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chore(order/filter/basic): rename using the zero subscript convention…
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… for groups with zero (#12952)
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sgouezel committed Mar 26, 2022
1 parent a491055 commit 1f11f3f
Showing 1 changed file with 3 additions and 12 deletions.
15 changes: 3 additions & 12 deletions src/order/filter/basic.lean
Expand Up @@ -1271,20 +1271,11 @@ lemma eventually_eq.inv [has_inv β] {f g : α → β} {l : filter α} (h : f =
((λ x, (f x)⁻¹) =ᶠ[l] (λ x, (g x)⁻¹)) :=
h.fun_comp has_inv.inv

lemma eventually_eq.div [group_with_zero β] {f f' g g' : α → β} {l : filter α} (h : f =ᶠ[l] g)
(h' : f' =ᶠ[l] g') :
((λ x, f x / f' x) =ᶠ[l] (λ x, g x / g' x)) :=
by simpa only [div_eq_mul_inv] using h.mul h'.inv

lemma eventually_eq.div' [group β] {f f' g g' : α → β} {l : filter α} (h : f =ᶠ[l] g)
@[to_additive]
lemma eventually_eq.div [has_div β] {f f' g g' : α → β} {l : filter α} (h : f =ᶠ[l] g)
(h' : f' =ᶠ[l] g') :
((λ x, f x / f' x) =ᶠ[l] (λ x, g x / g' x)) :=
by simpa only [div_eq_mul_inv] using h.mul h'.inv

lemma eventually_eq.sub [add_group β] {f f' g g' : α → β} {l : filter α} (h : f =ᶠ[l] g)
(h' : f' =ᶠ[l] g') :
((λ x, f x - f' x) =ᶠ[l] (λ x, g x - g' x)) :=
by simpa only [sub_eq_add_neg] using h.add h'.neg
h.comp₂ (/) h'

@[to_additive] lemma eventually_eq.const_smul {𝕜} [has_scalar 𝕜 β] {l : filter α} {f g : α → β}
(h : f =ᶠ[l] g) (c : 𝕜) :
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