order.liminf_limsup
⟷
Mathlib.Order.LiminfLimsup
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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Generalise lemmas from semilattices to codirected orders. Move topology-less lemmas from topology.algebra.order.liminf_limsup
to order.liminf_limsup
. Also turn arguments to bdd_above_insert
and friends implicit.
@@ -122,7 +122,7 @@ lemma not_is_bounded_under_of_tendsto_at_bot [preorder β] [no_min_order β] {f
¬ is_bounded_under (≥) l f :=
@not_is_bounded_under_of_tendsto_at_top α βᵒᵈ _ _ _ _ _ hf
-lemma is_bounded_under.bdd_above_range_of_cofinite [semilattice_sup β] {f : α → β}
+lemma is_bounded_under.bdd_above_range_of_cofinite [preorder β] [is_directed β (≤)] {f : α → β}
(hf : is_bounded_under (≤) cofinite f) : bdd_above (range f) :=
begin
rcases hf with ⟨b, hb⟩,
@@ -131,17 +131,17 @@ begin
exact ⟨⟨b, ball_image_iff.2 $ λ x, id⟩, (hb.image f).bdd_above⟩
end
-lemma is_bounded_under.bdd_below_range_of_cofinite [semilattice_inf β] {f : α → β}
+lemma is_bounded_under.bdd_below_range_of_cofinite [preorder β] [is_directed β (≥)] {f : α → β}
(hf : is_bounded_under (≥) cofinite f) : bdd_below (range f) :=
-@is_bounded_under.bdd_above_range_of_cofinite α βᵒᵈ _ _ hf
+@is_bounded_under.bdd_above_range_of_cofinite α βᵒᵈ _ _ _ hf
-lemma is_bounded_under.bdd_above_range [semilattice_sup β] {f : ℕ → β}
+lemma is_bounded_under.bdd_above_range [preorder β] [is_directed β (≤)] {f : ℕ → β}
(hf : is_bounded_under (≤) at_top f) : bdd_above (range f) :=
by { rw ← nat.cofinite_eq_at_top at hf, exact hf.bdd_above_range_of_cofinite }
-lemma is_bounded_under.bdd_below_range [semilattice_inf β] {f : ℕ → β}
+lemma is_bounded_under.bdd_below_range [preorder β] [is_directed β (≥)] {f : ℕ → β}
(hf : is_bounded_under (≥) at_top f) : bdd_below (range f) :=
-@is_bounded_under.bdd_above_range βᵒᵈ _ _ hf
+@is_bounded_under.bdd_above_range βᵒᵈ _ _ _ hf
/-- `is_cobounded (≺) f` states that the filter `f` does not tend to infinity w.r.t. `≺`. This is
also called frequently bounded. Will be usually instantiated with `≤` or `≥`.
@@ -198,6 +198,31 @@ lemma is_cobounded.mono (h : f ≤ g) : f.is_cobounded r → g.is_cobounded r
end relation
+section nonempty
+variables [preorder α] [nonempty α] {f : filter β} {u : β → α}
+
+lemma is_bounded_le_at_bot : (at_bot : filter α).is_bounded (≤) :=
+‹nonempty α›.elim $ λ a, ⟨a, eventually_le_at_bot _⟩
+
+lemma is_bounded_ge_at_top : (at_top : filter α).is_bounded (≥) :=
+‹nonempty α›.elim $ λ a, ⟨a, eventually_ge_at_top _⟩
+
+lemma tendsto.is_bounded_under_le_at_bot (h : tendsto u f at_bot) : f.is_bounded_under (≤) u :=
+is_bounded_le_at_bot.mono h
+
+lemma tendsto.is_bounded_under_ge_at_top (h : tendsto u f at_top) : f.is_bounded_under (≥) u :=
+is_bounded_ge_at_top.mono h
+
+lemma bdd_above_range_of_tendsto_at_top_at_bot [is_directed α (≤)] {u : ℕ → α}
+ (hx : tendsto u at_top at_bot) : bdd_above (set.range u) :=
+hx.is_bounded_under_le_at_bot.bdd_above_range
+
+lemma bdd_below_range_of_tendsto_at_top_at_top [is_directed α (≥)] {u : ℕ → α}
+ (hx : tendsto u at_top at_top) : bdd_below (set.range u) :=
+hx.is_bounded_under_ge_at_top.bdd_below_range
+
+end nonempty
+
lemma is_cobounded_le_of_bot [preorder α] [order_bot α] {f : filter α} : f.is_cobounded (≤) :=
⟨⊥, assume a h, bot_le⟩
@@ -955,6 +980,15 @@ lemma frequently_lt_of_liminf_lt {α β} [conditionally_complete_linear_order β
∃ᶠ x in f, u x < b :=
@frequently_lt_of_lt_limsup _ βᵒᵈ _ f u b hu h
+variables [conditionally_complete_linear_order α] {f : filter α} {b : α}
+
+lemma lt_mem_sets_of_Limsup_lt (h : f.is_bounded (≤)) (l : f.Limsup < b) : ∀ᶠ a in f, a < b :=
+let ⟨c, (h : ∀ᶠ a in f, a ≤ c), hcb⟩ := exists_lt_of_cInf_lt h l in
+mem_of_superset h $ λ a, hcb.trans_le'
+
+lemma gt_mem_sets_of_Liminf_gt : f.is_bounded (≥) → b < f.Liminf → ∀ᶠ a in f, b < a :=
+@lt_mem_sets_of_Limsup_lt αᵒᵈ _ _ _
+
end conditionally_complete_linear_order
end filter
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -154,7 +154,7 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
[l.ne_bot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f :=
by
rintro ⟨b, hb⟩
- rw [eventually_map] at hb
+ rw [eventually_map] at hb
obtain ⟨b', h⟩ := exists_gt b
have hb' := (tendsto_at_top.mp hf) b'
have : {x : α | f x ≤ b} ∩ {x : α | b' ≤ f x} = ∅ :=
@@ -191,7 +191,7 @@ theorem IsBoundedUnder.bddBelow_range_of_cofinite [Preorder β] [IsDirected β (
#print Filter.IsBoundedUnder.bddAbove_range /-
theorem IsBoundedUnder.bddAbove_range [Preorder β] [IsDirected β (· ≤ ·)] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
- rw [← Nat.cofinite_eq_atTop] at hf ; exact hf.bdd_above_range_of_cofinite
+ rw [← Nat.cofinite_eq_atTop] at hf; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
-/
@@ -1053,7 +1053,7 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
eventually_imp_distrib_left.mpr fun h => eventually_iff_exists_mem.2 ⟨s, h, fun x h₁ h₂ => _⟩
exact @le_iSup₂ α β (fun b => p b ∧ b ∈ s) _ (fun b hb => u b) x ⟨h₂, h₁⟩
· obtain ⟨s, hs, hs'⟩ := eventually_iff_exists_mem.mp ha'
- simp_rw [Imp.swap] at hs'
+ simp_rw [Imp.swap] at hs'
exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp])
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
-/
@@ -1462,8 +1462,8 @@ theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Se
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
∃ f : {i | q i} → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
by
- rw [blimsup_eq_infi_bsupr] at hx
- simp only [supr_eq_Union, infi_eq_Inter, mem_Inter, mem_Union, exists_prop] at hx
+ rw [blimsup_eq_infi_bsupr] at hx
+ simp only [supr_eq_Union, infi_eq_Inter, mem_Inter, mem_Union, exists_prop] at hx
choose g hg hg' using hx
refine' ⟨fun i : {i | q i} => g (b i) (hl.mem_of_mem i.2), fun i => ⟨_, _⟩⟩
· exact hg' (b i) (hl.mem_of_mem i.2)
@@ -1494,7 +1494,7 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
(h : a < limsSup f) : ∃ᶠ n in f, a < n :=
by
contrapose! h
- simp only [not_frequently, not_lt] at h
+ simp only [not_frequently, not_lt] at h
exact Limsup_le_of_le hf h
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
-/
@@ -1621,7 +1621,7 @@ theorem Monotone.isBoundedUnder_le_comp_iff [Nonempty β] [LinearOrder β] [Preo
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
by
refine' ⟨_, fun h => h.IsBoundedUnder hg⟩
- rintro ⟨c, hc⟩; rw [eventually_map] at hc
+ rintro ⟨c, hc⟩; rw [eventually_map] at hc
obtain ⟨b, hb⟩ : ∃ b, ∀ a ≥ b, c < g a := eventually_at_top.1 (hg'.eventually_gt_at_top c)
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp_iff
@@ -1666,7 +1666,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
l (limsup v f) ≤ limsup (fun x => l (v x)) f :=
by
refine' le_Limsup_of_le hlv fun c hc => _
- rw [Filter.eventually_map] at hc
+ rw [Filter.eventually_map] at hc
simp_rw [gc _ _] at hc ⊢
exact Limsup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010
@@ -1422,10 +1422,11 @@ variable {p : ι → Prop} {s : ι → Set α}
#print Filter.cofinite.blimsup_set_eq /-
theorem cofinite.blimsup_set_eq : blimsup s cofinite p = {x | {n | p n ∧ x ∈ s n}.Infinite} :=
by
- simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, Inf_eq_sInter, exists_prop]
+ simp only [blimsup_eq, le_eq_subset, eventually_cofinite, Classical.not_forall, Inf_eq_sInter,
+ exists_prop]
ext x
refine' ⟨fun h => _, fun hx t h => _⟩ <;> contrapose! h
- · simp only [mem_sInter, mem_set_of_eq, not_forall, exists_prop]
+ · simp only [mem_sInter, mem_set_of_eq, Classical.not_forall, exists_prop]
exact ⟨{x}ᶜ, by simpa using h, by simp⟩
· exact hx.mono fun i hi => ⟨hi.1, fun hit => h (hit hi.2)⟩
#align filter.cofinite.blimsup_set_eq Filter.cofinite.blimsup_set_eq
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-/
-import Mathbin.Order.Filter.Cofinite
-import Mathbin.Order.Hom.CompleteLattice
+import Order.Filter.Cofinite
+import Order.Hom.CompleteLattice
#align_import order.liminf_limsup from "leanprover-community/mathlib"@"ffde2d8a6e689149e44fd95fa862c23a57f8c780"
mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29
@@ -294,13 +294,17 @@ section Nonempty
variable [Preorder α] [Nonempty α] {f : Filter β} {u : β → α}
+#print Filter.isBounded_le_atBot /-
theorem isBounded_le_atBot : (atBot : Filter α).IsBounded (· ≤ ·) :=
‹Nonempty α›.elim fun a => ⟨a, eventually_le_atBot _⟩
#align filter.is_bounded_le_at_bot Filter.isBounded_le_atBot
+-/
+#print Filter.isBounded_ge_atTop /-
theorem isBounded_ge_atTop : (atTop : Filter α).IsBounded (· ≥ ·) :=
‹Nonempty α›.elim fun a => ⟨a, eventually_ge_atTop _⟩
#align filter.is_bounded_ge_at_top Filter.isBounded_ge_atTop
+-/
#print Filter.Tendsto.isBoundedUnder_le_atBot /-
theorem Tendsto.isBoundedUnder_le_atBot (h : Tendsto u f atBot) : f.IsBoundedUnder (· ≤ ·) u :=
@@ -314,15 +318,19 @@ theorem Tendsto.isBoundedUnder_ge_atTop (h : Tendsto u f atTop) : f.IsBoundedUnd
#align filter.tendsto.is_bounded_under_ge_at_top Filter.Tendsto.isBoundedUnder_ge_atTop
-/
+#print Filter.bddAbove_range_of_tendsto_atTop_atBot /-
theorem bddAbove_range_of_tendsto_atTop_atBot [IsDirected α (· ≤ ·)] {u : ℕ → α}
(hx : Tendsto u atTop atBot) : BddAbove (Set.range u) :=
hx.isBoundedUnder_le_atBot.bddAbove_range
#align filter.bdd_above_range_of_tendsto_at_top_at_bot Filter.bddAbove_range_of_tendsto_atTop_atBot
+-/
+#print Filter.bddBelow_range_of_tendsto_atTop_atTop /-
theorem bddBelow_range_of_tendsto_atTop_atTop [IsDirected α (· ≥ ·)] {u : ℕ → α}
(hx : Tendsto u atTop atTop) : BddBelow (Set.range u) :=
hx.isBoundedUnder_ge_atTop.bddBelow_range
#align filter.bdd_below_range_of_tendsto_at_top_at_top Filter.bddBelow_range_of_tendsto_atTop_atTop
+-/
end Nonempty
@@ -1584,15 +1592,19 @@ theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β]
variable [ConditionallyCompleteLinearOrder α] {f : Filter α} {b : α}
+#print Filter.lt_mem_sets_of_limsSup_lt /-
theorem lt_mem_sets_of_limsSup_lt (h : f.IsBounded (· ≤ ·)) (l : f.limsSup < b) :
∀ᶠ a in f, a < b :=
let ⟨c, (h : ∀ᶠ a in f, a ≤ c), hcb⟩ := exists_lt_of_csInf_lt h l
mem_of_superset h fun a => hcb.trans_le'
#align filter.lt_mem_sets_of_Limsup_lt Filter.lt_mem_sets_of_limsSup_lt
+-/
+#print Filter.gt_mem_sets_of_limsInf_gt /-
theorem gt_mem_sets_of_limsInf_gt : f.IsBounded (· ≥ ·) → b < f.limsInf → ∀ᶠ a in f, b < a :=
@lt_mem_sets_of_limsSup_lt αᵒᵈ _ _ _
#align filter.gt_mem_sets_of_Liminf_gt Filter.gt_mem_sets_of_limsInf_gt
+-/
end ConditionallyCompleteLinearOrder
mathlib commit https://github.com/leanprover-community/mathlib/commit/ffde2d8a6e689149e44fd95fa862c23a57f8c780
@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
import Mathbin.Order.Filter.Cofinite
import Mathbin.Order.Hom.CompleteLattice
-#align_import order.liminf_limsup from "leanprover-community/mathlib"@"3e32bc908f617039c74c06ea9a897e30c30803c2"
+#align_import order.liminf_limsup from "leanprover-community/mathlib"@"ffde2d8a6e689149e44fd95fa862c23a57f8c780"
/-!
# liminfs and limsups of functions and filters
@@ -171,7 +171,7 @@ theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f :
-/
#print Filter.IsBoundedUnder.bddAbove_range_of_cofinite /-
-theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
+theorem IsBoundedUnder.bddAbove_range_of_cofinite [Preorder β] [IsDirected β (· ≤ ·)] {f : α → β}
(hf : IsBoundedUnder (· ≤ ·) cofinite f) : BddAbove (range f) :=
by
rcases hf with ⟨b, hb⟩
@@ -182,23 +182,23 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
-/
#print Filter.IsBoundedUnder.bddBelow_range_of_cofinite /-
-theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
+theorem IsBoundedUnder.bddBelow_range_of_cofinite [Preorder β] [IsDirected β (· ≥ ·)] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
- @IsBoundedUnder.bddAbove_range_of_cofinite α βᵒᵈ _ _ hf
+ @IsBoundedUnder.bddAbove_range_of_cofinite α βᵒᵈ _ _ _ hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
-/
#print Filter.IsBoundedUnder.bddAbove_range /-
-theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
+theorem IsBoundedUnder.bddAbove_range [Preorder β] [IsDirected β (· ≤ ·)] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
rw [← Nat.cofinite_eq_atTop] at hf ; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
-/
#print Filter.IsBoundedUnder.bddBelow_range /-
-theorem IsBoundedUnder.bddBelow_range [SemilatticeInf β] {f : ℕ → β}
+theorem IsBoundedUnder.bddBelow_range [Preorder β] [IsDirected β (· ≥ ·)] {f : ℕ → β}
(hf : IsBoundedUnder (· ≥ ·) atTop f) : BddBelow (range f) :=
- @IsBoundedUnder.bddAbove_range βᵒᵈ _ _ hf
+ @IsBoundedUnder.bddAbove_range βᵒᵈ _ _ _ hf
#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_range
-/
@@ -290,6 +290,42 @@ theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
end Relation
+section Nonempty
+
+variable [Preorder α] [Nonempty α] {f : Filter β} {u : β → α}
+
+theorem isBounded_le_atBot : (atBot : Filter α).IsBounded (· ≤ ·) :=
+ ‹Nonempty α›.elim fun a => ⟨a, eventually_le_atBot _⟩
+#align filter.is_bounded_le_at_bot Filter.isBounded_le_atBot
+
+theorem isBounded_ge_atTop : (atTop : Filter α).IsBounded (· ≥ ·) :=
+ ‹Nonempty α›.elim fun a => ⟨a, eventually_ge_atTop _⟩
+#align filter.is_bounded_ge_at_top Filter.isBounded_ge_atTop
+
+#print Filter.Tendsto.isBoundedUnder_le_atBot /-
+theorem Tendsto.isBoundedUnder_le_atBot (h : Tendsto u f atBot) : f.IsBoundedUnder (· ≤ ·) u :=
+ isBounded_le_atBot.mono h
+#align filter.tendsto.is_bounded_under_le_at_bot Filter.Tendsto.isBoundedUnder_le_atBot
+-/
+
+#print Filter.Tendsto.isBoundedUnder_ge_atTop /-
+theorem Tendsto.isBoundedUnder_ge_atTop (h : Tendsto u f atTop) : f.IsBoundedUnder (· ≥ ·) u :=
+ isBounded_ge_atTop.mono h
+#align filter.tendsto.is_bounded_under_ge_at_top Filter.Tendsto.isBoundedUnder_ge_atTop
+-/
+
+theorem bddAbove_range_of_tendsto_atTop_atBot [IsDirected α (· ≤ ·)] {u : ℕ → α}
+ (hx : Tendsto u atTop atBot) : BddAbove (Set.range u) :=
+ hx.isBoundedUnder_le_atBot.bddAbove_range
+#align filter.bdd_above_range_of_tendsto_at_top_at_bot Filter.bddAbove_range_of_tendsto_atTop_atBot
+
+theorem bddBelow_range_of_tendsto_atTop_atTop [IsDirected α (· ≥ ·)] {u : ℕ → α}
+ (hx : Tendsto u atTop atTop) : BddBelow (Set.range u) :=
+ hx.isBoundedUnder_ge_atTop.bddBelow_range
+#align filter.bdd_below_range_of_tendsto_at_top_at_top Filter.bddBelow_range_of_tendsto_atTop_atTop
+
+end Nonempty
+
#print Filter.isCobounded_le_of_bot /-
theorem isCobounded_le_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsCobounded (· ≤ ·) :=
⟨⊥, fun a h => bot_le⟩
@@ -1546,6 +1582,18 @@ theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β]
#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_lt
-/
+variable [ConditionallyCompleteLinearOrder α] {f : Filter α} {b : α}
+
+theorem lt_mem_sets_of_limsSup_lt (h : f.IsBounded (· ≤ ·)) (l : f.limsSup < b) :
+ ∀ᶠ a in f, a < b :=
+ let ⟨c, (h : ∀ᶠ a in f, a ≤ c), hcb⟩ := exists_lt_of_csInf_lt h l
+ mem_of_superset h fun a => hcb.trans_le'
+#align filter.lt_mem_sets_of_Limsup_lt Filter.lt_mem_sets_of_limsSup_lt
+
+theorem gt_mem_sets_of_limsInf_gt : f.IsBounded (· ≥ ·) → b < f.limsInf → ∀ᶠ a in f, b < a :=
+ @lt_mem_sets_of_limsSup_lt αᵒᵈ _ _ _
+#align filter.gt_mem_sets_of_Liminf_gt Filter.gt_mem_sets_of_limsInf_gt
+
end ConditionallyCompleteLinearOrder
end Filter
mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f
@@ -1554,8 +1554,8 @@ section Order
open Filter
-#print Monotone.isBoundedUnder_le_comp /-
-theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
+#print Monotone.isBoundedUnder_le_comp_iff /-
+theorem Monotone.isBoundedUnder_le_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
by
@@ -1563,31 +1563,31 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
rintro ⟨c, hc⟩; rw [eventually_map] at hc
obtain ⟨b, hb⟩ : ∃ b, ∀ a ≥ b, c < g a := eventually_at_top.1 (hg'.eventually_gt_at_top c)
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
-#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp
+#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp_iff
-/
-#print Monotone.isBoundedUnder_ge_comp /-
-theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
+#print Monotone.isBoundedUnder_ge_comp_iff /-
+theorem Monotone.isBoundedUnder_ge_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual.isBoundedUnder_le_comp hg'
-#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp
+#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp_iff
-/
-#print Antitone.isBoundedUnder_le_comp /-
-theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
+#print Antitone.isBoundedUnder_le_comp_iff /-
+theorem Antitone.isBoundedUnder_le_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual_right.isBoundedUnder_ge_comp hg'
-#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp
+#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp_iff
-/
-#print Antitone.isBoundedUnder_ge_comp /-
-theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
+#print Antitone.isBoundedUnder_ge_comp_iff /-
+theorem Antitone.isBoundedUnder_ge_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
hg.dual_right.isBoundedUnder_le_comp hg'
-#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp
+#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp_iff
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-
-! This file was ported from Lean 3 source module order.liminf_limsup
-! leanprover-community/mathlib commit 3e32bc908f617039c74c06ea9a897e30c30803c2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Filter.Cofinite
import Mathbin.Order.Hom.CompleteLattice
+#align_import order.liminf_limsup from "leanprover-community/mathlib"@"3e32bc908f617039c74c06ea9a897e30c30803c2"
+
/-!
# liminfs and limsups of functions and filters
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -72,12 +72,14 @@ def IsBoundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
variable {r : α → α → Prop} {f g : Filter α}
+#print Filter.isBounded_iff /-
/-- `f` is eventually bounded if and only if, there exists an admissible set on which it is
bounded. -/
theorem isBounded_iff : f.IsBounded r ↔ ∃ s ∈ f.sets, ∃ b, s ⊆ {x | r x b} :=
Iff.intro (fun ⟨b, hb⟩ => ⟨{a | r a b}, hb, b, Subset.refl _⟩) fun ⟨s, hs, b, hb⟩ =>
⟨b, mem_of_superset hs hb⟩
#align filter.is_bounded_iff Filter.isBounded_iff
+-/
#print Filter.isBoundedUnder_of /-
/-- A bounded function `u` is in particular eventually bounded. -/
@@ -86,11 +88,15 @@ theorem isBoundedUnder_of {f : Filter β} {u : β → α} : (∃ b, ∀ x, r (u
#align filter.is_bounded_under_of Filter.isBoundedUnder_of
-/
+#print Filter.isBounded_bot /-
theorem isBounded_bot : IsBounded r ⊥ ↔ Nonempty α := by simp [is_bounded, exists_true_iff_nonempty]
#align filter.is_bounded_bot Filter.isBounded_bot
+-/
+#print Filter.isBounded_top /-
theorem isBounded_top : IsBounded r ⊤ ↔ ∃ t, ∀ x, r x t := by simp [is_bounded, eq_univ_iff_forall]
#align filter.is_bounded_top Filter.isBounded_top
+-/
#print Filter.isBounded_principal /-
theorem isBounded_principal (s : Set α) : IsBounded r (𝓟 s) ↔ ∃ t, ∀ x ∈ s, r x t := by
@@ -98,20 +104,26 @@ theorem isBounded_principal (s : Set α) : IsBounded r (𝓟 s) ↔ ∃ t, ∀ x
#align filter.is_bounded_principal Filter.isBounded_principal
-/
+#print Filter.isBounded_sup /-
theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r b₂ b) :
IsBounded r f → IsBounded r g → IsBounded r (f ⊔ g)
| ⟨b₁, h₁⟩, ⟨b₂, h₂⟩ =>
let ⟨b, rb₁b, rb₂b⟩ := hr b₁ b₂
⟨b, eventually_sup.mpr ⟨h₁.mono fun x h => trans h rb₁b, h₂.mono fun x h => trans h rb₂b⟩⟩
#align filter.is_bounded_sup Filter.isBounded_sup
+-/
+#print Filter.IsBounded.mono /-
theorem IsBounded.mono (h : f ≤ g) : IsBounded r g → IsBounded r f
| ⟨b, hb⟩ => ⟨b, h hb⟩
#align filter.is_bounded.mono Filter.IsBounded.mono
+-/
+#print Filter.IsBoundedUnder.mono /-
theorem IsBoundedUnder.mono {f g : Filter β} {u : β → α} (h : f ≤ g) :
g.IsBoundedUnder r u → f.IsBoundedUnder r u := fun hg => hg.mono (map_mono h)
#align filter.is_bounded_under.mono Filter.IsBoundedUnder.mono
+-/
#print Filter.IsBoundedUnder.mono_le /-
theorem IsBoundedUnder.mono_le [Preorder β] {l : Filter α} {u v : α → β}
@@ -127,14 +139,18 @@ theorem IsBoundedUnder.mono_ge [Preorder β] {l : Filter α} {u v : α → β}
#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_ge
-/
+#print Filter.isBoundedUnder_const /-
theorem isBoundedUnder_const [IsRefl α r] {l : Filter β} {a : α} : IsBoundedUnder r l fun _ => a :=
⟨a, eventually_map.2 <| eventually_of_forall fun _ => refl _⟩
#align filter.is_bounded_under_const Filter.isBoundedUnder_const
+-/
+#print Filter.IsBounded.isBoundedUnder /-
theorem IsBounded.isBoundedUnder {q : β → β → Prop} {u : α → β}
(hf : ∀ a₀ a₁, r a₀ a₁ → q (u a₀) (u a₁)) : f.IsBounded r → f.IsBoundedUnder q u
| ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hf x b⟩
#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnder
+-/
#print Filter.not_isBoundedUnder_of_tendsto_atTop /-
theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f : α → β} {l : Filter α}
@@ -214,6 +230,7 @@ def IsCoboundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
#align filter.is_cobounded_under Filter.IsCoboundedUnder
-/
+#print Filter.IsCobounded.mk /-
/-- To check that a filter is frequently bounded, it suffices to have a witness
which bounds `f` at some point for every admissible set.
