrder α] [IsOrderedAddMonoid α]
[IsDirected α (· ≤ ·)] (k : α) : map (fun a => a - k) atTop = atTop := by
simp_rw [sub_eq_add_neg]
apply map_add_atTop_eq

section LinearOrderedSemiring

variable [Semiring R] [LinearOrder R] [IsStrictOrderedRing R] [Archimedean R]
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5 changes: 5 additions & 0 deletions Mathlib/Order/Filter/AtTopBot/Field.lean
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Expand Up @@ -97,6 +97,11 @@ theorem tendsto_const_mul_pow_atTop_iff :
lemma tendsto_zpow_atTop_atTop {n : ℤ} (hn : 0 < n) : Tendsto (fun x : α ↦ x ^ n) atTop atTop := by
lift n to ℕ using hn.le; simp [(Int.natCast_pos.mp hn).ne']

theorem map_div_atTop_eq (k : α) (hk : 0 < k) : map (fun a => a / k) atTop = atTop :=
map_atTop_eq_of_gc (fun b => k * b) 1 (fun _ _ h => div_le_div_of_nonneg_right h (le_of_lt hk))
(fun a b _ => (by rw [div_le_iff₀' hk]))
fun b _ => (by rw [mul_div_assoc, mul_div_cancel₀]; exact ne_of_gt hk)

end LinearOrderedSemifield


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