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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -105,7 +105,6 @@ variable {ι : Type*} {f : Filter ι} {u : ι → ℝ≥0}
105105 · exact hx₀.trans hb₀
106106 · exact hb _ hx₀ hx
107107
108- set_option backward.isDefEq.respectTransparency false in
109108@[simp]
110109lemma limsSup_of_not_isBounded {f : Filter ℝ≥0 } (hf : ¬ f.IsBounded (· ≤ ·)) : limsSup f = 0 := by
111110 rw [limsSup, ← bot_eq_zero]
@@ -124,7 +123,6 @@ lemma limsup_of_not_isBoundedUnder (hf : ¬ f.IsBoundedUnder (· ≤ ·) u) : li
124123lemma liminf_of_not_isCoboundedUnder (hf : ¬ f.IsCoboundedUnder (· ≥ ·) u) : liminf u f = 0 :=
125124 limsInf_of_not_isCobounded hf
126125
127- set_option backward.isDefEq.respectTransparency false in
128126@ [simp, norm_cast]
129127lemma toReal_liminf : liminf (fun i ↦ (u i : ℝ)) f = liminf u f := by
130128 by_cases hf : f.IsCoboundedUnder (· ≥ ·) u; swap
@@ -136,7 +134,6 @@ lemma toReal_liminf : liminf (fun i ↦ (u i : ℝ)) f = liminf u f := by
136134 refine forall ₂_congr fun r hr ↦ ?_
137135 simpa using (le_or_gt 0 r).imp_right fun hr ↦ .of_forall fun i ↦ hr.trans_le (by simp)
138136
139- set_option backward.isDefEq.respectTransparency false in
140137@ [simp, norm_cast]
141138lemma toReal_limsup : limsup (fun i ↦ (u i : ℝ)) f = limsup u f := by
142139 obtain rfl | hf := f.eq_or_neBot
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