@@ -223,6 +240,7 @@ theorem IsCobounded.mk [IsTrans α r] (a : α) (h : ∀ s ∈ f, ∃ x ∈ s, r
let ⟨x, h₁, h₂⟩ := h _ s
trans h₂ h₁⟩
#align filter.is_cobounded.mk Filter.IsCobounded.mk
+-/
#print Filter.IsBounded.isCobounded_flip /-
/-- A filter which is eventually bounded is in particular frequently bounded (in the opposite
@@ -249,13 +267,17 @@ theorem IsBounded.isCobounded_le [Preorder α] [NeBot f] (h : f.IsBounded (·
#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_le
-/
+#print Filter.isCobounded_bot /-
theorem isCobounded_bot : IsCobounded r ⊥ ↔ ∃ b, ∀ x, r b x := by simp [is_cobounded]
#align filter.is_cobounded_bot Filter.isCobounded_bot
+-/
+#print Filter.isCobounded_top /-
theorem isCobounded_top : IsCobounded r ⊤ ↔ Nonempty α := by
simp (config := { contextual := true }) [is_cobounded, eq_univ_iff_forall,
exists_true_iff_nonempty]
#align filter.is_cobounded_top Filter.isCobounded_top
+-/
#print Filter.isCobounded_principal /-
theorem isCobounded_principal (s : Set α) :
@@ -263,9 +285,11 @@ theorem isCobounded_principal (s : Set α) :
#align filter.is_cobounded_principal Filter.isCobounded_principal
-/
+#print Filter.IsCobounded.mono /-
theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
| ⟨b, hb⟩ => ⟨b, fun a ha => hb a (h ha)⟩
#align filter.is_cobounded.mono Filter.IsCobounded.mono
+-/
end Relation
@@ -293,32 +317,41 @@ theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBo
#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_bot
-/
+#print OrderIso.isBoundedUnder_le_comp /-
@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
{u : γ → α} : (IsBoundedUnder (· ≤ ·) l fun x => e (u x)) ↔ IsBoundedUnder (· ≤ ·) l u :=
e.Surjective.exists.trans <| exists_congr fun a => by simp only [eventually_map, e.le_iff_le]
#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_comp
+-/
+#print OrderIso.isBoundedUnder_ge_comp /-
@[simp]
theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
{u : γ → α} : (IsBoundedUnder (· ≥ ·) l fun x => e (u x)) ↔ IsBoundedUnder (· ≥ ·) l u :=
e.dual.isBoundedUnder_le_comp
#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_comp
+-/
+#print Filter.isBoundedUnder_le_inv /-
@[simp, to_additive]
theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
(IsBoundedUnder (· ≤ ·) l fun x => (u x)⁻¹) ↔ IsBoundedUnder (· ≥ ·) l u :=
(OrderIso.inv α).isBoundedUnder_ge_comp
#align filter.is_bounded_under_le_inv Filter.isBoundedUnder_le_inv
#align filter.is_bounded_under_le_neg Filter.isBoundedUnder_le_neg
+-/
+#print Filter.isBoundedUnder_ge_inv /-
@[simp, to_additive]
theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
(IsBoundedUnder (· ≥ ·) l fun x => (u x)⁻¹) ↔ IsBoundedUnder (· ≤ ·) l u :=
(OrderIso.inv α).isBoundedUnder_le_comp
#align filter.is_bounded_under_ge_inv Filter.isBoundedUnder_ge_inv
#align filter.is_bounded_under_ge_neg Filter.isBoundedUnder_ge_neg
+-/
+#print Filter.IsBoundedUnder.sup /-
theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≤ ·) u →
f.IsBoundedUnder (· ≤ ·) v → f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a
@@ -326,7 +359,9 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
⟨bu ⊔ bv,
show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv by filter_upwards [hu, hv] with _ using sup_le_sup⟩
#align filter.is_bounded_under.sup Filter.IsBoundedUnder.sup
+-/
+#print Filter.isBoundedUnder_le_sup /-
@[simp]
theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a) ↔
@@ -336,25 +371,32 @@ theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β →
h.mono_le <| eventually_of_forall fun _ => le_sup_right⟩,
fun h => h.1.sup h.2⟩
#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_sup
+-/
+#print Filter.IsBoundedUnder.inf /-
theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≥ ·) u →
f.IsBoundedUnder (· ≥ ·) v → f.IsBoundedUnder (· ≥ ·) fun a => u a ⊓ v a :=
@IsBoundedUnder.sup αᵒᵈ β _ _ _ _
#align filter.is_bounded_under.inf Filter.IsBoundedUnder.inf
+-/
+#print Filter.isBoundedUnder_ge_inf /-
@[simp]
theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
(f.IsBoundedUnder (· ≥ ·) fun a => u a ⊓ v a) ↔
f.IsBoundedUnder (· ≥ ·) u ∧ f.IsBoundedUnder (· ≥ ·) v :=
@isBoundedUnder_le_sup αᵒᵈ _ _ _ _ _
#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_inf
+-/
+#print Filter.isBoundedUnder_le_abs /-
theorem isBoundedUnder_le_abs [LinearOrderedAddCommGroup α] {f : Filter β} {u : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => |u a|) ↔
f.IsBoundedUnder (· ≤ ·) u ∧ f.IsBoundedUnder (· ≥ ·) u :=
isBoundedUnder_le_sup.trans <| and_congr Iff.rfl isBoundedUnder_le_neg
#align filter.is_bounded_under_le_abs Filter.isBoundedUnder_le_abs
+-/
/-- Filters are automatically bounded or cobounded in complete lattices. To use the same statements
in complete and conditionally complete lattices but let automation fill automatically the
@@ -422,21 +464,29 @@ section
variable {f : Filter β} {u : β → α} {p : β → Prop}
+#print Filter.limsup_eq /-
theorem limsup_eq : limsup u f = sInf {a | ∀ᶠ n in f, u n ≤ a} :=
rfl
#align filter.limsup_eq Filter.limsup_eq
+-/
+#print Filter.liminf_eq /-
theorem liminf_eq : liminf u f = sSup {a | ∀ᶠ n in f, a ≤ u n} :=
rfl
#align filter.liminf_eq Filter.liminf_eq
+-/
+#print Filter.blimsup_eq /-
theorem blimsup_eq : blimsup u f p = sInf {a | ∀ᶠ x in f, p x → u x ≤ a} :=
rfl
#align filter.blimsup_eq Filter.blimsup_eq
+-/
+#print Filter.bliminf_eq /-
theorem bliminf_eq : bliminf u f p = sSup {a | ∀ᶠ x in f, p x → a ≤ u x} :=
rfl
#align filter.bliminf_eq Filter.bliminf_eq
+-/
end
@@ -501,6 +551,7 @@ theorem le_limsInf_of_le {f : Filter α} {a}
/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsSup_le_of_le /-
theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by
run_tac
@@ -508,6 +559,7 @@ theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ᶠ n in f, u n ≤ a) : limsup u f ≤ a :=
csInf_le hf h
#align filter.limsup_le_of_le Filter.limsSup_le_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_liminf_of_le /-
@@ -662,6 +714,7 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsSup_le_limsSup_of_le /-
theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -672,9 +725,11 @@ theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
limsSup f ≤ limsSup g :=
limsSup_le_limsSup hf hg fun a ha => h ha
#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsInf_le_limsInf_of_le /-
theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -685,9 +740,11 @@ theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
limsInf f ≤ limsInf g :=
limsInf_le_limsInf hf hg fun a ha => h ha
#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsup_le_limsup_of_le /-
theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : f ≤ g)
{u : α → β}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -699,9 +756,11 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
limsup u f ≤ limsup u g :=
limsSup_le_limsSup_of_le (map_mono h) hf hg
#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.liminf_le_liminf_of_le /-
theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : g ≤ f)
{u : α → β}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
@@ -713,14 +772,19 @@ theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g :
liminf u f ≤ liminf u g :=
limsInf_le_limsInf_of_le (map_mono h) hf hg
#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_le
+-/
+#print Filter.limsSup_principal /-
theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsSup (𝓟 s) = sSup s :=
by simp [Limsup] <;> exact csInf_upper_bounds_eq_csSup h hs
#align filter.Limsup_principal Filter.limsSup_principal
+-/
+#print Filter.limsInf_principal /-
theorem limsInf_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : limsInf (𝓟 s) = sInf s :=
@limsSup_principal αᵒᵈ _ s h hs
#align filter.Liminf_principal Filter.limsInf_principal
+-/
#print Filter.limsup_congr /-
theorem limsup_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
@@ -777,48 +841,65 @@ section CompleteLattice
variable [CompleteLattice α]
+#print Filter.limsSup_bot /-
@[simp]
theorem limsSup_bot : limsSup (⊥ : Filter α) = ⊥ :=
bot_unique <| sInf_le <| by simp
#align filter.Limsup_bot Filter.limsSup_bot
+-/
+#print Filter.limsInf_bot /-
@[simp]
theorem limsInf_bot : limsInf (⊥ : Filter α) = ⊤ :=
top_unique <| le_sSup <| by simp
#align filter.Liminf_bot Filter.limsInf_bot
+-/
+#print Filter.limsSup_top /-
@[simp]
theorem limsSup_top : limsSup (⊤ : Filter α) = ⊤ :=
top_unique <| le_sInf <| by simp [eq_univ_iff_forall] <;> exact fun b hb => top_unique <| hb _
#align filter.Limsup_top Filter.limsSup_top
+-/
+#print Filter.limsInf_top /-
@[simp]
theorem limsInf_top : limsInf (⊤ : Filter α) = ⊥ :=
bot_unique <| sSup_le <| by simp [eq_univ_iff_forall] <;> exact fun b hb => bot_unique <| hb _
#align filter.Liminf_top Filter.limsInf_top
+-/
+#print Filter.blimsup_false /-
@[simp]
theorem blimsup_false {f : Filter β} {u : β → α} : (blimsup u f fun x => False) = ⊥ := by
simp [blimsup_eq]
#align filter.blimsup_false Filter.blimsup_false
+-/
+#print Filter.bliminf_false /-
@[simp]
theorem bliminf_false {f : Filter β} {u : β → α} : (bliminf u f fun x => False) = ⊤ := by
simp [bliminf_eq]
#align filter.bliminf_false Filter.bliminf_false
+-/
+#print Filter.limsup_const_bot /-
/-- Same as limsup_const applied to `⊥` but without the `ne_bot f` assumption -/
theorem limsup_const_bot {f : Filter β} : limsup (fun x : β => (⊥ : α)) f = (⊥ : α) :=
by
rw [limsup_eq, eq_bot_iff]
exact sInf_le (eventually_of_forall fun x => le_rfl)
#align filter.limsup_const_bot Filter.limsup_const_bot
+-/
+#print Filter.liminf_const_top /-
/-- Same as limsup_const applied to `⊤` but without the `ne_bot f` assumption -/
theorem liminf_const_top {f : Filter β} : liminf (fun x : β => (⊤ : α)) f = (⊤ : α) :=
@limsup_const_bot αᵒᵈ β _ _
#align filter.liminf_const_top Filter.liminf_const_top
+-/
+#print Filter.HasBasis.limsSup_eq_iInf_sSup /-
theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
limsSup f = ⨅ (i) (hi : p i), sSup (s i) :=
le_antisymm (le_iInf₂ fun i hi => sInf_le <| h.eventually_iff.2 ⟨i, hi, fun x => le_sSup⟩)
@@ -826,21 +907,29 @@ theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α}
let ⟨i, hi, ha⟩ := h.eventually_iff.1 ha
iInf₂_le_of_le _ hi <| sSup_le ha)
#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSup
+-/
+#print Filter.HasBasis.limsInf_eq_iSup_sInf /-
theorem HasBasis.limsInf_eq_iSup_sInf {p : ι → Prop} {s : ι → Set α} {f : Filter α}
(h : f.HasBasis p s) : limsInf f = ⨆ (i) (hi : p i), sInf (s i) :=
@HasBasis.limsSup_eq_iInf_sSup αᵒᵈ _ _ _ _ _ h
#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInf
+-/
+#print Filter.limsSup_eq_iInf_sSup /-
theorem limsSup_eq_iInf_sSup {f : Filter α} : limsSup f = ⨅ s ∈ f, sSup s :=
f.basis_sets.limsSup_eq_iInf_sSup
#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSup
+-/
+#print Filter.limsInf_eq_iSup_sInf /-
theorem limsInf_eq_iSup_sInf {f : Filter α} : limsInf f = ⨆ s ∈ f, sInf s :=
@limsSup_eq_iInf_sSup αᵒᵈ _ _
#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInf
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print Filter.limsup_le_iSup /-
theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
limsSup_le_of_le
(by
@@ -848,8 +937,10 @@ theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u
is_bounded_default)
(eventually_of_forall (le_iSup u))
#align filter.limsup_le_supr Filter.limsup_le_iSup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print Filter.iInf_le_liminf /-
theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
le_liminf_of_le
(by
@@ -857,26 +948,36 @@ theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf
is_bounded_default)
(eventually_of_forall (iInf_le u))
#align filter.infi_le_liminf Filter.iInf_le_liminf
+-/
+#print Filter.limsup_eq_iInf_iSup /-
/-- In a complete lattice, the limsup of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
theorem limsup_eq_iInf_iSup {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
(f.basis_sets.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSup
+-/
+#print Filter.limsup_eq_iInf_iSup_of_nat /-
theorem limsup_eq_iInf_iSup_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
(atTop_basis.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, iInf_const] <;> rfl
#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_iInf_iSup_of_nat
+-/
+#print Filter.limsup_eq_iInf_iSup_of_nat' /-
theorem limsup_eq_iInf_iSup_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
simp only [limsup_eq_infi_supr_of_nat, iSup_ge_eq_iSup_nat_add]
#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'
+-/
+#print Filter.HasBasis.limsup_eq_iInf_iSup /-
theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : limsup u f = ⨅ (i) (hi : p i), ⨆ a ∈ s i, u a :=
(h.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSup
+-/
+#print Filter.blimsup_congr' /-
theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊥ → (p x ↔ q x)) : blimsup u f p = blimsup u f q :=
by
@@ -887,12 +988,16 @@ theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
cases' eq_or_ne (u b) ⊥ with hu hu; · simp [hu]
rw [hb hu]
#align filter.blimsup_congr' Filter.blimsup_congr'
+-/
+#print Filter.bliminf_congr' /-
theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊤ → (p x ↔ q x)) : bliminf u f p = bliminf u f q :=
@blimsup_congr' αᵒᵈ β _ _ _ _ _ h
#align filter.bliminf_congr' Filter.bliminf_congr'
+-/
+#print Filter.blimsup_eq_iInf_biSup /-
theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
blimsup u f p = ⨅ s ∈ f, ⨆ (b) (hb : p b ∧ b ∈ s), u b :=
by
@@ -910,43 +1015,59 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
simp_rw [Imp.swap] at hs'
exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp])
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
+-/
+#print Filter.blimsup_eq_iInf_biSup_of_nat /-
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (hj : p j ∧ i ≤ j), u j := by
simp only [blimsup_eq_limsup_subtype, mem_preimage, mem_Ici, Function.comp_apply, ciInf_pos,
iSup_subtype, (at_top_basis.comap (coe : {x | p x} → ℕ)).limsup_eq_iInf_iSup, mem_set_of_eq,
Subtype.coe_mk, iSup_and]
#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
+-/
+#print Filter.liminf_eq_iSup_iInf /-
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
theorem liminf_eq_iSup_iInf {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
@limsup_eq_iInf_iSup αᵒᵈ β _ _ _
#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInf
+-/
+#print Filter.liminf_eq_iSup_iInf_of_nat /-
theorem liminf_eq_iSup_iInf_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
@limsup_eq_iInf_iSup_of_nat αᵒᵈ _ u
#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_iSup_iInf_of_nat
+-/
+#print Filter.liminf_eq_iSup_iInf_of_nat' /-
theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
@limsup_eq_iInf_iSup_of_nat' αᵒᵈ _ _
#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'
+-/
+#print Filter.HasBasis.liminf_eq_iSup_iInf /-
theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : liminf u f = ⨆ (i) (hi : p i), ⨅ a ∈ s i, u a :=
@HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
+-/
+#print Filter.bliminf_eq_iSup_biInf /-
theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
bliminf u f p = ⨆ s ∈ f, ⨅ (b) (hb : p b ∧ b ∈ s), u b :=
@blimsup_eq_iInf_biSup αᵒᵈ β _ f p u
#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInf
+-/
+#print Filter.bliminf_eq_iSup_biInf_of_nat /-
theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
bliminf u atTop p = ⨆ i, ⨅ (j) (hj : p j ∧ i ≤ j), u j :=
@blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
+-/
+#print Filter.limsup_eq_sInf_sSup /-
theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) :=
by
@@ -962,11 +1083,14 @@ theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R]
rintro _ ⟨_, h, rfl⟩
exact h
#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSup
+-/
+#print Filter.liminf_eq_sSup_sInf /-
theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
liminf a F = sSup ((fun I => sInf (a '' I)) '' F.sets) :=
@Filter.limsup_eq_sInf_sSup ι (OrderDual R) _ _ a
#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInf
+-/
#print Filter.liminf_nat_add /-
@[simp]
@@ -982,6 +1106,7 @@ theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k))
#align filter.limsup_nat_add Filter.limsup_nat_add
-/
+#print Filter.liminf_le_of_frequently_le' /-
theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x :=
by
@@ -993,12 +1118,16 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
exact fun h => hb.mp (h.mono fun a hbx hba hax => hbx (hba.trans hax))
exact hbx.exists.some_spec
#align filter.liminf_le_of_frequently_le' Filter.liminf_le_of_frequently_le'
+-/
+#print Filter.le_limsup_of_frequently_le' /-
theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, x ≤ u a) : x ≤ limsup u f :=
@liminf_le_of_frequently_le' _ βᵒᵈ _ _ _ _ h
#align filter.le_limsup_of_frequently_le' Filter.le_limsup_of_frequently_le'
+-/
+#print Filter.CompleteLatticeHom.apply_limsup_iterate /-
/-- If `f : α → α` is a morphism of complete lattices, then the limsup of its iterates of any
`a : α` is a fixed point. -/
@[simp]
@@ -1013,23 +1142,30 @@ theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (
simp only [zero_add, Function.comp_apply, iSup_le_iff]
exact fun i => le_iSup (fun i => (f^[i]) a) (i + 1)
#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterate
+-/
+#print Filter.CompleteLatticeHom.apply_liminf_iterate /-
/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
`a : α` is a fixed point. -/
theorem CompleteLatticeHom.apply_liminf_iterate (f : CompleteLatticeHom α α) (a : α) :
f (liminf (fun n => (f^[n]) a) atTop) = liminf (fun n => (f^[n]) a) atTop :=
(CompleteLatticeHom.dual f).apply_limsup_iterate _
#align filter.complete_lattice_hom.apply_liminf_iterate Filter.CompleteLatticeHom.apply_liminf_iterate
+-/
variable {f g : Filter β} {p q : β → Prop} {u v : β → α}
+#print Filter.blimsup_mono /-
theorem blimsup_mono (h : ∀ x, p x → q x) : blimsup u f p ≤ blimsup u f q :=
sInf_le_sInf fun a ha => ha.mono <| by tauto
#align filter.blimsup_mono Filter.blimsup_mono
+-/
+#print Filter.bliminf_antitone /-
theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u f p :=
sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
+-/
#print Filter.mono_blimsup' /-
theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
@@ -1037,9 +1173,11 @@ theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p
#align filter.mono_blimsup' Filter.mono_blimsup'
-/
+#print Filter.mono_blimsup /-
theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
mono_blimsup' <| eventually_of_forall h
#align filter.mono_blimsup Filter.mono_blimsup
+-/
#print Filter.mono_bliminf' /-
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
@@ -1047,40 +1185,55 @@ theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p
#align filter.mono_bliminf' Filter.mono_bliminf'
-/
+#print Filter.mono_bliminf /-
theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
mono_bliminf' <| eventually_of_forall h
#align filter.mono_bliminf Filter.mono_bliminf
+-/
+#print Filter.bliminf_antitone_filter /-
theorem bliminf_antitone_filter (h : f ≤ g) : bliminf u g p ≤ bliminf u f p :=
sSup_le_sSup fun a ha => ha.filter_mono h
#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filter
+-/
+#print Filter.blimsup_monotone_filter /-
theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p :=
sInf_le_sInf fun a ha => ha.filter_mono h
#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filter
+-/
+#print Filter.blimsup_and_le_inf /-
@[simp]
theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p ⊓ blimsup u f q :=
le_inf (blimsup_mono <| by tauto) (blimsup_mono <| by tauto)
#align filter.blimsup_and_le_inf Filter.blimsup_and_le_inf
+-/
+#print Filter.bliminf_sup_le_and /-
@[simp]
theorem bliminf_sup_le_and : bliminf u f p ⊔ bliminf u f q ≤ bliminf u f fun x => p x ∧ q x :=
@blimsup_and_le_inf αᵒᵈ β _ f p q u
#align filter.bliminf_sup_le_and Filter.bliminf_sup_le_and
+-/
+#print Filter.blimsup_sup_le_or /-
/-- See also `filter.blimsup_or_eq_sup`. -/
@[simp]
theorem blimsup_sup_le_or : blimsup u f p ⊔ blimsup u f q ≤ blimsup u f fun x => p x ∨ q x :=
sup_le (blimsup_mono <| by tauto) (blimsup_mono <| by tauto)
#align filter.blimsup_sup_le_or Filter.blimsup_sup_le_or
+-/
+#print Filter.bliminf_or_le_inf /-
/-- See also `filter.bliminf_or_eq_inf`. -/
@[simp]
theorem bliminf_or_le_inf : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f p ⊓ bliminf u f q :=
@blimsup_sup_le_or αᵒᵈ β _ f p q u
#align filter.bliminf_or_le_inf Filter.bliminf_or_le_inf
+-/
+#print Filter.OrderIso.apply_blimsup /-
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
e (blimsup u f p) = blimsup (e ∘ u) f p :=
by
@@ -1090,12 +1243,16 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
obtain ⟨a, rfl⟩ := e.surjective c
simp
#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsup
+-/
+#print Filter.OrderIso.apply_bliminf /-
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
e (bliminf u f p) = bliminf (e ∘ u) f p :=
@OrderIso.apply_blimsup αᵒᵈ β γᵒᵈ _ f p u _ e.dual
#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminf
+-/
+#print Filter.SupHom.apply_blimsup_le /-
theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
g (blimsup u f p) ≤ blimsup (g ∘ u) f p :=
by
@@ -1103,11 +1260,14 @@ theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
refine' ((OrderHomClass.mono g).map_iInf₂_le _).trans _
simp only [_root_.map_supr]
#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_le
+-/
+#print Filter.InfHom.le_apply_bliminf /-
theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : sInfHom α γ) :
bliminf (g ∘ u) f p ≤ g (bliminf u f p) :=
@SupHom.apply_blimsup_le αᵒᵈ β γᵒᵈ _ f p u _ g.dual
#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminf
+-/
end CompleteLattice
@@ -1115,6 +1275,7 @@ section CompleteDistribLattice
variable [CompleteDistribLattice α] {f : Filter β} {p q : β → Prop} {u : β → α}
+#print Filter.blimsup_or_eq_sup /-
@[simp]
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q :=
by
@@ -1123,33 +1284,44 @@ theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p
refine' fun a' ha' a ha => sInf_le ((ha.And ha').mono fun b h hb => _)
exact Or.elim hb (fun hb => le_sup_of_le_left <| h.1 hb) fun hb => le_sup_of_le_right <| h.2 hb
#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_sup
+-/
+#print Filter.bliminf_or_eq_inf /-
@[simp]
theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p ⊓ bliminf u f q :=
@blimsup_or_eq_sup αᵒᵈ β _ f p q u
#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_inf
+-/
+#print Filter.sup_limsup /-
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f :=
by
simp only [limsup_eq_infi_supr, iSup_sup_eq, sup_iInf₂_eq]
congr; ext s; congr; ext hs; congr
exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
+-/
+#print Filter.inf_liminf /-
theorem inf_liminf [NeBot f] (a : α) : a ⊓ liminf u f = liminf (fun x => a ⊓ u x) f :=
@sup_limsup αᵒᵈ β _ f _ _ _
#align filter.inf_liminf Filter.inf_liminf
+-/
+#print Filter.sup_liminf /-
theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :=
by
simp only [liminf_eq_supr_infi]
rw [sup_comm, biSup_sup (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
simp_rw [iInf₂_sup_eq, @sup_comm _ _ a]
#align filter.sup_liminf Filter.sup_liminf
+-/
+#print Filter.inf_limsup /-
theorem inf_limsup (a : α) : a ⊓ limsup u f = limsup (fun x => a ⊓ u x) f :=
@sup_liminf αᵒᵈ β _ f _ _
#align filter.inf_limsup Filter.inf_limsup
+-/
end CompleteDistribLattice
@@ -1157,36 +1329,48 @@ section CompleteBooleanAlgebra
variable [CompleteBooleanAlgebra α] (f : Filter β) (u : β → α)
+#print Filter.limsup_compl /-
theorem limsup_compl : limsup u fᶜ = liminf (compl ∘ u) f := by
simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.limsup_compl Filter.limsup_compl
+-/
+#print Filter.liminf_compl /-
theorem liminf_compl : liminf u fᶜ = limsup (compl ∘ u) f := by
simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.liminf_compl Filter.liminf_compl
+-/
+#print Filter.limsup_sdiff /-
theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f :=
by
simp only [limsup_eq_infi_supr, sdiff_eq]
rw [biInf_inf (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
simp_rw [inf_comm, inf_iSup₂_eq, inf_comm]
#align filter.limsup_sdiff Filter.limsup_sdiff
+-/
+#print Filter.liminf_sdiff /-
theorem liminf_sdiff [NeBot f] (a : α) : liminf u f \ a = liminf (fun b => u b \ a) f := by
simp only [sdiff_eq, @inf_comm _ _ _ (aᶜ), inf_liminf]
#align filter.liminf_sdiff Filter.liminf_sdiff
+-/
+#print Filter.sdiff_limsup /-
theorem sdiff_limsup [NeBot f] (a : α) : a \ limsup u f = liminf (fun b => a \ u b) f :=
by
rw [← compl_inj_iff]
simp only [sdiff_eq, liminf_compl, (· ∘ ·), compl_inf, compl_compl, sup_limsup]
#align filter.sdiff_limsup Filter.sdiff_limsup
+-/
+#print Filter.sdiff_liminf /-
theorem sdiff_liminf (a : α) : a \ liminf u f = limsup (fun b => a \ u b) f :=
by
rw [← compl_inj_iff]
simp only [sdiff_eq, limsup_compl, (· ∘ ·), compl_inf, compl_compl, sup_liminf]
#align filter.sdiff_liminf Filter.sdiff_liminf
+-/
end CompleteBooleanAlgebra
@@ -1194,6 +1378,7 @@ section SetLattice
variable {p : ι → Prop} {s : ι → Set α}
+#print Filter.cofinite.blimsup_set_eq /-
theorem cofinite.blimsup_set_eq : blimsup s cofinite p = {x | {n | p n ∧ x ∈ s n}.Infinite} :=
by
simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, Inf_eq_sInter, exists_prop]
@@ -1203,26 +1388,34 @@ theorem cofinite.blimsup_set_eq : blimsup s cofinite p = {x | {n | p n ∧ x ∈
exact ⟨{x}ᶜ, by simpa using h, by simp⟩
· exact hx.mono fun i hi => ⟨hi.1, fun hit => h (hit hi.2)⟩
#align filter.cofinite.blimsup_set_eq Filter.cofinite.blimsup_set_eq
+-/
+#print Filter.cofinite.bliminf_set_eq /-
theorem cofinite.bliminf_set_eq : bliminf s cofinite p = {x | {n | p n ∧ x ∉ s n}.Finite} :=
by
rw [← compl_inj_iff]
simpa only [bliminf_eq_supr_binfi, compl_iInf, compl_iSup, ← blimsup_eq_infi_bsupr,
cofinite.blimsup_set_eq]
#align filter.cofinite.bliminf_set_eq Filter.cofinite.bliminf_set_eq
+-/
+#print Filter.cofinite.limsup_set_eq /-
/-- In other words, `limsup cofinite s` is the set of elements lying inside the family `s`
infinitely often. -/
theorem cofinite.limsup_set_eq : limsup s cofinite = {x | {n | x ∈ s n}.Infinite} := by
simp only [← cofinite.blimsup_true s, cofinite.blimsup_set_eq, true_and_iff]
#align filter.cofinite.limsup_set_eq Filter.cofinite.limsup_set_eq
+-/
+#print Filter.cofinite.liminf_set_eq /-
/-- In other words, `liminf cofinite s` is the set of elements lying outside the family `s`
finitely often. -/
theorem cofinite.liminf_set_eq : liminf s cofinite = {x | {n | x ∉ s n}.Finite} := by
simp only [← cofinite.bliminf_true s, cofinite.bliminf_set_eq, true_and_iff]
#align filter.cofinite.liminf_set_eq Filter.cofinite.liminf_set_eq
+-/
+#print Filter.exists_forall_mem_of_hasBasis_mem_blimsup /-
theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Set β} {q : ι → Prop}
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
∃ f : {i | q i} → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
@@ -1234,7 +1427,9 @@ theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Se
· exact hg' (b i) (hl.mem_of_mem i.2)
· exact hg (b i) (hl.mem_of_mem i.2)
#align filter.exists_forall_mem_of_has_basis_mem_blimsup Filter.exists_forall_mem_of_hasBasis_mem_blimsup
+-/
+#print Filter.exists_forall_mem_of_hasBasis_mem_blimsup' /-
theorem exists_forall_mem_of_hasBasis_mem_blimsup' {l : Filter β} {b : ι → Set β}
(hl : l.HasBasis (fun _ => True) b) {u : β → Set α} {p : β → Prop} {x : α}
(hx : x ∈ blimsup u l p) : ∃ f : ι → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
@@ -1242,6 +1437,7 @@ theorem exists_forall_mem_of_hasBasis_mem_blimsup' {l : Filter β} {b : ι → S
obtain ⟨f, hf⟩ := exists_forall_mem_of_has_basis_mem_blimsup hl hx
exact ⟨fun i => f ⟨i, trivial⟩, fun i => hf ⟨i, trivial⟩⟩
#align filter.exists_forall_mem_of_has_basis_mem_blimsup' Filter.exists_forall_mem_of_hasBasis_mem_blimsup'
+-/
end SetLattice
@@ -1273,6 +1469,7 @@ theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinear
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.eventually_lt_of_lt_liminf /-
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : b < liminf u f)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1284,8 +1481,10 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
exists_lt_of_lt_csSup hu h
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.eventually_lt_of_limsup_lt /-
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : limsup u f < b)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -1294,8 +1493,10 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
∀ᶠ a in f, u a < b :=
@eventually_lt_of_lt_liminf _ βᵒᵈ _ _ _ _ h hu
#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_lt
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.le_limsup_of_frequently_le /-
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, b ≤ u x)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -1307,8 +1508,10 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
simp_rw [← lt_iff_not_ge]
exact fun h => eventually_lt_of_limsup_lt h hu
#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.liminf_le_of_frequently_le /-
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, u x ≤ b)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1317,8 +1520,10 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
liminf u f ≤ b :=
@le_limsup_of_frequently_le _ βᵒᵈ _ f u b hu_le hu
#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.frequently_lt_of_lt_limsup /-
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
(hu : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -1330,8 +1535,10 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
apply Limsup_le_of_le hu
simpa using h
#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.frequently_lt_of_liminf_lt /-
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
(hu : f.IsCoboundedUnder (· ≥ ·) u := by
@@ -1340,6 +1547,7 @@ theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β]
(h : liminf u f < b) : ∃ᶠ x in f, u x < b :=
@frequently_lt_of_lt_limsup _ βᵒᵈ _ f u b hu h
#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_lt
+-/
end ConditionallyCompleteLinearOrder
@@ -1349,6 +1557,7 @@ section Order
open Filter
+#print Monotone.isBoundedUnder_le_comp /-
theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
@@ -1358,27 +1567,35 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
obtain ⟨b, hb⟩ : ∃ b, ∀ a ≥ b, c < g a := eventually_at_top.1 (hg'.eventually_gt_at_top c)
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp
+-/
+#print Monotone.isBoundedUnder_ge_comp /-
theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual.isBoundedUnder_le_comp hg'
#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp
+-/
+#print Antitone.isBoundedUnder_le_comp /-
theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual_right.isBoundedUnder_ge_comp hg'
#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp
+-/
+#print Antitone.isBoundedUnder_ge_comp /-
theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
hg.dual_right.isBoundedUnder_le_comp hg'
#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print GaloisConnection.l_limsup_le /-
theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
[ConditionallyCompleteLattice γ] {f : Filter α} {v : α → β} {l : β → γ} {u : γ → β}
(gc : GaloisConnection l u)
@@ -1395,11 +1612,13 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
simp_rw [gc _ _] at hc ⊢
exact Limsup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print OrderIso.limsup_apply /-
theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [ConditionallyCompleteLattice γ]
{f : Filter α} {u : α → β} (g : β ≃o γ)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -1425,11 +1644,13 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
simp_rw [g.symm_apply_apply]
exact hu
#align order_iso.limsup_apply OrderIso.limsup_apply
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print OrderIso.liminf_apply /-
theorem OrderIso.liminf_apply {γ} [ConditionallyCompleteLattice β] [ConditionallyCompleteLattice γ]
{f : Filter α} {u : α → β} (g : β ≃o γ)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1447,6 +1668,7 @@ theorem OrderIso.liminf_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
g (liminf u f) = liminf (fun x => g (u x)) f :=
@OrderIso.limsup_apply α βᵒᵈ γᵒᵈ _ _ f u g.dual hu hu_co hgu hgu_co
#align order_iso.liminf_apply OrderIso.liminf_apply
+-/
end Order
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -74,8 +74,8 @@ variable {r : α → α → Prop} {f g : Filter α}
/-- `f` is eventually bounded if and only if, there exists an admissible set on which it is
bounded. -/
-theorem isBounded_iff : f.IsBounded r ↔ ∃ s ∈ f.sets, ∃ b, s ⊆ { x | r x b } :=
- Iff.intro (fun ⟨b, hb⟩ => ⟨{ a | r a b }, hb, b, Subset.refl _⟩) fun ⟨s, hs, b, hb⟩ =>
+theorem isBounded_iff : f.IsBounded r ↔ ∃ s ∈ f.sets, ∃ b, s ⊆ {x | r x b} :=
+ Iff.intro (fun ⟨b, hb⟩ => ⟨{a | r a b}, hb, b, Subset.refl _⟩) fun ⟨s, hs, b, hb⟩ =>
⟨b, mem_of_superset hs hb⟩
#align filter.is_bounded_iff Filter.isBounded_iff
@@ -144,7 +144,7 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
rw [eventually_map] at hb
obtain ⟨b', h⟩ := exists_gt b
have hb' := (tendsto_at_top.mp hf) b'
- have : { x : α | f x ≤ b } ∩ { x : α | b' ≤ f x } = ∅ :=
+ have : {x : α | f x ≤ b} ∩ {x : α | b' ≤ f x} = ∅ :=
eq_empty_of_subset_empty fun x hx => (not_le_of_lt h) (le_trans hx.2 hx.1)
exact (nonempty_of_mem (hb.and hb')).ne_empty this
#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTop
@@ -163,7 +163,7 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
by
rcases hf with ⟨b, hb⟩
haveI : Nonempty β := ⟨b⟩
- rw [← image_univ, ← union_compl_self { x | f x ≤ b }, image_union, bddAbove_union]
+ rw [← image_univ, ← union_compl_self {x | f x ≤ b}, image_union, bddAbove_union]
exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).BddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
-/
@@ -323,7 +323,8 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
f.IsBoundedUnder (· ≤ ·) u →
f.IsBoundedUnder (· ≤ ·) v → f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a
| ⟨bu, (hu : ∀ᶠ x in f, u x ≤ bu)⟩, ⟨bv, (hv : ∀ᶠ x in f, v x ≤ bv)⟩ =>
- ⟨bu ⊔ bv, show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv by filter_upwards [hu, hv]with _ using sup_le_sup⟩
+ ⟨bu ⊔ bv,
+ show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv by filter_upwards [hu, hv] with _ using sup_le_sup⟩
#align filter.is_bounded_under.sup Filter.IsBoundedUnder.sup
@[simp]
@@ -373,7 +374,7 @@ variable [ConditionallyCompleteLattice α]
/-- The `Limsup` of a filter `f` is the infimum of the `a` such that, eventually for `f`,
holds `x ≤ a`. -/
def limsSup (f : Filter α) : α :=
- sInf { a | ∀ᶠ n in f, n ≤ a }
+ sInf {a | ∀ᶠ n in f, n ≤ a}
#align filter.Limsup Filter.limsSup
-/
@@ -381,7 +382,7 @@ def limsSup (f : Filter α) : α :=
/-- The `Liminf` of a filter `f` is the supremum of the `a` such that, eventually for `f`,
holds `x ≥ a`. -/
def limsInf (f : Filter α) : α :=
- sSup { a | ∀ᶠ n in f, a ≤ n }
+ sSup {a | ∀ᶠ n in f, a ≤ n}
#align filter.Liminf Filter.limsInf
-/
@@ -405,7 +406,7 @@ def liminf (u : β → α) (f : Filter β) : α :=
/-- The `blimsup` of a function `u` along a filter `f`, bounded by a predicate `p`, is the infimum
of the `a` such that, eventually for `f`, `u x ≤ a` whenever `p x` holds. -/
def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
- sInf { a | ∀ᶠ x in f, p x → u x ≤ a }
+ sInf {a | ∀ᶠ x in f, p x → u x ≤ a}
#align filter.blimsup Filter.blimsup
-/
@@ -413,7 +414,7 @@ def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
/-- The `bliminf` of a function `u` along a filter `f`, bounded by a predicate `p`, is the supremum
of the `a` such that, eventually for `f`, `a ≤ u x` whenever `p x` holds. -/
def bliminf (u : β → α) (f : Filter β) (p : β → Prop) :=
- sSup { a | ∀ᶠ x in f, p x → a ≤ u x }
+ sSup {a | ∀ᶠ x in f, p x → a ≤ u x}
#align filter.bliminf Filter.bliminf
-/
@@ -421,19 +422,19 @@ section
variable {f : Filter β} {u : β → α} {p : β → Prop}
-theorem limsup_eq : limsup u f = sInf { a | ∀ᶠ n in f, u n ≤ a } :=
+theorem limsup_eq : limsup u f = sInf {a | ∀ᶠ n in f, u n ≤ a} :=
rfl
#align filter.limsup_eq Filter.limsup_eq
-theorem liminf_eq : liminf u f = sSup { a | ∀ᶠ n in f, a ≤ u n } :=
+theorem liminf_eq : liminf u f = sSup {a | ∀ᶠ n in f, a ≤ u n} :=
rfl
#align filter.liminf_eq Filter.liminf_eq
-theorem blimsup_eq : blimsup u f p = sInf { a | ∀ᶠ x in f, p x → u x ≤ a } :=
+theorem blimsup_eq : blimsup u f p = sInf {a | ∀ᶠ x in f, p x → u x ≤ a} :=
rfl
#align filter.blimsup_eq Filter.blimsup_eq
-theorem bliminf_eq : bliminf u f p = sSup { a | ∀ᶠ x in f, p x → a ≤ u x } :=
+theorem bliminf_eq : bliminf u f p = sSup {a | ∀ᶠ x in f, p x → a ≤ u x} :=
rfl
#align filter.bliminf_eq Filter.bliminf_eq
@@ -455,7 +456,7 @@ theorem bliminf_true (f : Filter β) (u : β → α) : (bliminf u f fun x => Tru
#print Filter.blimsup_eq_limsup_subtype /-
theorem blimsup_eq_limsup_subtype {f : Filter β} {u : β → α} {p : β → Prop} :
- blimsup u f p = limsup (u ∘ (coe : { x | p x } → β)) (comap coe f) :=
+ blimsup u f p = limsup (u ∘ (coe : {x | p x} → β)) (comap coe f) :=
by
simp only [blimsup_eq, limsup_eq, Function.comp_apply, eventually_comap, SetCoe.forall,
Subtype.coe_mk, mem_set_of_eq]
@@ -470,7 +471,7 @@ theorem blimsup_eq_limsup_subtype {f : Filter β} {u : β → α} {p : β → Pr
#print Filter.bliminf_eq_liminf_subtype /-
theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Prop} :
- bliminf u f p = liminf (u ∘ (coe : { x | p x } → β)) (comap coe f) :=
+ bliminf u f p = liminf (u ∘ (coe : {x | p x} → β)) (comap coe f) :=
@blimsup_eq_limsup_subtype αᵒᵈ β _ f u p
#align filter.bliminf_eq_liminf_subtype Filter.bliminf_eq_liminf_subtype
-/
@@ -913,7 +914,7 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (hj : p j ∧ i ≤ j), u j := by
simp only [blimsup_eq_limsup_subtype, mem_preimage, mem_Ici, Function.comp_apply, ciInf_pos,
- iSup_subtype, (at_top_basis.comap (coe : { x | p x } → ℕ)).limsup_eq_iInf_iSup, mem_set_of_eq,
+ iSup_subtype, (at_top_basis.comap (coe : {x | p x} → ℕ)).limsup_eq_iInf_iSup, mem_set_of_eq,
Subtype.coe_mk, iSup_and]
#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
@@ -953,7 +954,7 @@ theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R]
· rw [limsup_eq]
refine' sInf_le_sInf fun x hx => _
rcases(mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
- filter_upwards [I_mem_F]with i hi
+ filter_upwards [I_mem_F] with i hi
exact hI ▸ le_sSup (mem_image_of_mem _ hi)
· refine'
le_Inf_iff.mpr fun b hb =>
@@ -1193,7 +1194,7 @@ section SetLattice
variable {p : ι → Prop} {s : ι → Set α}
-theorem cofinite.blimsup_set_eq : blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } :=
+theorem cofinite.blimsup_set_eq : blimsup s cofinite p = {x | {n | p n ∧ x ∈ s n}.Infinite} :=
by
simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, Inf_eq_sInter, exists_prop]
ext x
@@ -1203,7 +1204,7 @@ theorem cofinite.blimsup_set_eq : blimsup s cofinite p = { x | { n | p n ∧ x
· exact hx.mono fun i hi => ⟨hi.1, fun hit => h (hit hi.2)⟩
#align filter.cofinite.blimsup_set_eq Filter.cofinite.blimsup_set_eq
-theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x ∉ s n }.Finite } :=
+theorem cofinite.bliminf_set_eq : bliminf s cofinite p = {x | {n | p n ∧ x ∉ s n}.Finite} :=
by
rw [← compl_inj_iff]
simpa only [bliminf_eq_supr_binfi, compl_iInf, compl_iSup, ← blimsup_eq_infi_bsupr,
@@ -1212,24 +1213,24 @@ theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x
/-- In other words, `limsup cofinite s` is the set of elements lying inside the family `s`
infinitely often. -/
-theorem cofinite.limsup_set_eq : limsup s cofinite = { x | { n | x ∈ s n }.Infinite } := by
+theorem cofinite.limsup_set_eq : limsup s cofinite = {x | {n | x ∈ s n}.Infinite} := by
simp only [← cofinite.blimsup_true s, cofinite.blimsup_set_eq, true_and_iff]
#align filter.cofinite.limsup_set_eq Filter.cofinite.limsup_set_eq
/-- In other words, `liminf cofinite s` is the set of elements lying outside the family `s`
finitely often. -/
-theorem cofinite.liminf_set_eq : liminf s cofinite = { x | { n | x ∉ s n }.Finite } := by
+theorem cofinite.liminf_set_eq : liminf s cofinite = {x | {n | x ∉ s n}.Finite} := by
simp only [← cofinite.bliminf_true s, cofinite.bliminf_set_eq, true_and_iff]
#align filter.cofinite.liminf_set_eq Filter.cofinite.liminf_set_eq
theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Set β} {q : ι → Prop}
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
- ∃ f : { i | q i } → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
+ ∃ f : {i | q i} → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
by
rw [blimsup_eq_infi_bsupr] at hx
simp only [supr_eq_Union, infi_eq_Inter, mem_Inter, mem_Union, exists_prop] at hx
choose g hg hg' using hx
- refine' ⟨fun i : { i | q i } => g (b i) (hl.mem_of_mem i.2), fun i => ⟨_, _⟩⟩
+ refine' ⟨fun i : {i | q i} => g (b i) (hl.mem_of_mem i.2), fun i => ⟨_, _⟩⟩
· exact hg' (b i) (hl.mem_of_mem i.2)
· exact hg (b i) (hl.mem_of_mem i.2)
#align filter.exists_forall_mem_of_has_basis_mem_blimsup Filter.exists_forall_mem_of_hasBasis_mem_blimsup
@@ -1279,7 +1280,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
is_bounded_default) :
∀ᶠ a in f, b < u a :=
by
- obtain ⟨c, hc, hbc⟩ : ∃ (c : β) (hc : c ∈ { c : β | ∀ᶠ n : α in f, c ≤ u n }), b < c :=
+ obtain ⟨c, hc, hbc⟩ : ∃ (c : β) (hc : c ∈ {c : β | ∀ᶠ n : α in f, c ≤ u n}), b < c :=
exists_lt_of_lt_csSup hu h
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -141,7 +141,7 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
[l.ne_bot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f :=
by
rintro ⟨b, hb⟩
- rw [eventually_map] at hb
+ rw [eventually_map] at hb
obtain ⟨b', h⟩ := exists_gt b
have hb' := (tendsto_at_top.mp hf) b'
have : { x : α | f x ≤ b } ∩ { x : α | b' ≤ f x } = ∅ :=
@@ -178,7 +178,7 @@ theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α
#print Filter.IsBoundedUnder.bddAbove_range /-
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
- rw [← Nat.cofinite_eq_atTop] at hf; exact hf.bdd_above_range_of_cofinite
+ rw [← Nat.cofinite_eq_atTop] at hf ; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
-/
@@ -906,8 +906,8 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
eventually_imp_distrib_left.mpr fun h => eventually_iff_exists_mem.2 ⟨s, h, fun x h₁ h₂ => _⟩
exact @le_iSup₂ α β (fun b => p b ∧ b ∈ s) _ (fun b hb => u b) x ⟨h₂, h₁⟩
· obtain ⟨s, hs, hs'⟩ := eventually_iff_exists_mem.mp ha'
- simp_rw [Imp.swap] at hs'
- exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp] )
+ simp_rw [Imp.swap] at hs'
+ exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp])
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
@@ -1131,7 +1131,7 @@ theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f :=
by
simp only [limsup_eq_infi_supr, iSup_sup_eq, sup_iInf₂_eq]
- congr ; ext s; congr ; ext hs; congr
+ congr; ext s; congr; ext hs; congr
exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
@@ -1226,8 +1226,8 @@ theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Se
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
∃ f : { i | q i } → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
by
- rw [blimsup_eq_infi_bsupr] at hx
- simp only [supr_eq_Union, infi_eq_Inter, mem_Inter, mem_Union, exists_prop] at hx
+ rw [blimsup_eq_infi_bsupr] at hx
+ simp only [supr_eq_Union, infi_eq_Inter, mem_Inter, mem_Union, exists_prop] at hx
choose g hg hg' using hx
refine' ⟨fun i : { i | q i } => g (b i) (hl.mem_of_mem i.2), fun i => ⟨_, _⟩⟩
· exact hg' (b i) (hl.mem_of_mem i.2)
@@ -1255,7 +1255,7 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
(h : a < limsSup f) : ∃ᶠ n in f, a < n :=
by
contrapose! h
- simp only [not_frequently, not_lt] at h
+ simp only [not_frequently, not_lt] at h
exact Limsup_le_of_le hf h
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
-/
@@ -1279,7 +1279,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
is_bounded_default) :
∀ᶠ a in f, b < u a :=
by
- obtain ⟨c, hc, hbc⟩ : ∃ (c : β)(hc : c ∈ { c : β | ∀ᶠ n : α in f, c ≤ u n }), b < c :=
+ obtain ⟨c, hc, hbc⟩ : ∃ (c : β) (hc : c ∈ { c : β | ∀ᶠ n : α in f, c ≤ u n }), b < c :=
exists_lt_of_lt_csSup hu h
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
@@ -1353,7 +1353,7 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
by
refine' ⟨_, fun h => h.IsBoundedUnder hg⟩
- rintro ⟨c, hc⟩; rw [eventually_map] at hc
+ rintro ⟨c, hc⟩; rw [eventually_map] at hc
obtain ⟨b, hb⟩ : ∃ b, ∀ a ≥ b, c < g a := eventually_at_top.1 (hg'.eventually_gt_at_top c)
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp
@@ -1390,8 +1390,8 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
l (limsup v f) ≤ limsup (fun x => l (v x)) f :=
by
refine' le_Limsup_of_le hlv fun c hc => _
- rw [Filter.eventually_map] at hc
- simp_rw [gc _ _] at hc⊢
+ rw [Filter.eventually_map] at hc
+ simp_rw [gc _ _] at hc ⊢
exact Limsup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -45,7 +45,7 @@ In complete lattices, however, it coincides with the `Inf Sup` definition.
open Filter Set
-open Filter
+open scoped Filter
variable {α β γ ι : Type _}
@@ -113,15 +113,19 @@ theorem IsBoundedUnder.mono {f g : Filter β} {u : β → α} (h : f ≤ g) :
g.IsBoundedUnder r u → f.IsBoundedUnder r u := fun hg => hg.mono (map_mono h)
#align filter.is_bounded_under.mono Filter.IsBoundedUnder.mono
+#print Filter.IsBoundedUnder.mono_le /-
theorem IsBoundedUnder.mono_le [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≤ ·) l u) (hv : v ≤ᶠ[l] u) : IsBoundedUnder (· ≤ ·) l v :=
hu.imp fun b hb => (eventually_map.1 hb).mp <| hv.mono fun x => le_trans
#align filter.is_bounded_under.mono_le Filter.IsBoundedUnder.mono_le
+-/
+#print Filter.IsBoundedUnder.mono_ge /-
theorem IsBoundedUnder.mono_ge [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≥ ·) l u) (hv : u ≤ᶠ[l] v) : IsBoundedUnder (· ≥ ·) l v :=
@IsBoundedUnder.mono_le α βᵒᵈ _ _ _ _ hu hv
#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_ge
+-/
theorem isBoundedUnder_const [IsRefl α r] {l : Filter β} {a : α} : IsBoundedUnder r l fun _ => a :=
⟨a, eventually_map.2 <| eventually_of_forall fun _ => refl _⟩
@@ -132,6 +136,7 @@ theorem IsBounded.isBoundedUnder {q : β → β → Prop} {u : α → β}
| ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hf x b⟩
#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnder
+#print Filter.not_isBoundedUnder_of_tendsto_atTop /-
theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f :=
by
@@ -143,12 +148,16 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
eq_empty_of_subset_empty fun x hx => (not_le_of_lt h) (le_trans hx.2 hx.1)
exact (nonempty_of_mem (hb.and hb')).ne_empty this
#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTop
+-/
+#print Filter.not_isBoundedUnder_of_tendsto_atBot /-
theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atBot) : ¬IsBoundedUnder (· ≥ ·) l f :=
@not_isBoundedUnder_of_tendsto_atTop α βᵒᵈ _ _ _ _ _ hf
#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBot
+-/
+#print Filter.IsBoundedUnder.bddAbove_range_of_cofinite /-
theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
(hf : IsBoundedUnder (· ≤ ·) cofinite f) : BddAbove (range f) :=
by
@@ -157,21 +166,28 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
rw [← image_univ, ← union_compl_self { x | f x ≤ b }, image_union, bddAbove_union]
exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).BddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
+-/
+#print Filter.IsBoundedUnder.bddBelow_range_of_cofinite /-
theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range_of_cofinite α βᵒᵈ _ _ hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
+-/
+#print Filter.IsBoundedUnder.bddAbove_range /-
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
rw [← Nat.cofinite_eq_atTop] at hf; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
+-/
+#print Filter.IsBoundedUnder.bddBelow_range /-
theorem IsBoundedUnder.bddBelow_range [SemilatticeInf β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≥ ·) atTop f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range βᵒᵈ _ _ hf
#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_range
+-/
#print Filter.IsCobounded /-
/-- `is_cobounded (≺) f` states that the filter `f` does not tend to infinity w.r.t. `≺`. This is
@@ -219,15 +235,19 @@ theorem IsBounded.isCobounded_flip [IsTrans α r] [NeBot f] : f.IsBounded r →
#align filter.is_bounded.is_cobounded_flip Filter.IsBounded.isCobounded_flip
-/
+#print Filter.IsBounded.isCobounded_ge /-
theorem IsBounded.isCobounded_ge [Preorder α] [NeBot f] (h : f.IsBounded (· ≤ ·)) :
f.IsCobounded (· ≥ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_ge Filter.IsBounded.isCobounded_ge
+-/
+#print Filter.IsBounded.isCobounded_le /-
theorem IsBounded.isCobounded_le [Preorder α] [NeBot f] (h : f.IsBounded (· ≥ ·)) :
f.IsCobounded (· ≤ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_le
+-/
theorem isCobounded_bot : IsCobounded r ⊥ ↔ ∃ b, ∀ x, r b x := by simp [is_cobounded]
#align filter.is_cobounded_bot Filter.isCobounded_bot
@@ -249,21 +269,29 @@ theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
end Relation
+#print Filter.isCobounded_le_of_bot /-
theorem isCobounded_le_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsCobounded (· ≤ ·) :=
⟨⊥, fun a h => bot_le⟩
#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_bot
+-/
+#print Filter.isCobounded_ge_of_top /-
theorem isCobounded_ge_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsCobounded (· ≥ ·) :=
⟨⊤, fun a h => le_top⟩
#align filter.is_cobounded_ge_of_top Filter.isCobounded_ge_of_top
+-/
+#print Filter.isBounded_le_of_top /-
theorem isBounded_le_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsBounded (· ≤ ·) :=
⟨⊤, eventually_of_forall fun _ => le_top⟩
#align filter.is_bounded_le_of_top Filter.isBounded_le_of_top
+-/
+#print Filter.isBounded_ge_of_bot /-
theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBounded (· ≥ ·) :=
⟨⊥, eventually_of_forall fun _ => bot_le⟩
#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_bot
+-/
@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -448,6 +476,7 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsSup_le_of_le /-
theorem limsSup_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -455,8 +484,10 @@ theorem limsSup_le_of_le {f : Filter α} {a}
(h : ∀ᶠ n in f, n ≤ a) : limsSup f ≤ a :=
csInf_le hf h
#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.le_limsInf_of_le /-
theorem le_limsInf_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
@@ -464,6 +495,7 @@ theorem le_limsInf_of_le {f : Filter α} {a}
(h : ∀ᶠ n in f, a ≤ n) : a ≤ limsInf f :=
le_csSup hf h
#align filter.le_Liminf_of_le Filter.le_limsInf_of_le
+-/
/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
@@ -477,6 +509,7 @@ theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
#align filter.limsup_le_of_le Filter.limsSup_le_of_le
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.le_liminf_of_le /-
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≥ ·) u := by
run_tac
@@ -484,8 +517,10 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ᶠ n in f, a ≤ u n) : a ≤ liminf u f :=
le_csSup hf h
#align filter.le_liminf_of_le Filter.le_liminf_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.le_limsSup_of_le /-
theorem le_limsSup_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by
run_tac
@@ -493,8 +528,10 @@ theorem le_limsSup_of_le {f : Filter α} {a}
(h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsSup f :=
le_csInf hf h
#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsInf_le_of_le /-
theorem limsInf_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -502,8 +539,10 @@ theorem limsInf_le_of_le {f : Filter α} {a}
(h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : limsInf f ≤ a :=
csSup_le hf h
#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.le_limsup_of_le /-
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≤ ·) u := by
run_tac
@@ -511,8 +550,10 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ b, (∀ᶠ n in f, u n ≤ b) → a ≤ b) : a ≤ limsup u f :=
le_csInf hf h
#align filter.le_limsup_of_le Filter.le_limsup_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.liminf_le_of_le /-
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
run_tac
@@ -520,9 +561,11 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ b, (∀ᶠ n in f, b ≤ u n) → b ≤ a) : liminf u f ≤ a :=
csSup_le hf h
#align filter.liminf_le_of_le Filter.liminf_le_of_le
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsInf_le_limsSup /-
theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
(h₁ : f.IsBounded (· ≤ ·) := by
run_tac
@@ -537,9 +580,11 @@ theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
let ⟨b, hb₀, hb₁⟩ := (ha₀.And ha₁).exists
le_trans hb₀ hb₁
#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.liminf_le_limsup /-
theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
(h : f.IsBoundedUnder (· ≤ ·) u := by
run_tac
@@ -550,9 +595,11 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
liminf u f ≤ limsup u f :=
limsInf_le_limsSup h h'
#align filter.liminf_le_limsup Filter.liminf_le_limsup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsSup_le_limsSup /-
theorem limsSup_le_limsSup {f g : Filter α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -563,9 +610,11 @@ theorem limsSup_le_limsSup {f g : Filter α}
(h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsSup f ≤ limsSup g :=
csInf_le_csInf hf hg h
#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsInf_le_limsInf /-
theorem limsInf_le_limsInf {f g : Filter α}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -576,9 +625,11 @@ theorem limsInf_le_limsInf {f g : Filter α}
(h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : limsInf f ≤ limsInf g :=
csSup_le_csSup hg hf h
#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.limsup_le_limsup /-
theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : u ≤ᶠ[f] v)
(hu : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -590,9 +641,11 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
limsup u f ≤ limsup v f :=
limsSup_le_limsSup hu hv fun b => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.liminf_le_liminf /-
theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a ≤ v a)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -604,6 +657,7 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
liminf u f ≤ liminf v f :=
@limsup_le_limsup βᵒᵈ α _ _ _ _ h hv hu
#align filter.liminf_le_liminf Filter.liminf_le_liminf
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -976,17 +1030,21 @@ theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u
sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
+#print Filter.mono_blimsup' /-
theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
sInf_le_sInf fun a ha => (ha.And h).mono fun x hx hx' => (hx.2 hx').trans (hx.1 hx')
#align filter.mono_blimsup' Filter.mono_blimsup'
+-/
theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
mono_blimsup' <| eventually_of_forall h
#align filter.mono_blimsup Filter.mono_blimsup
+#print Filter.mono_bliminf' /-
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
sSup_le_sSup fun a ha => (ha.And h).mono fun x hx hx' => (hx.1 hx').trans (hx.2 hx')
#align filter.mono_bliminf' Filter.mono_bliminf'
+-/
theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
mono_bliminf' <| eventually_of_forall h
@@ -1189,6 +1247,7 @@ end SetLattice
section ConditionallyCompleteLinearOrder
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.frequently_lt_of_lt_limsSup /-
theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -1199,8 +1258,10 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
simp only [not_frequently, not_lt] at h
exact Limsup_le_of_le hf h
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print Filter.frequently_lt_of_limsInf_lt /-
theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
@@ -1208,6 +1269,7 @@ theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinear
(h : limsInf f < a) : ∃ᶠ n in f, n < a :=
@frequently_lt_of_lt_limsSup (OrderDual α) f _ a hf h
#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -72,12 +72,6 @@ def IsBoundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
variable {r : α → α → Prop} {f g : Filter α}
-/- warning: filter.is_bounded_iff -> Filter.isBounded_iff is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α}, Iff (Filter.IsBounded.{u1} α r f) (Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s (Filter.sets.{u1} α f)) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s (Filter.sets.{u1} α f)) => Exists.{succ u1} α (fun (b : α) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (setOf.{u1} α (fun (x : α) => r x b))))))
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α}, Iff (Filter.IsBounded.{u1} α r f) (Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s (Filter.sets.{u1} α f)) (Exists.{succ u1} α (fun (b : α) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (setOf.{u1} α (fun (x : α) => r x b))))))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_iff Filter.isBounded_iffₓ'. -/
/-- `f` is eventually bounded if and only if, there exists an admissible set on which it is
bounded. -/
theorem isBounded_iff : f.IsBounded r ↔ ∃ s ∈ f.sets, ∃ b, s ⊆ { x | r x b } :=
@@ -92,21 +86,9 @@ theorem isBoundedUnder_of {f : Filter β} {u : β → α} : (∃ b, ∀ x, r (u
#align filter.is_bounded_under_of Filter.isBoundedUnder_of
-/
-/- warning: filter.is_bounded_bot -> Filter.isBounded_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsBounded.{u1} α r (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Nonempty.{succ u1} α)
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsBounded.{u1} α r (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Nonempty.{succ u1} α)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_bot Filter.isBounded_botₓ'. -/
theorem isBounded_bot : IsBounded r ⊥ ↔ Nonempty α := by simp [is_bounded, exists_true_iff_nonempty]
#align filter.is_bounded_bot Filter.isBounded_bot
-/- warning: filter.is_bounded_top -> Filter.isBounded_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsBounded.{u1} α r (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Exists.{succ u1} α (fun (t : α) => forall (x : α), r x t))
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsBounded.{u1} α r (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Exists.{succ u1} α (fun (t : α) => forall (x : α), r x t))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_top Filter.isBounded_topₓ'. -/
theorem isBounded_top : IsBounded r ⊤ ↔ ∃ t, ∀ x, r x t := by simp [is_bounded, eq_univ_iff_forall]
#align filter.is_bounded_top Filter.isBounded_top
@@ -116,12 +98,6 @@ theorem isBounded_principal (s : Set α) : IsBounded r (𝓟 s) ↔ ∃ t, ∀ x
#align filter.is_bounded_principal Filter.isBounded_principal
-/
-/- warning: filter.is_bounded_sup -> Filter.isBounded_sup is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) f g))
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) f g))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_sup Filter.isBounded_supₓ'. -/
theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r b₂ b) :
IsBounded r f → IsBounded r g → IsBounded r (f ⊔ g)
| ⟨b₁, h₁⟩, ⟨b₂, h₂⟩ =>
@@ -129,75 +105,33 @@ theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r
⟨b, eventually_sup.mpr ⟨h₁.mono fun x h => trans h rb₁b, h₂.mono fun x h => trans h rb₂b⟩⟩
#align filter.is_bounded_sup Filter.isBounded_sup
-/- warning: filter.is_bounded.mono -> Filter.IsBounded.mono is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r f)
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r f)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded.mono Filter.IsBounded.monoₓ'. -/
theorem IsBounded.mono (h : f ≤ g) : IsBounded r g → IsBounded r f
| ⟨b, hb⟩ => ⟨b, h hb⟩
#align filter.is_bounded.mono Filter.IsBounded.mono
-/- warning: filter.is_bounded_under.mono -> Filter.IsBoundedUnder.mono is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u2} β} {g : Filter.{u2} β} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toHasLe.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (Filter.IsBoundedUnder.{u1, u2} α β r g u) -> (Filter.IsBoundedUnder.{u1, u2} α β r f u)
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u2} β} {g : Filter.{u2} β} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (Filter.IsBoundedUnder.{u1, u2} α β r g u) -> (Filter.IsBoundedUnder.{u1, u2} α β r f u)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono Filter.IsBoundedUnder.monoₓ'. -/
theorem IsBoundedUnder.mono {f g : Filter β} {u : β → α} (h : f ≤ g) :
g.IsBoundedUnder r u → f.IsBoundedUnder r u := fun hg => hg.mono (map_mono h)
#align filter.is_bounded_under.mono Filter.IsBoundedUnder.mono
-/- warning: filter.is_bounded_under.mono_le -> Filter.IsBoundedUnder.mono_le is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_1) l v u) -> (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l v)
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.747 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.749 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.747 x._@.Mathlib.Order.LiminfLimsup._hyg.749) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_1) l v u) -> (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.771 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.773 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.771 x._@.Mathlib.Order.LiminfLimsup._hyg.773) l v)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono_le Filter.IsBoundedUnder.mono_leₓ'. -/
theorem IsBoundedUnder.mono_le [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≤ ·) l u) (hv : v ≤ᶠ[l] u) : IsBoundedUnder (· ≤ ·) l v :=
hu.imp fun b hb => (eventually_map.1 hb).mp <| hv.mono fun x => le_trans
#align filter.is_bounded_under.mono_le Filter.IsBoundedUnder.mono_le
-/- warning: filter.is_bounded_under.mono_ge -> Filter.IsBoundedUnder.mono_ge is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_1) l u v) -> (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l v)
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.841 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.843 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.841 x._@.Mathlib.Order.LiminfLimsup._hyg.843) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_1) l u v) -> (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.865 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.867 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.865 x._@.Mathlib.Order.LiminfLimsup._hyg.867) l v)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_geₓ'. -/
theorem IsBoundedUnder.mono_ge [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≥ ·) l u) (hv : u ≤ᶠ[l] v) : IsBoundedUnder (· ≥ ·) l v :=
@IsBoundedUnder.mono_le α βᵒᵈ _ _ _ _ hu hv
#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_ge
-/- warning: filter.is_bounded_under_const -> Filter.isBoundedUnder_const is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} [_inst_1 : IsRefl.{u1} α r] {l : Filter.{u2} β} {a : α}, Filter.IsBoundedUnder.{u1, u2} α β r l (fun (_x : β) => a)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsRefl.{u2} α r] {l : Filter.{u1} β} {a : α}, Filter.IsBoundedUnder.{u2, u1} α β r l (fun (_x : β) => a)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_const Filter.isBoundedUnder_constₓ'. -/
theorem isBoundedUnder_const [IsRefl α r] {l : Filter β} {a : α} : IsBoundedUnder r l fun _ => a :=
⟨a, eventually_map.2 <| eventually_of_forall fun _ => refl _⟩
#align filter.is_bounded_under_const Filter.isBoundedUnder_const
-/- warning: filter.is_bounded.is_bounded_under -> Filter.IsBounded.isBoundedUnder is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u1} α} {q : β -> β -> Prop} {u : α -> β}, (forall (a₀ : α) (a₁ : α), (r a₀ a₁) -> (q (u a₀) (u a₁))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBoundedUnder.{u2, u1} β α q f u)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u2} α} {q : β -> β -> Prop} {u : α -> β}, (forall (a₀ : α) (a₁ : α), (r a₀ a₁) -> (q (u a₀) (u a₁))) -> (Filter.IsBounded.{u2} α r f) -> (Filter.IsBoundedUnder.{u1, u2} β α q f u)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnderₓ'. -/
theorem IsBounded.isBoundedUnder {q : β → β → Prop} {u : α → β}
(hf : ∀ a₀ a₁, r a₀ a₁ → q (u a₀) (u a₁)) : f.IsBounded r → f.IsBoundedUnder q u
| ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hf x b⟩
#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnder
-/- warning: filter.not_is_bounded_under_of_tendsto_at_top -> Filter.not_isBoundedUnder_of_tendsto_atTop is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMaxOrder.{u2} β (Preorder.toHasLt.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atTop.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l f))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMaxOrder.{u2} β (Preorder.toLT.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atTop.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1086 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1088 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1086 x._@.Mathlib.Order.LiminfLimsup._hyg.1088) l f))
-Case conversion may be inaccurate. Consider using '#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTopₓ'. -/
theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f :=
by
@@ -210,23 +144,11 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
exact (nonempty_of_mem (hb.and hb')).ne_empty this
#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTop
-/- warning: filter.not_is_bounded_under_of_tendsto_at_bot -> Filter.not_isBoundedUnder_of_tendsto_atBot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMinOrder.{u2} β (Preorder.toHasLt.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atBot.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l f))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMinOrder.{u2} β (Preorder.toLT.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atBot.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1278 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1280 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1278 x._@.Mathlib.Order.LiminfLimsup._hyg.1280) l f))
-Case conversion may be inaccurate. Consider using '#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBotₓ'. -/
theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atBot) : ¬IsBoundedUnder (· ≥ ·) l f :=
@not_isBoundedUnder_of_tendsto_atTop α βᵒᵈ _ _ _ _ _ hf
#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBot
-/- warning: filter.is_bounded_under.bdd_above_range_of_cofinite -> Filter.IsBoundedUnder.bddAbove_range_of_cofinite is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)))) (Filter.cofinite.{u1} α) f) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1326 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1328 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1326 x._@.Mathlib.Order.LiminfLimsup._hyg.1328) (Filter.cofinite.{u1} α) f) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofiniteₓ'. -/
theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
(hf : IsBoundedUnder (· ≤ ·) cofinite f) : BddAbove (range f) :=
by
@@ -236,34 +158,16 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).BddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
-/- warning: filter.is_bounded_under.bdd_below_range_of_cofinite -> Filter.IsBoundedUnder.bddBelow_range_of_cofinite is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)))) (Filter.cofinite.{u1} α) f) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1460 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1462 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1460 x._@.Mathlib.Order.LiminfLimsup._hyg.1462) (Filter.cofinite.{u1} α) f) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofiniteₓ'. -/
theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range_of_cofinite α βᵒᵈ _ _ hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
-/- warning: filter.is_bounded_under.bdd_above_range -> Filter.IsBoundedUnder.bddAbove_range is a dubious translation:
-lean 3 declaration is
- forall {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
-but is expected to have type
- forall {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1516 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1518 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1516 x._@.Mathlib.Order.LiminfLimsup._hyg.1518) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_rangeₓ'. -/
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
rw [← Nat.cofinite_eq_atTop] at hf; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
-/- warning: filter.is_bounded_under.bdd_below_range -> Filter.IsBoundedUnder.bddBelow_range is a dubious translation:
-lean 3 declaration is
- forall {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (GE.ge.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
-but is expected to have type
- forall {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1600 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1602 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1600 x._@.Mathlib.Order.LiminfLimsup._hyg.1602) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_rangeₓ'. -/
theorem IsBoundedUnder.bddBelow_range [SemilatticeInf β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≥ ·) atTop f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range βᵒᵈ _ _ hf
@@ -294,12 +198,6 @@ def IsCoboundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
#align filter.is_cobounded_under Filter.IsCoboundedUnder
-/
-/- warning: filter.is_cobounded.mk -> Filter.IsCobounded.mk is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r] (a : α), (forall (s : Set.{u1} α), (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => r a x)))) -> (Filter.IsCobounded.{u1} α r f)
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r] (a : α), (forall (s : Set.{u1} α), (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (r a x)))) -> (Filter.IsCobounded.{u1} α r f)
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded.mk Filter.IsCobounded.mkₓ'. -/
/-- To check that a filter is frequently bounded, it suffices to have a witness
which bounds `f` at some point for every admissible set.
@@ -321,43 +219,19 @@ theorem IsBounded.isCobounded_flip [IsTrans α r] [NeBot f] : f.IsBounded r →
#align filter.is_bounded.is_cobounded_flip Filter.IsBounded.isCobounded_flip
-/
-/- warning: filter.is_bounded.is_cobounded_ge -> Filter.IsBounded.isCobounded_ge is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f) -> (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f)
-but is expected to have type
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1955 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.1957 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1955 x._@.Mathlib.Order.LiminfLimsup._hyg.1957) f) -> (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1971 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.1973 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1971 x._@.Mathlib.Order.LiminfLimsup._hyg.1973) f)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded.is_cobounded_ge Filter.IsBounded.isCobounded_geₓ'. -/
theorem IsBounded.isCobounded_ge [Preorder α] [NeBot f] (h : f.IsBounded (· ≤ ·)) :
f.IsCobounded (· ≥ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_ge Filter.IsBounded.isCobounded_ge
-/- warning: filter.is_bounded.is_cobounded_le -> Filter.IsBounded.isCobounded_le is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f) -> (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f)
-but is expected to have type
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2013 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2015 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2013 x._@.Mathlib.Order.LiminfLimsup._hyg.2015) f) -> (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2029 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2031 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2029 x._@.Mathlib.Order.LiminfLimsup._hyg.2031) f)
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_leₓ'. -/
theorem IsBounded.isCobounded_le [Preorder α] [NeBot f] (h : f.IsBounded (· ≥ ·)) :
f.IsCobounded (· ≤ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_le
-/- warning: filter.is_cobounded_bot -> Filter.isCobounded_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsCobounded.{u1} α r (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Exists.{succ u1} α (fun (b : α) => forall (x : α), r b x))
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsCobounded.{u1} α r (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Exists.{succ u1} α (fun (b : α) => forall (x : α), r b x))
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_bot Filter.isCobounded_botₓ'. -/
theorem isCobounded_bot : IsCobounded r ⊥ ↔ ∃ b, ∀ x, r b x := by simp [is_cobounded]
#align filter.is_cobounded_bot Filter.isCobounded_bot
-/- warning: filter.is_cobounded_top -> Filter.isCobounded_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsCobounded.{u1} α r (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Nonempty.{succ u1} α)
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop}, Iff (Filter.IsCobounded.{u1} α r (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Nonempty.{succ u1} α)
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_top Filter.isCobounded_topₓ'. -/
theorem isCobounded_top : IsCobounded r ⊤ ↔ Nonempty α := by
simp (config := { contextual := true }) [is_cobounded, eq_univ_iff_forall,
exists_true_iff_nonempty]
@@ -369,88 +243,40 @@ theorem isCobounded_principal (s : Set α) :
#align filter.is_cobounded_principal Filter.isCobounded_principal
-/
-/- warning: filter.is_cobounded.mono -> Filter.IsCobounded.mono is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsCobounded.{u1} α r f) -> (Filter.IsCobounded.{u1} α r g)
-but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (Filter.IsCobounded.{u1} α r f) -> (Filter.IsCobounded.{u1} α r g)
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded.mono Filter.IsCobounded.monoₓ'. -/
theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
| ⟨b, hb⟩ => ⟨b, fun a ha => hb a (h ha)⟩
#align filter.is_cobounded.mono Filter.IsCobounded.mono
end Relation
-/- warning: filter.is_cobounded_le_of_bot -> Filter.isCobounded_le_of_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2280 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2282 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2280 x._@.Mathlib.Order.LiminfLimsup._hyg.2282) f
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_botₓ'. -/
theorem isCobounded_le_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsCobounded (· ≤ ·) :=
⟨⊥, fun a h => bot_le⟩
#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_bot
-/- warning: filter.is_cobounded_ge_of_top -> Filter.isCobounded_ge_of_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2322 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2324 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2322 x._@.Mathlib.Order.LiminfLimsup._hyg.2324) f
-Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_ge_of_top Filter.isCobounded_ge_of_topₓ'. -/
theorem isCobounded_ge_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsCobounded (· ≥ ·) :=
⟨⊤, fun a h => le_top⟩
#align filter.is_cobounded_ge_of_top Filter.isCobounded_ge_of_top
-/- warning: filter.is_bounded_le_of_top -> Filter.isBounded_le_of_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2364 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2366 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2364 x._@.Mathlib.Order.LiminfLimsup._hyg.2366) f
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_le_of_top Filter.isBounded_le_of_topₓ'. -/
theorem isBounded_le_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsBounded (· ≤ ·) :=
⟨⊤, eventually_of_forall fun _ => le_top⟩
#align filter.is_bounded_le_of_top Filter.isBounded_le_of_top
-/- warning: filter.is_bounded_ge_of_bot -> Filter.isBounded_ge_of_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2405 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2407 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2405 x._@.Mathlib.Order.LiminfLimsup._hyg.2407) f
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_botₓ'. -/
theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBounded (· ≥ ·) :=
⟨⊥, eventually_of_forall fun _ => bot_le⟩
#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_bot
-/- warning: order_iso.is_bounded_under_le_comp -> OrderIso.isBoundedUnder_le_comp is a dubious translation:
-lean 3 declaration is
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@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
{u : γ → α} : (IsBoundedUnder (· ≤ ·) l fun x => e (u x)) ↔ IsBoundedUnder (· ≤ ·) l u :=
e.Surjective.exists.trans <| exists_congr fun a => by simp only [eventually_map, e.le_iff_le]
#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_comp
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@[simp]
theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
{u : γ → α} : (IsBoundedUnder (· ≥ ·) l fun x => e (u x)) ↔ IsBoundedUnder (· ≥ ·) l u :=
e.dual.isBoundedUnder_le_comp
#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_comp
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-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_inv Filter.isBoundedUnder_le_invₓ'. -/
@[simp, to_additive]
theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
(IsBoundedUnder (· ≤ ·) l fun x => (u x)⁻¹) ↔ IsBoundedUnder (· ≥ ·) l u :=
@@ -458,12 +284,6 @@ theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β →
#align filter.is_bounded_under_le_inv Filter.isBoundedUnder_le_inv
#align filter.is_bounded_under_le_neg Filter.isBoundedUnder_le_neg
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-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inv Filter.isBoundedUnder_ge_invₓ'. -/
@[simp, to_additive]
theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
(IsBoundedUnder (· ≥ ·) l fun x => (u x)⁻¹) ↔ IsBoundedUnder (· ≤ ·) l u :=
@@ -471,12 +291,6 @@ theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β →
#align filter.is_bounded_under_ge_inv Filter.isBoundedUnder_ge_inv
#align filter.is_bounded_under_ge_neg Filter.isBoundedUnder_ge_neg
-/- warning: filter.is_bounded_under.sup -> Filter.IsBoundedUnder.sup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.sup Filter.IsBoundedUnder.supₓ'. -/
theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≤ ·) u →
f.IsBoundedUnder (· ≤ ·) v → f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a
@@ -484,12 +298,6 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
⟨bu ⊔ bv, show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv by filter_upwards [hu, hv]with _ using sup_le_sup⟩
#align filter.is_bounded_under.sup Filter.IsBoundedUnder.sup
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- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2987 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2985 x._@.Mathlib.Order.LiminfLimsup._hyg.2987) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3016 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3014 x._@.Mathlib.Order.LiminfLimsup._hyg.3016) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3033 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3031 x._@.Mathlib.Order.LiminfLimsup._hyg.3033) f v))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_supₓ'. -/
@[simp]
theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a) ↔
@@ -500,24 +308,12 @@ theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β →
fun h => h.1.sup h.2⟩
#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_sup
-/- warning: filter.is_bounded_under.inf -> Filter.IsBoundedUnder.inf is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3101 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3099 x._@.Mathlib.Order.LiminfLimsup._hyg.3101) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3119 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3117 x._@.Mathlib.Order.LiminfLimsup._hyg.3119) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3136 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3134 x._@.Mathlib.Order.LiminfLimsup._hyg.3136) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a)))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.inf Filter.IsBoundedUnder.infₓ'. -/
theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≥ ·) u →
f.IsBoundedUnder (· ≥ ·) v → f.IsBoundedUnder (· ≥ ·) fun a => u a ⊓ v a :=
@IsBoundedUnder.sup αᵒᵈ β _ _ _ _
#align filter.is_bounded_under.inf Filter.IsBoundedUnder.inf
-/- warning: filter.is_bounded_under_ge_inf -> Filter.isBoundedUnder_ge_inf is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3190 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3188 x._@.Mathlib.Order.LiminfLimsup._hyg.3190) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3219 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3217 x._@.Mathlib.Order.LiminfLimsup._hyg.3219) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3236 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3234 x._@.Mathlib.Order.LiminfLimsup._hyg.3236) f v))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_infₓ'. -/
@[simp]
theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
(f.IsBoundedUnder (· ≥ ·) fun a => u a ⊓ v a) ↔
@@ -525,12 +321,6 @@ theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β →
@isBoundedUnder_le_sup αᵒᵈ _ _ _ _ _
#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_inf
-/- warning: filter.is_bounded_under_le_abs -> Filter.isBoundedUnder_le_abs is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f (fun (a : β) => Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (u a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3277 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3275 x._@.Mathlib.Order.LiminfLimsup._hyg.3277) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3304 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3302 x._@.Mathlib.Order.LiminfLimsup._hyg.3304) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3321 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3319 x._@.Mathlib.Order.LiminfLimsup._hyg.3321) f u))
-Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_abs Filter.isBoundedUnder_le_absₓ'. -/
theorem isBoundedUnder_le_abs [LinearOrderedAddCommGroup α] {f : Filter β} {u : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => |u a|) ↔
f.IsBoundedUnder (· ≤ ·) u ∧ f.IsBoundedUnder (· ≥ ·) u :=
@@ -603,42 +393,18 @@ section
variable {f : Filter β} {u : β → α} {p : β → Prop}
-/- warning: filter.limsup_eq -> Filter.limsup_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β _inst_1 u f) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) a) f)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.limsup.{u2, u1} α β _inst_1 u f) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u n) a) f)))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq Filter.limsup_eqₓ'. -/
theorem limsup_eq : limsup u f = sInf { a | ∀ᶠ n in f, u n ≤ a } :=
rfl
#align filter.limsup_eq Filter.limsup_eq
-/- warning: filter.liminf_eq -> Filter.liminf_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β _inst_1 u f) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.liminf.{u2, u1} α β _inst_1 u f) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u n)) f)))
-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq Filter.liminf_eqₓ'. -/
theorem liminf_eq : liminf u f = sSup { a | ∀ᶠ n in f, a ≤ u n } :=
rfl
#align filter.liminf_eq Filter.liminf_eq
-/- warning: filter.blimsup_eq -> Filter.blimsup_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β _inst_1 u f p) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u x) a)) f)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β _inst_1 u f p) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u x) a)) f)))
-Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq Filter.blimsup_eqₓ'. -/
theorem blimsup_eq : blimsup u f p = sInf { a | ∀ᶠ x in f, p x → u x ≤ a } :=
rfl
#align filter.blimsup_eq Filter.blimsup_eq
-/- warning: filter.bliminf_eq -> Filter.bliminf_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β _inst_1 u f p) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u x))) f)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β _inst_1 u f p) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u x))) f)))
-Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq Filter.bliminf_eqₓ'. -/
theorem bliminf_eq : bliminf u f p = sSup { a | ∀ᶠ x in f, p x → a ≤ u x } :=
rfl
#align filter.bliminf_eq Filter.bliminf_eq
@@ -681,9 +447,6 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
#align filter.bliminf_eq_liminf_subtype Filter.bliminf_eq_liminf_subtype
-/
-/- warning: filter.Limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by
@@ -693,9 +456,6 @@ theorem limsSup_le_of_le {f : Filter α} {a}
csInf_le hf h
#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
-/- warning: filter.le_Liminf_of_le -> Filter.le_limsInf_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.le_Liminf_of_le Filter.le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsInf_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by
@@ -706,8 +466,6 @@ theorem le_limsInf_of_le {f : Filter α} {a}
#align filter.le_Liminf_of_le Filter.le_limsInf_of_le
/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
-warning: filter.limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
-<too large>
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
@@ -718,9 +476,6 @@ theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
csInf_le hf h
#align filter.limsup_le_of_le Filter.limsSup_le_of_le
-/- warning: filter.le_liminf_of_le -> Filter.le_liminf_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.le_liminf_of_le Filter.le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≥ ·) u := by
@@ -730,9 +485,6 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
le_csSup hf h
#align filter.le_liminf_of_le Filter.le_liminf_of_le
-/- warning: filter.le_Limsup_of_le -> Filter.le_limsSup_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.le_Limsup_of_le Filter.le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsSup_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by
@@ -742,9 +494,6 @@ theorem le_limsSup_of_le {f : Filter α} {a}
le_csInf hf h
#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
-/- warning: filter.Liminf_le_of_le -> Filter.limsInf_le_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_of_le Filter.limsInf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsInf_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by
@@ -754,9 +503,6 @@ theorem limsInf_le_of_le {f : Filter α} {a}
csSup_le hf h
#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
-/- warning: filter.le_limsup_of_le -> Filter.le_limsup_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_le Filter.le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≤ ·) u := by
@@ -766,9 +512,6 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
le_csInf hf h
#align filter.le_limsup_of_le Filter.le_limsup_of_le
-/- warning: filter.liminf_le_of_le -> Filter.liminf_le_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_le Filter.liminf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
@@ -778,9 +521,6 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
csSup_le hf h
#align filter.liminf_le_of_le Filter.liminf_le_of_le
-/- warning: filter.Liminf_le_Limsup -> Filter.limsInf_le_limsSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
@@ -798,9 +538,6 @@ theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
le_trans hb₀ hb₁
#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
-/- warning: filter.liminf_le_limsup -> Filter.liminf_le_limsup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_limsup Filter.liminf_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
@@ -814,9 +551,6 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
limsInf_le_limsSup h h'
#align filter.liminf_le_limsup Filter.liminf_le_limsup
-/- warning: filter.Limsup_le_Limsup -> Filter.limsSup_le_limsSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_limsSup {f g : Filter α}
@@ -830,9 +564,6 @@ theorem limsSup_le_limsSup {f g : Filter α}
csInf_le_csInf hf hg h
#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
-/- warning: filter.Liminf_le_Liminf -> Filter.limsInf_le_limsInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsInf_le_limsInf {f g : Filter α}
@@ -846,9 +577,6 @@ theorem limsInf_le_limsInf {f g : Filter α}
csSup_le_csSup hg hf h
#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
-/- warning: filter.limsup_le_limsup -> Filter.limsup_le_limsup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup Filter.limsup_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
@@ -863,9 +591,6 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
limsSup_le_limsSup hu hv fun b => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
-/- warning: filter.liminf_le_liminf -> Filter.liminf_le_liminf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf Filter.liminf_le_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
@@ -880,9 +605,6 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
@limsup_le_limsup βᵒᵈ α _ _ _ _ h hv hu
#align filter.liminf_le_liminf Filter.liminf_le_liminf
-/- warning: filter.Limsup_le_Limsup_of_le -> Filter.limsSup_le_limsSup_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
@@ -896,9 +618,6 @@ theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
limsSup_le_limsSup hf hg fun a ha => h ha
#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_le
-/- warning: filter.Liminf_le_Liminf_of_le -> Filter.limsInf_le_limsInf_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
@@ -912,9 +631,6 @@ theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
limsInf_le_limsInf hf hg fun a ha => h ha
#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_le
-/- warning: filter.limsup_le_limsup_of_le -> Filter.limsup_le_limsup_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : f ≤ g)
@@ -929,9 +645,6 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
limsSup_le_limsSup_of_le (map_mono h) hf hg
#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_le
-/- warning: filter.liminf_le_liminf_of_le -> Filter.liminf_le_liminf_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : g ≤ f)
@@ -946,22 +659,10 @@ theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g :
limsInf_le_limsInf_of_le (map_mono h) hf hg
#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_le
-/- warning: filter.Limsup_principal -> Filter.limsSup_principal is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_principal Filter.limsSup_principalₓ'. -/
theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsSup (𝓟 s) = sSup s :=
by simp [Limsup] <;> exact csInf_upper_bounds_eq_csSup h hs
#align filter.Limsup_principal Filter.limsSup_principal
-/- warning: filter.Liminf_principal -> Filter.limsInf_principal is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsInf.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsInf.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_principal Filter.limsInf_principalₓ'. -/
theorem limsInf_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : limsInf (𝓟 s) = sInf s :=
@limsSup_principal αᵒᵈ _ s h hs
#align filter.Liminf_principal Filter.limsInf_principal
@@ -1021,78 +722,36 @@ section CompleteLattice
variable [CompleteLattice α]
-/- warning: filter.Limsup_bot -> Filter.limsSup_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_bot Filter.limsSup_botₓ'. -/
@[simp]
theorem limsSup_bot : limsSup (⊥ : Filter α) = ⊥ :=
bot_unique <| sInf_le <| by simp
#align filter.Limsup_bot Filter.limsSup_bot
-/- warning: filter.Liminf_bot -> Filter.limsInf_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_bot Filter.limsInf_botₓ'. -/
@[simp]
theorem limsInf_bot : limsInf (⊥ : Filter α) = ⊤ :=
top_unique <| le_sSup <| by simp
#align filter.Liminf_bot Filter.limsInf_bot
-/- warning: filter.Limsup_top -> Filter.limsSup_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_top Filter.limsSup_topₓ'. -/
@[simp]
theorem limsSup_top : limsSup (⊤ : Filter α) = ⊤ :=
top_unique <| le_sInf <| by simp [eq_univ_iff_forall] <;> exact fun b hb => top_unique <| hb _
#align filter.Limsup_top Filter.limsSup_top
-/- warning: filter.Liminf_top -> Filter.limsInf_top is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_top Filter.limsInf_topₓ'. -/
@[simp]
theorem limsInf_top : limsInf (⊤ : Filter α) = ⊥ :=
bot_unique <| sSup_le <| by simp [eq_univ_iff_forall] <;> exact fun b hb => bot_unique <| hb _
#align filter.Liminf_top Filter.limsInf_top
-/- warning: filter.blimsup_false -> Filter.blimsup_false is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => False)) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => False)) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.blimsup_false Filter.blimsup_falseₓ'. -/
@[simp]
theorem blimsup_false {f : Filter β} {u : β → α} : (blimsup u f fun x => False) = ⊥ := by
simp [blimsup_eq]
#align filter.blimsup_false Filter.blimsup_false
-/- warning: filter.bliminf_false -> Filter.bliminf_false is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => False)) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => False)) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.bliminf_false Filter.bliminf_falseₓ'. -/
@[simp]
theorem bliminf_false {f : Filter β} {u : β → α} : (bliminf u f fun x => False) = ⊤ := by
simp [bliminf_eq]
#align filter.bliminf_false Filter.bliminf_false
-/- warning: filter.limsup_const_bot -> Filter.limsup_const_bot is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (x : β) => Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)) f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_const_bot Filter.limsup_const_botₓ'. -/
/-- Same as limsup_const applied to `⊥` but without the `ne_bot f` assumption -/
theorem limsup_const_bot {f : Filter β} : limsup (fun x : β => (⊥ : α)) f = (⊥ : α) :=
by
@@ -1100,23 +759,11 @@ theorem limsup_const_bot {f : Filter β} : limsup (fun x : β => (⊥ : α)) f =
exact sInf_le (eventually_of_forall fun x => le_rfl)
#align filter.limsup_const_bot Filter.limsup_const_bot
-/- warning: filter.liminf_const_top -> Filter.liminf_const_top is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_const_top Filter.liminf_const_topₓ'. -/
/-- Same as limsup_const applied to `⊤` but without the `ne_bot f` assumption -/
theorem liminf_const_top {f : Filter β} : liminf (fun x : β => (⊤ : α)) f = (⊤ : α) :=
@limsup_const_bot αᵒᵈ β _ _
#align filter.liminf_const_top Filter.liminf_const_top
-/- warning: filter.has_basis.Limsup_eq_infi_Sup -> Filter.HasBasis.limsSup_eq_iInf_sSup is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSupₓ'. -/
theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
limsSup f = ⨅ (i) (hi : p i), sSup (s i) :=
le_antisymm (le_iInf₂ fun i hi => sInf_le <| h.eventually_iff.2 ⟨i, hi, fun x => le_sSup⟩)
@@ -1125,43 +772,19 @@ theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α}
iInf₂_le_of_le _ hi <| sSup_le ha)
#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSup
-/- warning: filter.has_basis.Liminf_eq_supr_Inf -> Filter.HasBasis.limsInf_eq_iSup_sInf is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInfₓ'. -/
theorem HasBasis.limsInf_eq_iSup_sInf {p : ι → Prop} {s : ι → Set α} {f : Filter α}
(h : f.HasBasis p s) : limsInf f = ⨆ (i) (hi : p i), sInf (s i) :=
@HasBasis.limsSup_eq_iInf_sSup αᵒᵈ _ _ _ _ _ h
#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInf
-/- warning: filter.Limsup_eq_infi_Sup -> Filter.limsSup_eq_iInf_sSup is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSupₓ'. -/
theorem limsSup_eq_iInf_sSup {f : Filter α} : limsSup f = ⨅ s ∈ f, sSup s :=
f.basis_sets.limsSup_eq_iInf_sSup
#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSup
-/- warning: filter.Liminf_eq_supr_Inf -> Filter.limsInf_eq_iSup_sInf is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInfₓ'. -/
theorem limsInf_eq_iSup_sInf {f : Filter α} : limsInf f = ⨆ s ∈ f, sInf s :=
@limsSup_eq_iInf_sSup αᵒᵈ _ _
#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInf
-/- warning: filter.limsup_le_supr -> Filter.limsup_le_iSup is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_le_supr Filter.limsup_le_iSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
limsSup_le_of_le
@@ -1171,12 +794,6 @@ theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u
(eventually_of_forall (le_iSup u))
#align filter.limsup_le_supr Filter.limsup_le_iSup
-/- warning: filter.infi_le_liminf -> Filter.iInf_le_liminf is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.infi_le_liminf Filter.iInf_le_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
le_liminf_of_le
@@ -1186,55 +803,25 @@ theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf
(eventually_of_forall (iInf_le u))
#align filter.infi_le_liminf Filter.iInf_le_liminf
-/- warning: filter.limsup_eq_infi_supr -> Filter.limsup_eq_iInf_iSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSupₓ'. -/
/-- In a complete lattice, the limsup of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
theorem limsup_eq_iInf_iSup {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
(f.basis_sets.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSup
-/- warning: filter.limsup_eq_infi_supr_of_nat -> Filter.limsup_eq_iInf_iSup_of_nat is a dubious translation:
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theorem limsup_eq_iInf_iSup_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
(atTop_basis.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, iInf_const] <;> rfl
#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_iInf_iSup_of_nat
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'ₓ'. -/
theorem limsup_eq_iInf_iSup_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
simp only [limsup_eq_infi_supr_of_nat, iSup_ge_eq_iSup_nat_add]
#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'
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theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : limsup u f = ⨅ (i) (hi : p i), ⨆ a ∈ s i, u a :=
(h.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSup
-/- warning: filter.blimsup_congr' -> Filter.blimsup_congr' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_congr' Filter.blimsup_congr'ₓ'. -/
theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊥ → (p x ↔ q x)) : blimsup u f p = blimsup u f q :=
by
@@ -1246,23 +833,11 @@ theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
rw [hb hu]
#align filter.blimsup_congr' Filter.blimsup_congr'
-/- warning: filter.bliminf_congr' -> Filter.bliminf_congr' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_congr' Filter.bliminf_congr'ₓ'. -/
theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊤ → (p x ↔ q x)) : bliminf u f p = bliminf u f q :=
@blimsup_congr' αᵒᵈ β _ _ _ _ _ h
#align filter.bliminf_congr' Filter.bliminf_congr'
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theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
blimsup u f p = ⨅ s ∈ f, ⨆ (b) (hb : p b ∧ b ∈ s), u b :=
by
@@ -1281,12 +856,6 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp] )
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_natₓ'. -/
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (hj : p j ∧ i ≤ j), u j := by
simp only [blimsup_eq_limsup_subtype, mem_preimage, mem_Ici, Function.comp_apply, ciInf_pos,
@@ -1294,77 +863,35 @@ theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
Subtype.coe_mk, iSup_and]
#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInfₓ'. -/
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
theorem liminf_eq_iSup_iInf {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
@limsup_eq_iInf_iSup αᵒᵈ β _ _ _
#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInf
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theorem liminf_eq_iSup_iInf_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
@limsup_eq_iInf_iSup_of_nat αᵒᵈ _ u
#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_iSup_iInf_of_nat
-/- warning: filter.liminf_eq_supr_infi_of_nat' -> Filter.liminf_eq_iSup_iInf_of_nat' is a dubious translation:
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theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
@limsup_eq_iInf_iSup_of_nat' αᵒᵈ _ _
#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'
-/- warning: filter.has_basis.liminf_eq_supr_infi -> Filter.HasBasis.liminf_eq_iSup_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInfₓ'. -/
theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : liminf u f = ⨆ (i) (hi : p i), ⨅ a ∈ s i, u a :=
@HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
-/- warning: filter.bliminf_eq_supr_binfi -> Filter.bliminf_eq_iSup_biInf is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInfₓ'. -/
theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
bliminf u f p = ⨆ s ∈ f, ⨅ (b) (hb : p b ∧ b ∈ s), u b :=
@blimsup_eq_iInf_biSup αᵒᵈ β _ f p u
#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInf
-/- warning: filter.bliminf_eq_supr_binfi_of_nat -> Filter.bliminf_eq_iSup_biInf_of_nat is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_natₓ'. -/
theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
bliminf u atTop p = ⨆ i, ⨅ (j) (hj : p j ∧ i ≤ j), u j :=
@blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
-/- warning: filter.limsup_eq_Inf_Sup -> Filter.limsup_eq_sInf_sSup is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSupₓ'. -/
theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) :=
by
@@ -1381,12 +908,6 @@ theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R]
exact h
#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSup
-/- warning: filter.liminf_eq_Sup_Inf -> Filter.liminf_eq_sSup_sInf is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInfₓ'. -/
theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
liminf a F = sSup ((fun I => sInf (a '' I)) '' F.sets) :=
@Filter.limsup_eq_sInf_sSup ι (OrderDual R) _ _ a
@@ -1406,12 +927,6 @@ theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k))
#align filter.limsup_nat_add Filter.limsup_nat_add
-/
-/- warning: filter.liminf_le_of_frequently_le' -> Filter.liminf_le_of_frequently_le' is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le' Filter.liminf_le_of_frequently_le'ₓ'. -/
theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x :=
by
@@ -1424,23 +939,11 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
exact hbx.exists.some_spec
#align filter.liminf_le_of_frequently_le' Filter.liminf_le_of_frequently_le'
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le' Filter.le_limsup_of_frequently_le'ₓ'. -/
theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, x ≤ u a) : x ≤ limsup u f :=
@liminf_le_of_frequently_le' _ βᵒᵈ _ _ _ _ h
#align filter.le_limsup_of_frequently_le' Filter.le_limsup_of_frequently_le'
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-Case conversion may be inaccurate. Consider using '#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterateₓ'. -/
/-- If `f : α → α` is a morphism of complete lattices, then the limsup of its iterates of any
`a : α` is a fixed point. -/
@[simp]
@@ -1456,12 +959,6 @@ theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (
exact fun i => le_iSup (fun i => (f^[i]) a) (i + 1)
#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterate
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/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
`a : α` is a fixed point. -/
theorem CompleteLatticeHom.apply_liminf_iterate (f : CompleteLatticeHom α α) (a : α) :
@@ -1471,135 +968,60 @@ theorem CompleteLatticeHom.apply_liminf_iterate (f : CompleteLatticeHom α α) (
variable {f g : Filter β} {p q : β → Prop} {u v : β → α}
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theorem blimsup_mono (h : ∀ x, p x → q x) : blimsup u f p ≤ blimsup u f q :=
sInf_le_sInf fun a ha => ha.mono <| by tauto
#align filter.blimsup_mono Filter.blimsup_mono
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theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u f p :=
sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
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theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
sInf_le_sInf fun a ha => (ha.And h).mono fun x hx hx' => (hx.2 hx').trans (hx.1 hx')
#align filter.mono_blimsup' Filter.mono_blimsup'
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-Case conversion may be inaccurate. Consider using '#align filter.mono_blimsup Filter.mono_blimsupₓ'. -/
theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
mono_blimsup' <| eventually_of_forall h
#align filter.mono_blimsup Filter.mono_blimsup
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theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
sSup_le_sSup fun a ha => (ha.And h).mono fun x hx hx' => (hx.1 hx').trans (hx.2 hx')
#align filter.mono_bliminf' Filter.mono_bliminf'
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-Case conversion may be inaccurate. Consider using '#align filter.mono_bliminf Filter.mono_bliminfₓ'. -/
theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
mono_bliminf' <| eventually_of_forall h
#align filter.mono_bliminf Filter.mono_bliminf
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filterₓ'. -/
theorem bliminf_antitone_filter (h : f ≤ g) : bliminf u g p ≤ bliminf u f p :=
sSup_le_sSup fun a ha => ha.filter_mono h
#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filter
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filterₓ'. -/
theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p :=
sInf_le_sInf fun a ha => ha.filter_mono h
#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filter
-/- warning: filter.blimsup_and_le_inf -> Filter.blimsup_and_le_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_and_le_inf Filter.blimsup_and_le_infₓ'. -/
@[simp]
theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p ⊓ blimsup u f q :=
le_inf (blimsup_mono <| by tauto) (blimsup_mono <| by tauto)
#align filter.blimsup_and_le_inf Filter.blimsup_and_le_inf
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_sup_le_and Filter.bliminf_sup_le_andₓ'. -/
@[simp]
theorem bliminf_sup_le_and : bliminf u f p ⊔ bliminf u f q ≤ bliminf u f fun x => p x ∧ q x :=
@blimsup_and_le_inf αᵒᵈ β _ f p q u
#align filter.bliminf_sup_le_and Filter.bliminf_sup_le_and
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_sup_le_or Filter.blimsup_sup_le_orₓ'. -/
/-- See also `filter.blimsup_or_eq_sup`. -/
@[simp]
theorem blimsup_sup_le_or : blimsup u f p ⊔ blimsup u f q ≤ blimsup u f fun x => p x ∨ q x :=
sup_le (blimsup_mono <| by tauto) (blimsup_mono <| by tauto)
#align filter.blimsup_sup_le_or Filter.blimsup_sup_le_or
-/- warning: filter.bliminf_or_le_inf -> Filter.bliminf_or_le_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_or_le_inf Filter.bliminf_or_le_infₓ'. -/
/-- See also `filter.bliminf_or_eq_inf`. -/
@[simp]
theorem bliminf_or_le_inf : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f p ⊓ bliminf u f q :=
@blimsup_sup_le_or αᵒᵈ β _ f p q u
#align filter.bliminf_or_le_inf Filter.bliminf_or_le_inf
-/- warning: filter.order_iso.apply_blimsup -> Filter.OrderIso.apply_blimsup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsupₓ'. -/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
e (blimsup u f p) = blimsup (e ∘ u) f p :=
by
@@ -1610,20 +1032,11 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
simp
#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsup
-/- warning: filter.order_iso.apply_bliminf -> Filter.OrderIso.apply_bliminf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminfₓ'. -/
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
e (bliminf u f p) = bliminf (e ∘ u) f p :=
@OrderIso.apply_blimsup αᵒᵈ β γᵒᵈ _ f p u _ e.dual
#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminf
-/- warning: filter.Sup_hom.apply_blimsup_le -> Filter.SupHom.apply_blimsup_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_leₓ'. -/
theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
g (blimsup u f p) ≤ blimsup (g ∘ u) f p :=
by
@@ -1632,12 +1045,6 @@ theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
simp only [_root_.map_supr]
#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_le
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-Case conversion may be inaccurate. Consider using '#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminfₓ'. -/
theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : sInfHom α γ) :
bliminf (g ∘ u) f p ≤ g (bliminf u f p) :=
@SupHom.apply_blimsup_le αᵒᵈ β γᵒᵈ _ f p u _ g.dual
@@ -1649,12 +1056,6 @@ section CompleteDistribLattice
variable [CompleteDistribLattice α] {f : Filter β} {p q : β → Prop} {u : β → α}
-/- warning: filter.blimsup_or_eq_sup -> Filter.blimsup_or_eq_sup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_supₓ'. -/
@[simp]
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q :=
by
@@ -1664,23 +1065,11 @@ theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p
exact Or.elim hb (fun hb => le_sup_of_le_left <| h.1 hb) fun hb => le_sup_of_le_right <| h.2 hb
#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_sup
-/- warning: filter.bliminf_or_eq_inf -> Filter.bliminf_or_eq_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_infₓ'. -/
@[simp]
theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p ⊓ bliminf u f q :=
@blimsup_or_eq_sup αᵒᵈ β _ f p q u
#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_inf
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-Case conversion may be inaccurate. Consider using '#align filter.sup_limsup Filter.sup_limsupₓ'. -/
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f :=
by
simp only [limsup_eq_infi_supr, iSup_sup_eq, sup_iInf₂_eq]
@@ -1688,22 +1077,10 @@ theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a
exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
-/- warning: filter.inf_liminf -> Filter.inf_liminf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.inf_liminf Filter.inf_liminfₓ'. -/
theorem inf_liminf [NeBot f] (a : α) : a ⊓ liminf u f = liminf (fun x => a ⊓ u x) f :=
@sup_limsup αᵒᵈ β _ f _ _ _
#align filter.inf_liminf Filter.inf_liminf
-/- warning: filter.sup_liminf -> Filter.sup_liminf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.sup_liminf Filter.sup_liminfₓ'. -/
theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :=
by
simp only [liminf_eq_supr_infi]
@@ -1711,12 +1088,6 @@ theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :
simp_rw [iInf₂_sup_eq, @sup_comm _ _ a]
#align filter.sup_liminf Filter.sup_liminf
-/- warning: filter.inf_limsup -> Filter.inf_limsup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.inf_limsup Filter.inf_limsupₓ'. -/
theorem inf_limsup (a : α) : a ⊓ limsup u f = limsup (fun x => a ⊓ u x) f :=
@sup_liminf αᵒᵈ β _ f _ _
#align filter.inf_limsup Filter.inf_limsup
@@ -1727,32 +1098,14 @@ section CompleteBooleanAlgebra
variable [CompleteBooleanAlgebra α] (f : Filter β) (u : β → α)
-/- warning: filter.limsup_compl -> Filter.limsup_compl is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteBooleanAlgebra.{u1} α] (f : Filter.{u2} β) (u : β -> α), Eq.{succ u1} α (HasCompl.compl.{u1} α (BooleanAlgebra.toHasCompl.{u1} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u1} α _inst_1)) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} α _inst_1)))) u f)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} α _inst_1)))) (Function.comp.{succ u2, succ u1, succ u1} β α α (HasCompl.compl.{u1} α (BooleanAlgebra.toHasCompl.{u1} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u1} α _inst_1))) u) f)
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_compl Filter.limsup_complₓ'. -/
theorem limsup_compl : limsup u fᶜ = liminf (compl ∘ u) f := by
simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.limsup_compl Filter.limsup_compl
-/- warning: filter.liminf_compl -> Filter.liminf_compl is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_compl Filter.liminf_complₓ'. -/
theorem liminf_compl : liminf u fᶜ = limsup (compl ∘ u) f := by
simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.liminf_compl Filter.liminf_compl
-/- warning: filter.limsup_sdiff -> Filter.limsup_sdiff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.limsup_sdiff Filter.limsup_sdiffₓ'. -/
theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f :=
by
simp only [limsup_eq_infi_supr, sdiff_eq]
@@ -1760,34 +1113,16 @@ theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f :=
simp_rw [inf_comm, inf_iSup₂_eq, inf_comm]
#align filter.limsup_sdiff Filter.limsup_sdiff
-/- warning: filter.liminf_sdiff -> Filter.liminf_sdiff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.liminf_sdiff Filter.liminf_sdiffₓ'. -/
theorem liminf_sdiff [NeBot f] (a : α) : liminf u f \ a = liminf (fun b => u b \ a) f := by
simp only [sdiff_eq, @inf_comm _ _ _ (aᶜ), inf_liminf]
#align filter.liminf_sdiff Filter.liminf_sdiff
-/- warning: filter.sdiff_limsup -> Filter.sdiff_limsup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.sdiff_limsup Filter.sdiff_limsupₓ'. -/
theorem sdiff_limsup [NeBot f] (a : α) : a \ limsup u f = liminf (fun b => a \ u b) f :=
by
rw [← compl_inj_iff]
simp only [sdiff_eq, liminf_compl, (· ∘ ·), compl_inf, compl_compl, sup_limsup]
#align filter.sdiff_limsup Filter.sdiff_limsup
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theorem sdiff_liminf (a : α) : a \ liminf u f = limsup (fun b => a \ u b) f :=
by
rw [← compl_inj_iff]
@@ -1800,12 +1135,6 @@ section SetLattice
variable {p : ι → Prop} {s : ι → Set α}
-/- warning: filter.cofinite.blimsup_set_eq -> Filter.cofinite.blimsup_set_eq is a dubious translation:
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theorem cofinite.blimsup_set_eq : blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } :=
by
simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, Inf_eq_sInter, exists_prop]
@@ -1816,12 +1145,6 @@ theorem cofinite.blimsup_set_eq : blimsup s cofinite p = { x | { n | p n ∧ x
· exact hx.mono fun i hi => ⟨hi.1, fun hit => h (hit hi.2)⟩
#align filter.cofinite.blimsup_set_eq Filter.cofinite.blimsup_set_eq
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theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x ∉ s n }.Finite } :=
by
rw [← compl_inj_iff]
@@ -1829,36 +1152,18 @@ theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x
cofinite.blimsup_set_eq]
#align filter.cofinite.bliminf_set_eq Filter.cofinite.bliminf_set_eq
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/-- In other words, `limsup cofinite s` is the set of elements lying inside the family `s`
infinitely often. -/
theorem cofinite.limsup_set_eq : limsup s cofinite = { x | { n | x ∈ s n }.Infinite } := by
simp only [← cofinite.blimsup_true s, cofinite.blimsup_set_eq, true_and_iff]
#align filter.cofinite.limsup_set_eq Filter.cofinite.limsup_set_eq
-/- warning: filter.cofinite.liminf_set_eq -> Filter.cofinite.liminf_set_eq is a dubious translation:
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/-- In other words, `liminf cofinite s` is the set of elements lying outside the family `s`
finitely often. -/
theorem cofinite.liminf_set_eq : liminf s cofinite = { x | { n | x ∉ s n }.Finite } := by
simp only [← cofinite.bliminf_true s, cofinite.bliminf_set_eq, true_and_iff]
#align filter.cofinite.liminf_set_eq Filter.cofinite.liminf_set_eq
-/- warning: filter.exists_forall_mem_of_has_basis_mem_blimsup -> Filter.exists_forall_mem_of_hasBasis_mem_blimsup is a dubious translation:
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theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Set β} {q : ι → Prop}
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
∃ f : { i | q i } → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
@@ -1871,12 +1176,6 @@ theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Se
· exact hg (b i) (hl.mem_of_mem i.2)
#align filter.exists_forall_mem_of_has_basis_mem_blimsup Filter.exists_forall_mem_of_hasBasis_mem_blimsup
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-Case conversion may be inaccurate. Consider using '#align filter.exists_forall_mem_of_has_basis_mem_blimsup' Filter.exists_forall_mem_of_hasBasis_mem_blimsup'ₓ'. -/
theorem exists_forall_mem_of_hasBasis_mem_blimsup' {l : Filter β} {b : ι → Set β}
(hl : l.HasBasis (fun _ => True) b) {u : β → Set α} {p : β → Prop} {x : α}
(hx : x ∈ blimsup u l p) : ∃ f : ι → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i :=
@@ -1889,9 +1188,6 @@ end SetLattice
section ConditionallyCompleteLinearOrder
-/- warning: filter.frequently_lt_of_lt_Limsup -> Filter.frequently_lt_of_lt_limsSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by
@@ -1904,9 +1200,6 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
exact Limsup_le_of_le hf h
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
-/- warning: filter.frequently_lt_of_Liminf_lt -> Filter.frequently_lt_of_limsInf_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by
@@ -1916,9 +1209,6 @@ theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinear
@frequently_lt_of_lt_limsSup (OrderDual α) f _ a hf h
#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
-/- warning: filter.eventually_lt_of_lt_liminf -> Filter.eventually_lt_of_lt_liminf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : b < liminf u f)
@@ -1932,9 +1222,6 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
-/- warning: filter.eventually_lt_of_limsup_lt -> Filter.eventually_lt_of_limsup_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : limsup u f < b)
@@ -1945,9 +1232,6 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
@eventually_lt_of_lt_liminf _ βᵒᵈ _ _ _ _ h hu
#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_lt
-/- warning: filter.le_limsup_of_frequently_le -> Filter.le_limsup_of_frequently_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, b ≤ u x)
@@ -1961,9 +1245,6 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
exact fun h => eventually_lt_of_limsup_lt h hu
#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_le
-/- warning: filter.liminf_le_of_frequently_le -> Filter.liminf_le_of_frequently_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, u x ≤ b)
@@ -1974,9 +1255,6 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
@le_limsup_of_frequently_le _ βᵒᵈ _ f u b hu_le hu
#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_le
-/- warning: filter.frequently_lt_of_lt_limsup -> Filter.frequently_lt_of_lt_limsup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
@@ -1990,9 +1268,6 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
simpa using h
#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsup
-/- warning: filter.frequently_lt_of_liminf_lt -> Filter.frequently_lt_of_liminf_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
@@ -2011,12 +1286,6 @@ section Order
open Filter
-/- warning: monotone.is_bounded_under_le_comp -> Monotone.isBoundedUnder_le_comp is a dubious translation:
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- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
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-Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_compₓ'. -/
theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
@@ -2027,45 +1296,24 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp
-/- warning: monotone.is_bounded_under_ge_comp -> Monotone.isBoundedUnder_ge_comp is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_compₓ'. -/
theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual.isBoundedUnder_le_comp hg'
#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp
-/- warning: antitone.is_bounded_under_le_comp -> Antitone.isBoundedUnder_le_comp is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_compₓ'. -/
theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
hg.dual_right.isBoundedUnder_ge_comp hg'
#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp
-/- warning: antitone.is_bounded_under_ge_comp -> Antitone.isBoundedUnder_ge_comp is a dubious translation:
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- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
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-Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_compₓ'. -/
theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
hg.dual_right.isBoundedUnder_le_comp hg'
#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp
-/- warning: galois_connection.l_limsup_le -> GaloisConnection.l_limsup_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
@@ -2085,9 +1333,6 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
exact Limsup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
-/- warning: order_iso.limsup_apply -> OrderIso.limsup_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2118,9 +1363,6 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
exact hu
#align order_iso.limsup_apply OrderIso.limsup_apply
-/- warning: order_iso.liminf_apply -> OrderIso.liminf_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -254,10 +254,8 @@ but is expected to have type
forall {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1516 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1518 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1516 x._@.Mathlib.Order.LiminfLimsup._hyg.1518) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_rangeₓ'. -/
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
- (hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) :=
- by
- rw [← Nat.cofinite_eq_atTop] at hf
- exact hf.bdd_above_range_of_cofinite
+ (hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
+ rw [← Nat.cofinite_eq_atTop] at hf; exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
/- warning: filter.is_bounded_under.bdd_below_range -> Filter.IsBoundedUnder.bddBelow_range is a dubious translation:
@@ -984,10 +982,8 @@ theorem blimsup_congr {f : Filter β} {u v : β → α} {p : β → Prop} (h :
rw [blimsup_eq]
congr with b
refine' eventually_congr (h.mono fun x hx => ⟨fun h₁ h₂ => _, fun h₁ h₂ => _⟩)
- · rw [← hx h₂]
- exact h₁ h₂
- · rw [hx h₂]
- exact h₁ h₂
+ · rw [← hx h₂]; exact h₁ h₂
+ · rw [hx h₂]; exact h₁ h₂
#align filter.blimsup_congr Filter.blimsup_congr
-/
@@ -1399,9 +1395,7 @@ theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R]
#print Filter.liminf_nat_add /-
@[simp]
theorem liminf_nat_add (f : ℕ → α) (k : ℕ) : liminf (fun i => f (i + k)) atTop = liminf f atTop :=
- by
- simp_rw [liminf_eq_supr_infi_of_nat]
- exact iSup_iInf_ge_nat_add f k
+ by simp_rw [liminf_eq_supr_infi_of_nat]; exact iSup_iInf_ge_nat_add f k
#align filter.liminf_nat_add Filter.liminf_nat_add
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -684,10 +684,7 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
-/
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_of_le {f : Filter α} {a}
@@ -699,10 +696,7 @@ theorem limsSup_le_of_le {f : Filter α} {a}
#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
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Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsInf.{u1} α _inst_1 f))
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- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4502 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4504 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4502 x._@.Mathlib.Order.LiminfLimsup._hyg.4504) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4474) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsInf.{u1} α _inst_1 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.le_Liminf_of_le Filter.le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsInf_of_le {f : Filter α} {a}
@@ -715,10 +709,7 @@ theorem le_limsInf_of_le {f : Filter α} {a}
/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
warning: filter.limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
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Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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(Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u_2} β (fun (n : β) => LE.le.{u_1} α (Preorder.toHasLe.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (u n) a) f) -> (LE.le.{u_1} α (Preorder.toHasLe.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (Filter.limsup.{u_1, u_2} α β _inst_1 u f) a)
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
@@ -730,10 +721,7 @@ theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
#align filter.limsup_le_of_le Filter.limsSup_le_of_le
/- warning: filter.le_liminf_of_le -> Filter.le_liminf_of_le is a dubious translation:
-lean 3 declaration is
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(Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α 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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.le_liminf_of_le Filter.le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
@@ -745,10 +733,7 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
#align filter.le_liminf_of_le Filter.le_liminf_of_le
/- warning: filter.le_Limsup_of_le -> Filter.le_limsSup_of_le is a dubious translation:
-lean 3 declaration is
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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n b) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsSup.{u1} α _inst_1 f))
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- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4772 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4774 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4772 x._@.Mathlib.Order.LiminfLimsup._hyg.4774) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4744) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n b) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsSup.{u1} α _inst_1 f))
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.le_Limsup_of_le Filter.le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsSup_of_le {f : Filter α} {a}
@@ -760,10 +745,7 @@ theorem le_limsSup_of_le {f : Filter α} {a}
#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
/- warning: filter.Liminf_le_of_le -> Filter.limsInf_le_of_le is a dubious translation:
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a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) a)
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_of_le Filter.limsInf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsInf_le_of_le {f : Filter α} {a}
@@ -775,10 +757,7 @@ theorem limsInf_le_of_le {f : Filter α} {a}
#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
/- warning: filter.le_limsup_of_le -> Filter.le_limsup_of_le is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_le Filter.le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
@@ -790,10 +769,7 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
#align filter.le_limsup_of_le Filter.le_limsup_of_le
/- warning: filter.liminf_le_of_le -> Filter.liminf_le_of_le is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_le Filter.liminf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
@@ -805,10 +781,7 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
#align filter.liminf_le_of_le Filter.liminf_le_of_le
/- warning: filter.Liminf_le_Limsup -> Filter.limsInf_le_limsSup is a dubious translation:
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(LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 f))
-but is expected to have type
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -828,10 +801,7 @@ theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
/- warning: filter.liminf_le_limsup -> Filter.liminf_le_limsup is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_limsup Filter.liminf_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -847,10 +817,7 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
#align filter.liminf_le_limsup Filter.liminf_le_limsup
/- warning: filter.Limsup_le_Limsup -> Filter.limsSup_le_limsSup is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -866,10 +833,7 @@ theorem limsSup_le_limsSup {f g : Filter α}
#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
/- warning: filter.Liminf_le_Liminf -> Filter.limsInf_le_limsInf is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -885,10 +849,7 @@ theorem limsInf_le_limsInf {f g : Filter α}
#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
/- warning: filter.limsup_le_limsup -> Filter.limsup_le_limsup is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup Filter.limsup_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -905,10 +866,7 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
#align filter.limsup_le_limsup Filter.limsup_le_limsup
/- warning: filter.liminf_le_liminf -> Filter.liminf_le_liminf is a dubious translation:
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-but is expected to have type
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf Filter.liminf_le_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -925,10 +883,7 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
#align filter.liminf_le_liminf Filter.liminf_le_liminf
/- warning: filter.Limsup_le_Limsup_of_le -> Filter.limsSup_le_limsSup_of_le is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -944,10 +899,7 @@ theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_le
/- warning: filter.Liminf_le_Liminf_of_le -> Filter.limsInf_le_limsInf_of_le is a dubious translation:
-lean 3 declaration is
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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd 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Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -963,10 +915,7 @@ theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_le
/- warning: filter.limsup_le_limsup_of_le -> Filter.limsup_le_limsup_of_le is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6315 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6315 x._@.Mathlib.Order.LiminfLimsup._hyg.6317) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6287) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6357 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6357 x._@.Mathlib.Order.LiminfLimsup._hyg.6359) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6329) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -983,10 +932,7 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_le
/- warning: filter.liminf_le_liminf_of_le -> Filter.liminf_le_liminf_of_le is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6441 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6441 x._@.Mathlib.Order.LiminfLimsup._hyg.6443) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6413) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6483 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6483 x._@.Mathlib.Order.LiminfLimsup._hyg.6485) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6455) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -1658,10 +1604,7 @@ theorem bliminf_or_le_inf : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f p
#align filter.bliminf_or_le_inf Filter.bliminf_or_le_inf
/- warning: filter.order_iso.apply_blimsup -> Filter.OrderIso.apply_blimsup is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsupₓ'. -/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
e (blimsup u f p) = blimsup (e ∘ u) f p :=
@@ -1674,10 +1617,7 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsup
/- warning: filter.order_iso.apply_bliminf -> Filter.OrderIso.apply_bliminf is a dubious translation:
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(x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e) u) f p)
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminfₓ'. -/
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
e (bliminf u f p) = bliminf (e ∘ u) f p :=
@@ -1956,10 +1896,7 @@ end SetLattice
section ConditionallyCompleteLinearOrder
/- warning: filter.frequently_lt_of_lt_Limsup -> Filter.frequently_lt_of_lt_limsSup is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a (Filter.limsSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f)) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a n) f)
-but is expected to have type
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13376 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.13378 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13376 x._@.Mathlib.Order.LiminfLimsup._hyg.13378) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13348) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a (Filter.limsSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f)) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a n) f)
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
@@ -1974,10 +1911,7 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
/- warning: filter.frequently_lt_of_Liminf_lt -> Filter.frequently_lt_of_limsInf_lt is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.limsInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f) a) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) n a) f)
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
@@ -1989,10 +1923,7 @@ theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinear
#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
/- warning: filter.eventually_lt_of_lt_liminf -> Filter.eventually_lt_of_lt_liminf is a dubious translation:
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Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -2008,10 +1939,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
/- warning: filter.eventually_lt_of_limsup_lt -> Filter.eventually_lt_of_limsup_lt is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -2024,10 +1952,7 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_lt
/- warning: filter.le_limsup_of_frequently_le -> Filter.le_limsup_of_frequently_le is a dubious translation:
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(Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -2043,10 +1968,7 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_le
/- warning: filter.liminf_le_of_frequently_le -> Filter.liminf_le_of_frequently_le is a dubious translation:
-lean 3 declaration is
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- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14005 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14007 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14005 x._@.Mathlib.Order.LiminfLimsup._hyg.14007) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13977) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
+<too large>
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -2059,10 +1981,7 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_le
/- warning: filter.frequently_lt_of_lt_limsup -> Filter.frequently_lt_of_lt_limsup is a dubious translation:
-lean 3 declaration is
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -2078,10 +1997,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsup
/- warning: filter.frequently_lt_of_liminf_lt -> Filter.frequently_lt_of_liminf_lt is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -2154,10 +2070,7 @@ theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp
/- warning: galois_connection.l_limsup_le -> GaloisConnection.l_limsup_le is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str 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-but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14739 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14741 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14739 x._@.Mathlib.Order.LiminfLimsup._hyg.14741) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14711) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14788 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14790 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14788 x._@.Mathlib.Order.LiminfLimsup._hyg.14790) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14760) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2179,10 +2092,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
/- warning: order_iso.limsup_apply -> OrderIso.limsup_apply is a dubious translation:
-lean 3 declaration is
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x._@.Mathlib.Order.LiminfLimsup._hyg.14930) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14900) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14970 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14972 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14970 x._@.Mathlib.Order.LiminfLimsup._hyg.14972) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14942) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15012 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15014 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15012 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x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x)) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2215,10 +2125,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
#align order_iso.limsup_apply OrderIso.limsup_apply
/- warning: order_iso.liminf_apply -> OrderIso.liminf_apply is a dubious translation:
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(Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15419) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x)) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -427,7 +427,7 @@ theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBo
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -439,7 +439,7 @@ theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -1677,7 +1677,7 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) u) f p)
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminfₓ'. -/
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
e (bliminf u f p) = bliminf (e ∘ u) f p :=
@@ -2182,7 +2182,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14984) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15062 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15064 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15062 x._@.Mathlib.Order.LiminfLimsup._hyg.15064) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15034) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14928 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14930 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14928 x._@.Mathlib.Order.LiminfLimsup._hyg.14930) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14900) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14970 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14972 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14970 x._@.Mathlib.Order.LiminfLimsup._hyg.14972) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14942) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15012 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15014 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15012 x._@.Mathlib.Order.LiminfLimsup._hyg.15014) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14984) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15062 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15064 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15062 x._@.Mathlib.Order.LiminfLimsup._hyg.15064) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15034) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2218,7 +2218,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} 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(ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))))) g (u x)) f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15313 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15315 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15313 x._@.Mathlib.Order.LiminfLimsup._hyg.15315) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15285) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15355 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15357 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15355 x._@.Mathlib.Order.LiminfLimsup._hyg.15357) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15327) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15397 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15399 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15397 x._@.Mathlib.Order.LiminfLimsup._hyg.15399) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15369) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15447 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15449 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15447 x._@.Mathlib.Order.LiminfLimsup._hyg.15449) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15419) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15313 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15315 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15313 x._@.Mathlib.Order.LiminfLimsup._hyg.15315) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15285) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15355 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15357 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15355 x._@.Mathlib.Order.LiminfLimsup._hyg.15357) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15327) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15397 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15399 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15397 x._@.Mathlib.Order.LiminfLimsup._hyg.15399) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15369) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15447 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15449 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15447 x._@.Mathlib.Order.LiminfLimsup._hyg.15449) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15419) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -131,7 +131,7 @@ theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r
/- warning: filter.is_bounded.mono -> Filter.IsBounded.mono is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r f)
+ forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r f)
but is expected to have type
forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r f)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded.mono Filter.IsBounded.monoₓ'. -/
@@ -141,7 +141,7 @@ theorem IsBounded.mono (h : f ≤ g) : IsBounded r g → IsBounded r f
/- warning: filter.is_bounded_under.mono -> Filter.IsBoundedUnder.mono is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u2} β} {g : Filter.{u2} β} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (Filter.IsBoundedUnder.{u1, u2} α β r g u) -> (Filter.IsBoundedUnder.{u1, u2} α β r f u)
+ forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u2} β} {g : Filter.{u2} β} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toHasLe.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (Filter.IsBoundedUnder.{u1, u2} α β r g u) -> (Filter.IsBoundedUnder.{u1, u2} α β r f u)
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {f : Filter.{u2} β} {g : Filter.{u2} β} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (Filter.IsBoundedUnder.{u1, u2} α β r g u) -> (Filter.IsBoundedUnder.{u1, u2} α β r f u)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono Filter.IsBoundedUnder.monoₓ'. -/
@@ -149,19 +149,27 @@ theorem IsBoundedUnder.mono {f g : Filter β} {u : β → α} (h : f ≤ g) :
g.IsBoundedUnder r u → f.IsBoundedUnder r u := fun hg => hg.mono (map_mono h)
#align filter.is_bounded_under.mono Filter.IsBoundedUnder.mono
-#print Filter.IsBoundedUnder.mono_le /-
+/- warning: filter.is_bounded_under.mono_le -> Filter.IsBoundedUnder.mono_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_1) l v u) -> (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l v)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.747 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.749 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.747 x._@.Mathlib.Order.LiminfLimsup._hyg.749) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_1) l v u) -> (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.771 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.773 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.771 x._@.Mathlib.Order.LiminfLimsup._hyg.773) l v)
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono_le Filter.IsBoundedUnder.mono_leₓ'. -/
theorem IsBoundedUnder.mono_le [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≤ ·) l u) (hv : v ≤ᶠ[l] u) : IsBoundedUnder (· ≤ ·) l v :=
hu.imp fun b hb => (eventually_map.1 hb).mp <| hv.mono fun x => le_trans
#align filter.is_bounded_under.mono_le Filter.IsBoundedUnder.mono_le
--/
-#print Filter.IsBoundedUnder.mono_ge /-
+/- warning: filter.is_bounded_under.mono_ge -> Filter.IsBoundedUnder.mono_ge is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_1) l u v) -> (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l v)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] {l : Filter.{u1} α} {u : α -> β} {v : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.841 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.843 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.841 x._@.Mathlib.Order.LiminfLimsup._hyg.843) l u) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_1) l u v) -> (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.865 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.867 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.865 x._@.Mathlib.Order.LiminfLimsup._hyg.867) l v)
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_geₓ'. -/
theorem IsBoundedUnder.mono_ge [Preorder β] {l : Filter α} {u v : α → β}
(hu : IsBoundedUnder (· ≥ ·) l u) (hv : u ≤ᶠ[l] v) : IsBoundedUnder (· ≥ ·) l v :=
@IsBoundedUnder.mono_le α βᵒᵈ _ _ _ _ hu hv
#align filter.is_bounded_under.mono_ge Filter.IsBoundedUnder.mono_ge
--/
/- warning: filter.is_bounded_under_const -> Filter.isBoundedUnder_const is a dubious translation:
lean 3 declaration is
@@ -184,7 +192,12 @@ theorem IsBounded.isBoundedUnder {q : β → β → Prop} {u : α → β}
| ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hf x b⟩
#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnder
-#print Filter.not_isBoundedUnder_of_tendsto_atTop /-
+/- warning: filter.not_is_bounded_under_of_tendsto_at_top -> Filter.not_isBoundedUnder_of_tendsto_atTop is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMaxOrder.{u2} β (Preorder.toHasLt.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atTop.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMaxOrder.{u2} β (Preorder.toLT.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atTop.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1086 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1088 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1086 x._@.Mathlib.Order.LiminfLimsup._hyg.1088) l f))
+Case conversion may be inaccurate. Consider using '#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTopₓ'. -/
theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f :=
by
@@ -196,16 +209,24 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
eq_empty_of_subset_empty fun x hx => (not_le_of_lt h) (le_trans hx.2 hx.1)
exact (nonempty_of_mem (hb.and hb')).ne_empty this
#align filter.not_is_bounded_under_of_tendsto_at_top Filter.not_isBoundedUnder_of_tendsto_atTop
--/
-#print Filter.not_isBoundedUnder_of_tendsto_atBot /-
+/- warning: filter.not_is_bounded_under_of_tendsto_at_bot -> Filter.not_isBoundedUnder_of_tendsto_atBot is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMinOrder.{u2} β (Preorder.toHasLt.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atBot.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_1)) l f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u2} β] [_inst_2 : NoMinOrder.{u2} β (Preorder.toLT.{u2} β _inst_1)] {f : α -> β} {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], (Filter.Tendsto.{u1, u2} α β f l (Filter.atBot.{u2} β _inst_1)) -> (Not (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1278 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1280 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1278 x._@.Mathlib.Order.LiminfLimsup._hyg.1280) l f))
+Case conversion may be inaccurate. Consider using '#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBotₓ'. -/
theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f : α → β} {l : Filter α}
[l.ne_bot] (hf : Tendsto f l atBot) : ¬IsBoundedUnder (· ≥ ·) l f :=
@not_isBoundedUnder_of_tendsto_atTop α βᵒᵈ _ _ _ _ _ hf
#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBot
--/
-#print Filter.IsBoundedUnder.bddAbove_range_of_cofinite /-
+/- warning: filter.is_bounded_under.bdd_above_range_of_cofinite -> Filter.IsBoundedUnder.bddAbove_range_of_cofinite is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)))) (Filter.cofinite.{u1} α) f) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1326 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1328 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1326 x._@.Mathlib.Order.LiminfLimsup._hyg.1328) (Filter.cofinite.{u1} α) f) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofiniteₓ'. -/
theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
(hf : IsBoundedUnder (· ≤ ·) cofinite f) : BddAbove (range f) :=
by
@@ -214,30 +235,41 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
rw [← image_univ, ← union_compl_self { x | f x ≤ b }, image_union, bddAbove_union]
exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).BddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
--/
-#print Filter.IsBoundedUnder.bddBelow_range_of_cofinite /-
+/- warning: filter.is_bounded_under.bdd_below_range_of_cofinite -> Filter.IsBoundedUnder.bddBelow_range_of_cofinite is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)))) (Filter.cofinite.{u1} α) f) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u2} β] {f : α -> β}, (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1460 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1462 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1460 x._@.Mathlib.Order.LiminfLimsup._hyg.1462) (Filter.cofinite.{u1} α) f) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_1)) (Set.range.{u2, succ u1} β α f))
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofiniteₓ'. -/
theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range_of_cofinite α βᵒᵈ _ _ hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
--/
-#print Filter.IsBoundedUnder.bddAbove_range /-
+/- warning: filter.is_bounded_under.bdd_above_range -> Filter.IsBoundedUnder.bddAbove_range is a dubious translation:
+lean 3 declaration is
+ forall {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
+but is expected to have type
+ forall {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1516 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1518 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1516 x._@.Mathlib.Order.LiminfLimsup._hyg.1518) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_rangeₓ'. -/
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) :=
by
rw [← Nat.cofinite_eq_atTop] at hf
exact hf.bdd_above_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
--/
-#print Filter.IsBoundedUnder.bddBelow_range /-
+/- warning: filter.is_bounded_under.bdd_below_range -> Filter.IsBoundedUnder.bddBelow_range is a dubious translation:
+lean 3 declaration is
+ forall {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (GE.ge.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) f) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
+but is expected to have type
+ forall {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} β] {f : Nat -> β}, (Filter.IsBoundedUnder.{u1, 0} β Nat (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1600 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.1602 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.1600 x._@.Mathlib.Order.LiminfLimsup._hyg.1602) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) f) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_1)) (Set.range.{u1, 1} β Nat f))
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_rangeₓ'. -/
theorem IsBoundedUnder.bddBelow_range [SemilatticeInf β] {f : ℕ → β}
(hf : IsBoundedUnder (· ≥ ·) atTop f) : BddBelow (range f) :=
@IsBoundedUnder.bddAbove_range βᵒᵈ _ _ hf
#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_range
--/
#print Filter.IsCobounded /-
/-- `is_cobounded (≺) f` states that the filter `f` does not tend to infinity w.r.t. `≺`. This is
@@ -291,19 +323,27 @@ theorem IsBounded.isCobounded_flip [IsTrans α r] [NeBot f] : f.IsBounded r →
#align filter.is_bounded.is_cobounded_flip Filter.IsBounded.isCobounded_flip
-/
-#print Filter.IsBounded.isCobounded_ge /-
+/- warning: filter.is_bounded.is_cobounded_ge -> Filter.IsBounded.isCobounded_ge is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f) -> (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f)
+but is expected to have type
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1955 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.1957 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1955 x._@.Mathlib.Order.LiminfLimsup._hyg.1957) f) -> (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.1971 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.1973 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.1971 x._@.Mathlib.Order.LiminfLimsup._hyg.1973) f)
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded.is_cobounded_ge Filter.IsBounded.isCobounded_geₓ'. -/
theorem IsBounded.isCobounded_ge [Preorder α] [NeBot f] (h : f.IsBounded (· ≤ ·)) :
f.IsCobounded (· ≥ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_ge Filter.IsBounded.isCobounded_ge
--/
-#print Filter.IsBounded.isCobounded_le /-
+/- warning: filter.is_bounded.is_cobounded_le -> Filter.IsBounded.isCobounded_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f) -> (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f)
+but is expected to have type
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : Preorder.{u1} α] [_inst_2 : Filter.NeBot.{u1} α f], (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2013 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2015 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2013 x._@.Mathlib.Order.LiminfLimsup._hyg.2015) f) -> (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2029 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2031 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2029 x._@.Mathlib.Order.LiminfLimsup._hyg.2031) f)
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_leₓ'. -/
theorem IsBounded.isCobounded_le [Preorder α] [NeBot f] (h : f.IsBounded (· ≥ ·)) :
f.IsCobounded (· ≤ ·) :=
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_le
--/
/- warning: filter.is_cobounded_bot -> Filter.isCobounded_bot is a dubious translation:
lean 3 declaration is
@@ -333,7 +373,7 @@ theorem isCobounded_principal (s : Set α) :
/- warning: filter.is_cobounded.mono -> Filter.IsCobounded.mono is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsCobounded.{u1} α r f) -> (Filter.IsCobounded.{u1} α r g)
+ forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (Filter.IsCobounded.{u1} α r f) -> (Filter.IsCobounded.{u1} α r g)
but is expected to have type
forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (Filter.IsCobounded.{u1} α r f) -> (Filter.IsCobounded.{u1} α r g)
Case conversion may be inaccurate. Consider using '#align filter.is_cobounded.mono Filter.IsCobounded.monoₓ'. -/
@@ -343,33 +383,49 @@ theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
end Relation
-#print Filter.isCobounded_le_of_bot /-
+/- warning: filter.is_cobounded_le_of_bot -> Filter.isCobounded_le_of_bot is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2280 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2282 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2280 x._@.Mathlib.Order.LiminfLimsup._hyg.2282) f
+Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_botₓ'. -/
theorem isCobounded_le_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsCobounded (· ≤ ·) :=
⟨⊥, fun a h => bot_le⟩
#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_bot
--/
-#print Filter.isCobounded_ge_of_top /-
+/- warning: filter.is_cobounded_ge_of_top -> Filter.isCobounded_ge_of_top is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2322 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2324 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2322 x._@.Mathlib.Order.LiminfLimsup._hyg.2324) f
+Case conversion may be inaccurate. Consider using '#align filter.is_cobounded_ge_of_top Filter.isCobounded_ge_of_topₓ'. -/
theorem isCobounded_ge_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsCobounded (· ≥ ·) :=
⟨⊤, fun a h => le_top⟩
#align filter.is_cobounded_ge_of_top Filter.isCobounded_ge_of_top
--/
-#print Filter.isBounded_le_of_top /-
+/- warning: filter.is_bounded_le_of_top -> Filter.isBounded_le_of_top is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2364 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2366 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2364 x._@.Mathlib.Order.LiminfLimsup._hyg.2366) f
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_le_of_top Filter.isBounded_le_of_topₓ'. -/
theorem isBounded_le_of_top [Preorder α] [OrderTop α] {f : Filter α} : f.IsBounded (· ≤ ·) :=
⟨⊤, eventually_of_forall fun _ => le_top⟩
#align filter.is_bounded_le_of_top Filter.isBounded_le_of_top
--/
-#print Filter.isBounded_ge_of_bot /-
+/- warning: filter.is_bounded_ge_of_bot -> Filter.isBounded_ge_of_bot is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) f
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)] {f : Filter.{u1} α}, Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2405 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2407 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2405 x._@.Mathlib.Order.LiminfLimsup._hyg.2407) f
+Case conversion may be inaccurate. Consider using '#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_botₓ'. -/
theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBounded (· ≥ ·) :=
⟨⊥, eventually_of_forall fun _ => bot_le⟩
#align filter.is_bounded_ge_of_bot Filter.isBounded_ge_of_bot
--/
/- warning: order_iso.is_bounded_under_le_comp -> OrderIso.isBoundedUnder_le_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) l u)
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) l u)
but is expected to have type
forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_compₓ'. -/
@@ -381,7 +437,7 @@ theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o
/- warning: order_iso.is_bounded_under_ge_comp -> OrderIso.isBoundedUnder_ge_comp is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (GE.ge.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (GE.ge.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) l u)
but is expected to have type
forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_compₓ'. -/
@@ -393,7 +449,7 @@ theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o
/- warning: filter.is_bounded_under_le_inv -> Filter.isBoundedUnder_le_inv is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2611 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2613 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2611 x._@.Mathlib.Order.LiminfLimsup._hyg.2613) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2638 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2640 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2638 x._@.Mathlib.Order.LiminfLimsup._hyg.2640) l u)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_inv Filter.isBoundedUnder_le_invₓ'. -/
@@ -406,7 +462,7 @@ theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β →
/- warning: filter.is_bounded_under_ge_inv -> Filter.isBoundedUnder_ge_inv is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2681 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2683 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2681 x._@.Mathlib.Order.LiminfLimsup._hyg.2683) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2708 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2710 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2708 x._@.Mathlib.Order.LiminfLimsup._hyg.2710) l u)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inv Filter.isBoundedUnder_ge_invₓ'. -/
@@ -419,7 +475,7 @@ theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β →
/- warning: filter.is_bounded_under.sup -> Filter.IsBoundedUnder.sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2753 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2755 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2753 x._@.Mathlib.Order.LiminfLimsup._hyg.2755) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2771 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2773 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2771 x._@.Mathlib.Order.LiminfLimsup._hyg.2773) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2788 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2790 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2788 x._@.Mathlib.Order.LiminfLimsup._hyg.2790) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.sup Filter.IsBoundedUnder.supₓ'. -/
@@ -432,7 +488,7 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
/- warning: filter.is_bounded_under_le_sup -> Filter.isBoundedUnder_le_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2987 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2985 x._@.Mathlib.Order.LiminfLimsup._hyg.2987) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3016 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3014 x._@.Mathlib.Order.LiminfLimsup._hyg.3016) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3033 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3031 x._@.Mathlib.Order.LiminfLimsup._hyg.3033) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_supₓ'. -/
@@ -448,7 +504,7 @@ theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β →
/- warning: filter.is_bounded_under.inf -> Filter.IsBoundedUnder.inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3101 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3099 x._@.Mathlib.Order.LiminfLimsup._hyg.3101) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3119 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3117 x._@.Mathlib.Order.LiminfLimsup._hyg.3119) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3136 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3134 x._@.Mathlib.Order.LiminfLimsup._hyg.3136) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.inf Filter.IsBoundedUnder.infₓ'. -/
@@ -460,7 +516,7 @@ theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α}
/- warning: filter.is_bounded_under_ge_inf -> Filter.isBoundedUnder_ge_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3190 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3188 x._@.Mathlib.Order.LiminfLimsup._hyg.3190) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3219 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3217 x._@.Mathlib.Order.LiminfLimsup._hyg.3219) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3236 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3234 x._@.Mathlib.Order.LiminfLimsup._hyg.3236) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_infₓ'. -/
@@ -473,7 +529,7 @@ theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β →
/- warning: filter.is_bounded_under_le_abs -> Filter.isBoundedUnder_le_abs is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f (fun (a : β) => Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (u a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f (fun (a : β) => Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (u a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3277 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3275 x._@.Mathlib.Order.LiminfLimsup._hyg.3277) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3304 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3302 x._@.Mathlib.Order.LiminfLimsup._hyg.3304) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3321 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3319 x._@.Mathlib.Order.LiminfLimsup._hyg.3321) f u))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_abs Filter.isBoundedUnder_le_absₓ'. -/
@@ -551,7 +607,7 @@ variable {f : Filter β} {u : β → α} {p : β → Prop}
/- warning: filter.limsup_eq -> Filter.limsup_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β _inst_1 u f) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) a) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β _inst_1 u f) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) a) f)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.limsup.{u2, u1} α β _inst_1 u f) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u n) a) f)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_eq Filter.limsup_eqₓ'. -/
@@ -561,7 +617,7 @@ theorem limsup_eq : limsup u f = sInf { a | ∀ᶠ n in f, u n ≤ a } :=
/- warning: filter.liminf_eq -> Filter.liminf_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β _inst_1 u f) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β _inst_1 u f) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.liminf.{u2, u1} α β _inst_1 u f) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u n)) f)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_eq Filter.liminf_eqₓ'. -/
@@ -571,7 +627,7 @@ theorem liminf_eq : liminf u f = sSup { a | ∀ᶠ n in f, a ≤ u n } :=
/- warning: filter.blimsup_eq -> Filter.blimsup_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β _inst_1 u f p) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u x) a)) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β _inst_1 u f p) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u x) a)) f)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β _inst_1 u f p) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u x) a)) f)))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq Filter.blimsup_eqₓ'. -/
@@ -581,7 +637,7 @@ theorem blimsup_eq : blimsup u f p = sInf { a | ∀ᶠ x in f, p x → u x ≤ a
/- warning: filter.bliminf_eq -> Filter.bliminf_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β _inst_1 u f p) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u x))) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β _inst_1 u f p) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u x))) f)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β _inst_1 u f p) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u x))) f)))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq Filter.bliminf_eqₓ'. -/
@@ -627,8 +683,13 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
#align filter.bliminf_eq_liminf_subtype Filter.bliminf_eq_liminf_subtype
-/
+/- warning: filter.Limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) a)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) a)
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsSup_le_of_le /-
theorem limsSup_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -636,10 +697,14 @@ theorem limsSup_le_of_le {f : Filter α} {a}
(h : ∀ᶠ n in f, n ≤ a) : limsSup f ≤ a :=
csInf_le hf h
#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
--/
+/- warning: filter.le_Liminf_of_le -> Filter.le_limsInf_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(Filter.limsInf.{u1} α _inst_1 f))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4502 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4504 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4502 x._@.Mathlib.Order.LiminfLimsup._hyg.4504) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4474) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsInf.{u1} α _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align filter.le_Liminf_of_le Filter.le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_limsInf_of_le /-
theorem le_limsInf_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
@@ -647,12 +712,11 @@ theorem le_limsInf_of_le {f : Filter α} {a}
(h : ∀ᶠ n in f, a ≤ n) : a ≤ limsInf f :=
le_csSup hf h
#align filter.le_Liminf_of_le Filter.le_limsInf_of_le
--/
/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
warning: filter.limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
lean 3 declaration is
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101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd 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(bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u_2} β (fun (n : β) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (u n) a) f) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (Filter.limsup.{u_1, u_2} α β _inst_1 u f) a)
+ forall {α : Type.{u_1}} {β : Type.{u_2}} [_inst_1 : ConditionallyCompleteLattice.{u_1} α] {f : Filter.{u_2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u_1, u_2} α β (LE.le.{u_1} α (Preorder.toHasLe.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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(OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat 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(Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u_2} β (fun (n : β) => LE.le.{u_1} α (Preorder.toHasLe.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (u n) a) f) -> (LE.le.{u_1} α (Preorder.toHasLe.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (Filter.limsup.{u_1, u_2} α β _inst_1 u f) a)
but is expected to have type
forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsSup.{u_1} α β _inst_1) f)
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
@@ -665,8 +729,13 @@ theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
csInf_le hf h
#align filter.limsup_le_of_le Filter.limsSup_le_of_le
+/- warning: filter.le_liminf_of_le -> Filter.le_liminf_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat 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Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.liminf.{u1, u2} α β _inst_1 u f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4685 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4687 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4685 x._@.Mathlib.Order.LiminfLimsup._hyg.4687) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4657) -> (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.liminf.{u1, u2} α β _inst_1 u f))
+Case conversion may be inaccurate. Consider using '#align filter.le_liminf_of_le Filter.le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_liminf_of_le /-
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≥ ·) u := by
run_tac
@@ -674,10 +743,14 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ᶠ n in f, a ≤ u n) : a ≤ liminf u f :=
le_csSup hf h
#align filter.le_liminf_of_le Filter.le_liminf_of_le
--/
+/- warning: filter.le_Limsup_of_le -> Filter.le_limsSup_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParamₓ.{0} (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n b) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsSup.{u1} α _inst_1 f))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4772 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4774 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4772 x._@.Mathlib.Order.LiminfLimsup._hyg.4774) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4744) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n b) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsSup.{u1} α _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align filter.le_Limsup_of_le Filter.le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_limsSup_of_le /-
theorem le_limsSup_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by
run_tac
@@ -685,10 +758,14 @@ theorem le_limsSup_of_le {f : Filter α} {a}
(h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsSup f :=
le_csInf hf h
#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
--/
+/- warning: filter.Liminf_le_of_le -> Filter.limsInf_le_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} 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Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b n) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) a)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {a : α}, (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4873 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4875 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4873 x._@.Mathlib.Order.LiminfLimsup._hyg.4875) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4845) -> (forall (b : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b n) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) a)
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_of_le Filter.limsInf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsInf_le_of_le /-
theorem limsInf_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -696,10 +773,14 @@ theorem limsInf_le_of_le {f : Filter α} {a}
(h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : limsInf f ≤ a :=
csSup_le hf h
#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
--/
+/- warning: filter.le_limsup_of_le -> Filter.le_limsup_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} 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Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (forall (b : α), (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) b) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsup.{u1, u2} α β _inst_1 u f))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4977 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4979 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4977 x._@.Mathlib.Order.LiminfLimsup._hyg.4979) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4949) -> (forall (b : α), (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) b) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (Filter.limsup.{u1, u2} α β _inst_1 u f))
+Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_le Filter.le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_limsup_of_le /-
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≤ ·) u := by
run_tac
@@ -707,10 +788,14 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ b, (∀ᶠ n in f, u n ≤ b) → a ≤ b) : a ≤ limsup u f :=
le_csInf hf h
#align filter.le_limsup_of_le Filter.le_limsup_of_le
--/
+/- warning: filter.liminf_le_of_le -> Filter.liminf_le_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (forall (b : α), (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (u n)) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminf.{u1, u2} α β _inst_1 u f) a)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5078 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5080 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5078 x._@.Mathlib.Order.LiminfLimsup._hyg.5080) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5050) -> (forall (b : α), (Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (u n)) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminf.{u1, u2} α β _inst_1 u f) a)
+Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_le Filter.liminf_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminf_le_of_le /-
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
run_tac
@@ -718,11 +803,15 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(h : ∀ b, (∀ᶠ n in f, b ≤ u n) → b ≤ a) : liminf u f ≤ a :=
csSup_le hf h
#align filter.liminf_le_of_le Filter.liminf_le_of_le
--/
+/- warning: filter.Liminf_le_Limsup -> Filter.limsInf_le_limsSup is a dubious translation:
+lean 3 declaration is
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(LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 f))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} [_inst_2 : Filter.NeBot.{u1} α f], (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5178 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5180 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5178 x._@.Mathlib.Order.LiminfLimsup._hyg.5180) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5150) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5219 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5221 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5219 x._@.Mathlib.Order.LiminfLimsup._hyg.5221) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5191) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsInf_le_limsSup /-
theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
(h₁ : f.IsBounded (· ≤ ·) := by
run_tac
@@ -737,11 +826,15 @@ theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
let ⟨b, hb₀, hb₁⟩ := (ha₀.And ha₁).exists
le_trans hb₀ hb₁
#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
--/
+/- warning: filter.liminf_le_limsup -> Filter.liminf_le_limsup is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} [_inst_2 : Filter.NeBot.{u2} β f] {u : β -> α}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5349 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5351 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5349 x._@.Mathlib.Order.LiminfLimsup._hyg.5351) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5321) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5391 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5393 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5391 x._@.Mathlib.Order.LiminfLimsup._hyg.5393) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5363) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminf.{u1, u2} α β _inst_1 u f) (Filter.limsup.{u1, u2} α β _inst_1 u f))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_le_limsup Filter.liminf_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminf_le_limsup /-
theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
(h : f.IsBoundedUnder (· ≤ ·) u := by
run_tac
@@ -752,11 +845,15 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
liminf u f ≤ limsup u f :=
limsInf_le_limsSup h h'
#align filter.liminf_le_limsup Filter.liminf_le_limsup
--/
+/- warning: filter.Limsup_le_Limsup -> Filter.limsSup_le_limsSup is a dubious translation:
+lean 3 declaration is
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(Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) g) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) f)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5458 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5460 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5458 x._@.Mathlib.Order.LiminfLimsup._hyg.5460) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5430) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5499 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5501 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5499 x._@.Mathlib.Order.LiminfLimsup._hyg.5501) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5471) -> (forall (a : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) g) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) n a) f)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsSup_le_limsSup /-
theorem limsSup_le_limsSup {f g : Filter α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -767,11 +864,15 @@ theorem limsSup_le_limsSup {f g : Filter α}
(h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsSup f ≤ limsSup g :=
csInf_le_csInf hf hg h
#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
--/
+/- warning: filter.Liminf_le_Liminf -> Filter.limsInf_le_limsInf is a dubious translation:
+lean 3 declaration is
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(Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) f) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) g)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5620 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5622 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5620 x._@.Mathlib.Order.LiminfLimsup._hyg.5622) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5592) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5661 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.5663 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5661 x._@.Mathlib.Order.LiminfLimsup._hyg.5663) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5633) -> (forall (a : α), (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) f) -> (Filter.Eventually.{u1} α (fun (n : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a n) g)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsInf_le_limsInf /-
theorem limsInf_le_limsInf {f g : Filter α}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -782,11 +883,15 @@ theorem limsInf_le_limsInf {f g : Filter α}
(h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : limsInf f ≤ limsInf g :=
csSup_le_csSup hg hf h
#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
--/
+/- warning: filter.limsup_le_limsup -> Filter.limsup_le_limsup is a dubious translation:
+lean 3 declaration is
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(bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u1, u2} β α (LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) f v) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 v f))
+but is expected to have type
+ forall {β : Type.{u1}} {α : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {u : α -> β} {v : α -> β}, (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) f u v) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5796 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.5798 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5796 x._@.Mathlib.Order.LiminfLimsup._hyg.5798) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5768) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5838 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.5840 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5838 x._@.Mathlib.Order.LiminfLimsup._hyg.5840) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5810) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 v f))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup Filter.limsup_le_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsup_le_limsup /-
theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : u ≤ᶠ[f] v)
(hu : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -798,11 +903,15 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
limsup u f ≤ limsup v f :=
limsSup_le_limsSup hu hv fun b => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
--/
+/- warning: filter.liminf_le_liminf -> Filter.liminf_le_liminf is a dubious translation:
+lean 3 declaration is
+ forall {β : Type.{u1}} {α : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {u : α -> β} {v : α -> β}, (Filter.Eventually.{u2} α (fun (a : α) => LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (u a) (v a)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u1, u2} β α (GE.ge.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} β (Preorder.toHasLe.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 v f))
+but is expected to have type
+ forall {β : Type.{u1}} {α : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {u : α -> β} {v : α -> β}, (Filter.Eventually.{u2} α (fun (a : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (u a) (v a)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5942 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.5944 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5942 x._@.Mathlib.Order.LiminfLimsup._hyg.5944) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5914) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.5984 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.5986 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.5984 x._@.Mathlib.Order.LiminfLimsup._hyg.5986) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.5956) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 v f))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf Filter.liminf_le_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminf_le_liminf /-
theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a ≤ v a)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -814,11 +923,10 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
liminf u f ≤ liminf v f :=
@limsup_le_limsup βᵒᵈ α _ _ _ _ h hv hu
#align filter.liminf_le_liminf Filter.liminf_le_liminf
--/
/- warning: filter.Limsup_le_Limsup_of_le -> Filter.limsSup_le_limsSup_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_leₓ'. -/
@@ -837,7 +945,7 @@ theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
/- warning: filter.Liminf_le_Liminf_of_le -> Filter.limsInf_le_limsInf_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_leₓ'. -/
@@ -856,7 +964,7 @@ theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
/- warning: filter.limsup_le_limsup_of_le -> Filter.limsup_le_limsup_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.limsup.{u2, u1} β α _inst_2 u f) (Filter.limsup.{u2, u1} β α _inst_2 u g)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.limsup.{u2, u1} β α _inst_2 u f) (Filter.limsup.{u2, u1} β α _inst_2 u g)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6315 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6315 x._@.Mathlib.Order.LiminfLimsup._hyg.6317) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6287) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6357 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6357 x._@.Mathlib.Order.LiminfLimsup._hyg.6359) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6329) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
@@ -876,7 +984,7 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
/- warning: filter.liminf_le_liminf_of_le -> Filter.liminf_le_liminf_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.liminf.{u2, u1} β α _inst_2 u f) (Filter.liminf.{u2, u1} β α _inst_2 u g)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6441 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6441 x._@.Mathlib.Order.LiminfLimsup._hyg.6443) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6413) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6483 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6483 x._@.Mathlib.Order.LiminfLimsup._hyg.6485) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6455) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
@@ -1108,7 +1216,7 @@ theorem limsInf_eq_iSup_sInf {f : Filter α} : limsInf f = ⨆ s ∈ f, sInf s :
/- warning: filter.limsup_le_supr -> Filter.limsup_le_iSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_supr Filter.limsup_le_iSupₓ'. -/
@@ -1123,7 +1231,7 @@ theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u
/- warning: filter.infi_le_liminf -> Filter.iInf_le_liminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
Case conversion may be inaccurate. Consider using '#align filter.infi_le_liminf Filter.iInf_le_liminfₓ'. -/
@@ -1360,7 +1468,7 @@ theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k))
/- warning: filter.liminf_le_of_frequently_le' -> Filter.liminf_le_of_frequently_le' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : CompleteLattice.{u2} β] {f : Filter.{u1} α} {u : α -> β} {x : β}, (Filter.Frequently.{u1} α (fun (a : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (u a) x) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (Filter.liminf.{u2, u1} β α (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) u f) x)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : CompleteLattice.{u2} β] {f : Filter.{u1} α} {u : α -> β} {x : β}, (Filter.Frequently.{u1} α (fun (a : α) => LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (u a) x) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (Filter.liminf.{u2, u1} β α (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) u f) x)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : CompleteLattice.{u1} β] {f : Filter.{u2} α} {u : α -> β} {x : β}, (Filter.Frequently.{u2} α (fun (a : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2)))) (u a) x) f) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2)))) (Filter.liminf.{u1, u2} β α (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_2) u f) x)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le' Filter.liminf_le_of_frequently_le'ₓ'. -/
@@ -1378,7 +1486,7 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
/- warning: filter.le_limsup_of_frequently_le' -> Filter.le_limsup_of_frequently_le' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : CompleteLattice.{u2} β] {f : Filter.{u1} α} {u : α -> β} {x : β}, (Filter.Frequently.{u1} α (fun (a : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x (u a)) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x (Filter.limsup.{u2, u1} β α (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) u f))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : CompleteLattice.{u2} β] {f : Filter.{u1} α} {u : α -> β} {x : β}, (Filter.Frequently.{u1} α (fun (a : α) => LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x (u a)) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x (Filter.limsup.{u2, u1} β α (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) u f))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : CompleteLattice.{u1} β] {f : Filter.{u2} α} {u : α -> β} {x : β}, (Filter.Frequently.{u2} α (fun (a : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2)))) x (u a)) f) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2)))) x (Filter.limsup.{u1, u2} β α (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_2) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le' Filter.le_limsup_of_frequently_le'ₓ'. -/
@@ -1425,7 +1533,7 @@ variable {f g : Filter β} {p q : β → Prop} {u v : β → α}
/- warning: filter.blimsup_mono -> Filter.blimsup_mono is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_mono Filter.blimsup_monoₓ'. -/
@@ -1435,7 +1543,7 @@ theorem blimsup_mono (h : ∀ x, p x → q x) : blimsup u f p ≤ blimsup u f q
/- warning: filter.bliminf_antitone -> Filter.bliminf_antitone is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_antitone Filter.bliminf_antitoneₓ'. -/
@@ -1443,15 +1551,19 @@ theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u
sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
-#print Filter.mono_blimsup' /-
+/- warning: filter.mono_blimsup' -> Filter.mono_blimsup' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+Case conversion may be inaccurate. Consider using '#align filter.mono_blimsup' Filter.mono_blimsup'ₓ'. -/
theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
sInf_le_sInf fun a ha => (ha.And h).mono fun x hx hx' => (hx.2 hx').trans (hx.1 hx')
#align filter.mono_blimsup' Filter.mono_blimsup'
--/
/- warning: filter.mono_blimsup -> Filter.mono_blimsup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (u x) (v x))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) v f p))
Case conversion may be inaccurate. Consider using '#align filter.mono_blimsup Filter.mono_blimsupₓ'. -/
@@ -1459,15 +1571,19 @@ theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsu
mono_blimsup' <| eventually_of_forall h
#align filter.mono_blimsup Filter.mono_blimsup
-#print Filter.mono_bliminf' /-
+/- warning: filter.mono_bliminf' -> Filter.mono_bliminf' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+Case conversion may be inaccurate. Consider using '#align filter.mono_bliminf' Filter.mono_bliminf'ₓ'. -/
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
sSup_le_sSup fun a ha => (ha.And h).mono fun x hx hx' => (hx.1 hx').trans (hx.2 hx')
#align filter.mono_bliminf' Filter.mono_bliminf'
--/
/- warning: filter.mono_bliminf -> Filter.mono_bliminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (u x) (v x))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) v f p))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} {v : β -> α}, (forall (x : β), (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (u x) (v x))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) v f p))
Case conversion may be inaccurate. Consider using '#align filter.mono_bliminf Filter.mono_bliminfₓ'. -/
@@ -1477,7 +1593,7 @@ theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ blimin
/- warning: filter.bliminf_antitone_filter -> Filter.bliminf_antitone_filter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toHasLe.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filterₓ'. -/
@@ -1487,7 +1603,7 @@ theorem bliminf_antitone_filter (h : f ≤ g) : bliminf u g p ≤ bliminf u f p
/- warning: filter.blimsup_monotone_filter -> Filter.blimsup_monotone_filter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toHasLe.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.partialOrder.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filterₓ'. -/
@@ -1497,7 +1613,7 @@ theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p
/- warning: filter.blimsup_and_le_inf -> Filter.blimsup_and_le_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_and_le_inf Filter.blimsup_and_le_infₓ'. -/
@@ -1508,7 +1624,7 @@ theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f
/- warning: filter.bliminf_sup_le_and -> Filter.bliminf_sup_le_and is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_sup_le_and Filter.bliminf_sup_le_andₓ'. -/
@@ -1519,7 +1635,7 @@ theorem bliminf_sup_le_and : bliminf u f p ⊔ bliminf u f q ≤ bliminf u f fun
/- warning: filter.blimsup_sup_le_or -> Filter.blimsup_sup_le_or is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_sup_le_or Filter.blimsup_sup_le_orₓ'. -/
@@ -1531,7 +1647,7 @@ theorem blimsup_sup_le_or : blimsup u f p ⊔ blimsup u f q ≤ blimsup u f fun
/- warning: filter.bliminf_or_le_inf -> Filter.bliminf_or_le_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_or_le_inf Filter.bliminf_or_le_infₓ'. -/
@@ -1543,7 +1659,7 @@ theorem bliminf_or_le_inf : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f p
/- warning: filter.order_iso.apply_blimsup -> Filter.OrderIso.apply_blimsup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.tosInfHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.tosInfHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsupₓ'. -/
@@ -1559,7 +1675,7 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
/- warning: filter.order_iso.apply_bliminf -> Filter.OrderIso.apply_bliminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminfₓ'. -/
@@ -1570,7 +1686,7 @@ theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
/- warning: filter.Sup_hom.apply_blimsup_le -> Filter.SupHom.apply_blimsup_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p)
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Preorder.toLE.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (PartialOrder.toPreorder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteSemilatticeInf.toPartialOrder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteLattice.toCompleteSemilatticeInf.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (sSupHomClass.toFunLike.{max u2 u3, u2, u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sSupHom.instSSupHomClassSSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (sSupHomClass.toFunLike.{max u2 u3, u2, u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sSupHom.instSSupHomClassSSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_leₓ'. -/
@@ -1584,7 +1700,7 @@ theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
/- warning: filter.Inf_hom.le_apply_bliminf -> Filter.InfHom.le_apply_bliminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sInfHom.instSInfHomClassSInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sInfHom.instSInfHomClassSInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminfₓ'. -/
@@ -1839,8 +1955,13 @@ end SetLattice
section ConditionallyCompleteLinearOrder
+/- warning: filter.frequently_lt_of_lt_Limsup -> Filter.frequently_lt_of_lt_limsSup is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat 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Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a (Filter.limsSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f)) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a n) f)
+but is expected to have type
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13376 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.13378 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13376 x._@.Mathlib.Order.LiminfLimsup._hyg.13378) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13348) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a (Filter.limsSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f)) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a n) f)
+Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.frequently_lt_of_lt_limsSup /-
theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -1851,10 +1972,14 @@ theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinear
simp only [not_frequently, not_lt] at h
exact Limsup_le_of_le hf h
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
--/
+/- warning: filter.frequently_lt_of_Liminf_lt -> Filter.frequently_lt_of_limsInf_lt is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.limsInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f) a) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) n a) f)
+but is expected to have type
+ forall {α : Type.{u1}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α}, (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13489 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.13491 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13489 x._@.Mathlib.Order.LiminfLimsup._hyg.13491) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13461) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.limsInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1) f) a) -> (Filter.Frequently.{u1} α (fun (n : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) n a) f)
+Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.frequently_lt_of_limsInf_lt /-
theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
@@ -1862,11 +1987,10 @@ theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinear
(h : limsInf f < a) : ∃ᶠ n in f, n < a :=
@frequently_lt_of_lt_limsSup (OrderDual α) f _ a hf h
#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
--/
/- warning: filter.eventually_lt_of_lt_liminf -> Filter.eventually_lt_of_lt_liminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13591 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13593 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13591 x._@.Mathlib.Order.LiminfLimsup._hyg.13593) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13563) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
@@ -1885,7 +2009,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
/- warning: filter.eventually_lt_of_limsup_lt -> Filter.eventually_lt_of_limsup_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str 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(bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u a) b) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u a) b) f)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13760 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13762 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13760 x._@.Mathlib.Order.LiminfLimsup._hyg.13762) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13732) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
@@ -1901,7 +2025,7 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
/- warning: filter.le_limsup_of_frequently_le -> Filter.le_limsup_of_frequently_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13872 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13874 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13872 x._@.Mathlib.Order.LiminfLimsup._hyg.13874) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13844) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
@@ -1920,7 +2044,7 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
/- warning: filter.liminf_le_of_frequently_le -> Filter.liminf_le_of_frequently_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14005 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14007 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14005 x._@.Mathlib.Order.LiminfLimsup._hyg.14007) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13977) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
@@ -1936,7 +2060,7 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
/- warning: filter.frequently_lt_of_lt_limsup -> Filter.frequently_lt_of_lt_limsup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) 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(OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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(OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14078 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14080 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14078 x._@.Mathlib.Order.LiminfLimsup._hyg.14080) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14050) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
@@ -1955,7 +2079,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
/- warning: filter.frequently_lt_of_liminf_lt -> Filter.frequently_lt_of_liminf_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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(OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14195 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14197 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14195 x._@.Mathlib.Order.LiminfLimsup._hyg.14197) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14167) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
@@ -1979,7 +2103,7 @@ open Filter
/- warning: monotone.is_bounded_under_le_comp -> Monotone.isBoundedUnder_le_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14292 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14294 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14292 x._@.Mathlib.Order.LiminfLimsup._hyg.14294) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14316 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14318 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14316 x._@.Mathlib.Order.LiminfLimsup._hyg.14318) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_compₓ'. -/
@@ -1995,7 +2119,7 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
/- warning: monotone.is_bounded_under_ge_comp -> Monotone.isBoundedUnder_ge_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14475 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14477 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14475 x._@.Mathlib.Order.LiminfLimsup._hyg.14477) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14499 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14501 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14499 x._@.Mathlib.Order.LiminfLimsup._hyg.14501) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_compₓ'. -/
@@ -2007,7 +2131,7 @@ theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
/- warning: antitone.is_bounded_under_le_comp -> Antitone.isBoundedUnder_le_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14558 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14560 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14558 x._@.Mathlib.Order.LiminfLimsup._hyg.14560) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14582 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14584 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14582 x._@.Mathlib.Order.LiminfLimsup._hyg.14584) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_compₓ'. -/
@@ -2019,7 +2143,7 @@ theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
/- warning: antitone.is_bounded_under_ge_comp -> Antitone.isBoundedUnder_ge_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toHasLt.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14641 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14643 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14641 x._@.Mathlib.Order.LiminfLimsup._hyg.14643) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14665 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14667 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14665 x._@.Mathlib.Order.LiminfLimsup._hyg.14667) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_compₓ'. -/
@@ -2031,7 +2155,7 @@ theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
/- warning: galois_connection.l_limsup_le -> GaloisConnection.l_limsup_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd 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Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f v) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) (l (Filter.limsup.{u2, u1} β α _inst_1 v f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toHasLe.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str 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Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f v) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14739 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14741 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14739 x._@.Mathlib.Order.LiminfLimsup._hyg.14741) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14711) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14788 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14790 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14788 x._@.Mathlib.Order.LiminfLimsup._hyg.14790) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14760) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
@@ -2056,7 +2180,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
/- warning: order_iso.limsup_apply -> OrderIso.limsup_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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(ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
@@ -2092,7 +2216,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
/- warning: order_iso.liminf_apply -> OrderIso.liminf_apply is a dubious translation:
lean 3 declaration is
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forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15313 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15315 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15313 x._@.Mathlib.Order.LiminfLimsup._hyg.15315) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15285) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15355 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15357 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15355 x._@.Mathlib.Order.LiminfLimsup._hyg.15357) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15327) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15397 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15399 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15397 x._@.Mathlib.Order.LiminfLimsup._hyg.15399) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15369) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15447 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15449 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15447 x._@.Mathlib.Order.LiminfLimsup._hyg.15449) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15419) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -497,27 +497,27 @@ section ConditionallyCompleteLattice
variable [ConditionallyCompleteLattice α]
-#print Filter.limsupₛ /-
+#print Filter.limsSup /-
/-- The `Limsup` of a filter `f` is the infimum of the `a` such that, eventually for `f`,
holds `x ≤ a`. -/
-def limsupₛ (f : Filter α) : α :=
- infₛ { a | ∀ᶠ n in f, n ≤ a }
-#align filter.Limsup Filter.limsupₛ
+def limsSup (f : Filter α) : α :=
+ sInf { a | ∀ᶠ n in f, n ≤ a }
+#align filter.Limsup Filter.limsSup
-/
-#print Filter.liminfₛ /-
+#print Filter.limsInf /-
/-- The `Liminf` of a filter `f` is the supremum of the `a` such that, eventually for `f`,
holds `x ≥ a`. -/
-def liminfₛ (f : Filter α) : α :=
- supₛ { a | ∀ᶠ n in f, a ≤ n }
-#align filter.Liminf Filter.liminfₛ
+def limsInf (f : Filter α) : α :=
+ sSup { a | ∀ᶠ n in f, a ≤ n }
+#align filter.Liminf Filter.limsInf
-/
#print Filter.limsup /-
/-- The `limsup` of a function `u` along a filter `f` is the infimum of the `a` such that,
eventually for `f`, holds `u x ≤ a`. -/
def limsup (u : β → α) (f : Filter β) : α :=
- limsupₛ (map u f)
+ limsSup (map u f)
#align filter.limsup Filter.limsup
-/
@@ -525,7 +525,7 @@ def limsup (u : β → α) (f : Filter β) : α :=
/-- The `liminf` of a function `u` along a filter `f` is the supremum of the `a` such that,
eventually for `f`, holds `u x ≥ a`. -/
def liminf (u : β → α) (f : Filter β) : α :=
- liminfₛ (map u f)
+ limsInf (map u f)
#align filter.liminf Filter.liminf
-/
@@ -533,7 +533,7 @@ def liminf (u : β → α) (f : Filter β) : α :=
/-- The `blimsup` of a function `u` along a filter `f`, bounded by a predicate `p`, is the infimum
of the `a` such that, eventually for `f`, `u x ≤ a` whenever `p x` holds. -/
def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
- infₛ { a | ∀ᶠ x in f, p x → u x ≤ a }
+ sInf { a | ∀ᶠ x in f, p x → u x ≤ a }
#align filter.blimsup Filter.blimsup
-/
@@ -541,7 +541,7 @@ def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
/-- The `bliminf` of a function `u` along a filter `f`, bounded by a predicate `p`, is the supremum
of the `a` such that, eventually for `f`, `a ≤ u x` whenever `p x` holds. -/
def bliminf (u : β → α) (f : Filter β) (p : β → Prop) :=
- supₛ { a | ∀ᶠ x in f, p x → a ≤ u x }
+ sSup { a | ∀ᶠ x in f, p x → a ≤ u x }
#align filter.bliminf Filter.bliminf
-/
@@ -551,41 +551,41 @@ variable {f : Filter β} {u : β → α} {p : β → Prop}
/- warning: filter.limsup_eq -> Filter.limsup_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β _inst_1 u f) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) a) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β _inst_1 u f) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u n) a) f)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.limsup.{u2, u1} α β _inst_1 u f) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u n) a) f)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.limsup.{u2, u1} α β _inst_1 u f) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u n) a) f)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_eq Filter.limsup_eqₓ'. -/
-theorem limsup_eq : limsup u f = infₛ { a | ∀ᶠ n in f, u n ≤ a } :=
+theorem limsup_eq : limsup u f = sInf { a | ∀ᶠ n in f, u n ≤ a } :=
rfl
#align filter.limsup_eq Filter.limsup_eq
/- warning: filter.liminf_eq -> Filter.liminf_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β _inst_1 u f) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β _inst_1 u f) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (n : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u n)) f)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.liminf.{u2, u1} α β _inst_1 u f) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u n)) f)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Eq.{succ u2} α (Filter.liminf.{u2, u1} α β _inst_1 u f) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (n : β) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u n)) f)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_eq Filter.liminf_eqₓ'. -/
-theorem liminf_eq : liminf u f = supₛ { a | ∀ᶠ n in f, a ≤ u n } :=
+theorem liminf_eq : liminf u f = sSup { a | ∀ᶠ n in f, a ≤ u n } :=
rfl
#align filter.liminf_eq Filter.liminf_eq
/- warning: filter.blimsup_eq -> Filter.blimsup_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β _inst_1 u f p) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u x) a)) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β _inst_1 u f p) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (u x) a)) f)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β _inst_1 u f p) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u x) a)) f)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β _inst_1 u f p) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (u x) a)) f)))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq Filter.blimsup_eqₓ'. -/
-theorem blimsup_eq : blimsup u f p = infₛ { a | ∀ᶠ x in f, p x → u x ≤ a } :=
+theorem blimsup_eq : blimsup u f p = sInf { a | ∀ᶠ x in f, p x → u x ≤ a } :=
rfl
#align filter.blimsup_eq Filter.blimsup_eq
/- warning: filter.bliminf_eq -> Filter.bliminf_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β _inst_1 u f p) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u x))) f)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β _inst_1 u f p) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => Filter.Eventually.{u2} β (fun (x : β) => (p x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (u x))) f)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β _inst_1 u f p) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u x))) f)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} {p : β -> Prop}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β _inst_1 u f p) (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) (setOf.{u2} α (fun (a : α) => Filter.Eventually.{u1} β (fun (x : β) => (p x) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (u x))) f)))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq Filter.bliminf_eqₓ'. -/
-theorem bliminf_eq : bliminf u f p = supₛ { a | ∀ᶠ x in f, p x → a ≤ u x } :=
+theorem bliminf_eq : bliminf u f p = sSup { a | ∀ᶠ x in f, p x → a ≤ u x } :=
rfl
#align filter.bliminf_eq Filter.bliminf_eq
@@ -628,42 +628,42 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsupₛ_le_of_le /-
-theorem limsupₛ_le_of_le {f : Filter α} {a}
+#print Filter.limsSup_le_of_le /-
+theorem limsSup_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
is_bounded_default)
- (h : ∀ᶠ n in f, n ≤ a) : limsupₛ f ≤ a :=
- cinfₛ_le hf h
-#align filter.Limsup_le_of_le Filter.limsupₛ_le_of_le
+ (h : ∀ᶠ n in f, n ≤ a) : limsSup f ≤ a :=
+ csInf_le hf h
+#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_liminfₛ_of_le /-
-theorem le_liminfₛ_of_le {f : Filter α} {a}
+#print Filter.le_limsInf_of_le /-
+theorem le_limsInf_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
is_bounded_default)
- (h : ∀ᶠ n in f, a ≤ n) : a ≤ liminfₛ f :=
- le_csupₛ hf h
-#align filter.le_Liminf_of_le Filter.le_liminfₛ_of_le
+ (h : ∀ᶠ n in f, a ≤ n) : a ≤ limsInf f :=
+ le_csSup hf h
+#align filter.le_Liminf_of_le Filter.le_limsInf_of_le
-/
-/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsupₛ_le_of_le
-warning: filter.limsup_le_of_le -> Filter.limsupₛ_le_of_le is a dubious translation:
+/- warning: filter.limsup_le_of_le clashes with filter.Limsup_le_of_le -> Filter.limsSup_le_of_le
+warning: filter.limsup_le_of_le -> Filter.limsSup_le_of_le is a dubious translation:
lean 3 declaration is
forall {α : Type.{u_1}} {β : Type.{u_2}} [_inst_1 : ConditionallyCompleteLattice.{u_1} α] {f : Filter.{u_2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u_1, u_2} α β (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat 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(bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u_2} β (fun (n : β) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (u n) a) f) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (Filter.limsup.{u_1, u_2} α β _inst_1 u f) a)
but is expected to have type
- forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
-Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsupₛ_le_of_leₓ'. -/
+ forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsSup.{u_1} α β _inst_1) f)
+Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsSup_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-theorem limsupₛ_le_of_le {f : Filter β} {u : β → α} {a}
+theorem limsSup_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by
run_tac
is_bounded_default)
(h : ∀ᶠ n in f, u n ≤ a) : limsup u f ≤ a :=
- cinfₛ_le hf h
-#align filter.limsup_le_of_le Filter.limsupₛ_le_of_le
+ csInf_le hf h
+#align filter.limsup_le_of_le Filter.limsSup_le_of_le
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_liminf_of_le /-
@@ -672,30 +672,30 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
run_tac
is_bounded_default)
(h : ∀ᶠ n in f, a ≤ u n) : a ≤ liminf u f :=
- le_csupₛ hf h
+ le_csSup hf h
#align filter.le_liminf_of_le Filter.le_liminf_of_le
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.le_limsupₛ_of_le /-
-theorem le_limsupₛ_of_le {f : Filter α} {a}
+#print Filter.le_limsSup_of_le /-
+theorem le_limsSup_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by
run_tac
is_bounded_default)
- (h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsupₛ f :=
- le_cinfₛ hf h
-#align filter.le_Limsup_of_le Filter.le_limsupₛ_of_le
+ (h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsSup f :=
+ le_csInf hf h
+#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminfₛ_le_of_le /-
-theorem liminfₛ_le_of_le {f : Filter α} {a}
+#print Filter.limsInf_le_of_le /-
+theorem limsInf_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
is_bounded_default)
- (h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : liminfₛ f ≤ a :=
- csupₛ_le hf h
-#align filter.Liminf_le_of_le Filter.liminfₛ_le_of_le
+ (h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : limsInf f ≤ a :=
+ csSup_le hf h
+#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -705,7 +705,7 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
run_tac
is_bounded_default)
(h : ∀ b, (∀ᶠ n in f, u n ≤ b) → a ≤ b) : a ≤ limsup u f :=
- le_cinfₛ hf h
+ le_csInf hf h
#align filter.le_limsup_of_le Filter.le_limsup_of_le
-/
@@ -716,27 +716,27 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
run_tac
is_bounded_default)
(h : ∀ b, (∀ᶠ n in f, b ≤ u n) → b ≤ a) : liminf u f ≤ a :=
- csupₛ_le hf h
+ csSup_le hf h
#align filter.liminf_le_of_le Filter.liminf_le_of_le
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminfₛ_le_limsupₛ /-
-theorem liminfₛ_le_limsupₛ {f : Filter α} [NeBot f]
+#print Filter.limsInf_le_limsSup /-
+theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
(h₁ : f.IsBounded (· ≤ ·) := by
run_tac
is_bounded_default)
(h₂ : f.IsBounded (· ≥ ·) := by
run_tac
is_bounded_default) :
- liminfₛ f ≤ limsupₛ f :=
- liminfₛ_le_of_le h₂ fun a₀ ha₀ =>
- le_limsupₛ_of_le h₁ fun a₁ ha₁ =>
+ limsInf f ≤ limsSup f :=
+ limsInf_le_of_le h₂ fun a₀ ha₀ =>
+ le_limsSup_of_le h₁ fun a₁ ha₁ =>
show a₀ ≤ a₁ from
let ⟨b, hb₀, hb₁⟩ := (ha₀.And ha₁).exists
le_trans hb₀ hb₁
-#align filter.Liminf_le_Limsup Filter.liminfₛ_le_limsupₛ
+#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -750,38 +750,38 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
run_tac
is_bounded_default) :
liminf u f ≤ limsup u f :=
- liminfₛ_le_limsupₛ h h'
+ limsInf_le_limsSup h h'
#align filter.liminf_le_limsup Filter.liminf_le_limsup
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.limsupₛ_le_limsupₛ /-
-theorem limsupₛ_le_limsupₛ {f g : Filter α}
+#print Filter.limsSup_le_limsSup /-
+theorem limsSup_le_limsSup {f g : Filter α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
is_bounded_default)
(hg : g.IsBounded (· ≤ ·) := by
run_tac
is_bounded_default)
- (h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsupₛ f ≤ limsupₛ g :=
- cinfₛ_le_cinfₛ hf hg h
-#align filter.Limsup_le_Limsup Filter.limsupₛ_le_limsupₛ
+ (h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsSup f ≤ limsSup g :=
+ csInf_le_csInf hf hg h
+#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.liminfₛ_le_liminfₛ /-
-theorem liminfₛ_le_liminfₛ {f g : Filter α}
+#print Filter.limsInf_le_limsInf /-
+theorem limsInf_le_limsInf {f g : Filter α}
(hf : f.IsBounded (· ≥ ·) := by
run_tac
is_bounded_default)
(hg : g.IsCobounded (· ≥ ·) := by
run_tac
is_bounded_default)
- (h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : liminfₛ f ≤ liminfₛ g :=
- csupₛ_le_csupₛ hg hf h
-#align filter.Liminf_le_Liminf Filter.liminfₛ_le_liminfₛ
+ (h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : limsInf f ≤ limsInf g :=
+ csSup_le_csSup hg hf h
+#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -796,7 +796,7 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
run_tac
is_bounded_default) :
limsup u f ≤ limsup v f :=
- limsupₛ_le_limsupₛ hu hv fun b => h.trans
+ limsSup_le_limsSup hu hv fun b => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
-/
@@ -816,43 +816,43 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
#align filter.liminf_le_liminf Filter.liminf_le_liminf
-/
-/- warning: filter.Limsup_le_Limsup_of_le -> Filter.limsupₛ_le_limsupₛ_of_le is a dubious translation:
+/- warning: filter.Limsup_le_Limsup_of_le -> Filter.limsSup_le_limsSup_of_le is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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(OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_leₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsSup.{u1} α _inst_1 f) (Filter.limsSup.{u1} α _inst_1 g))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-theorem limsupₛ_le_limsupₛ_of_le {f g : Filter α} (h : f ≤ g)
+theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
is_bounded_default)
(hg : g.IsBounded (· ≤ ·) := by
run_tac
is_bounded_default) :
- limsupₛ f ≤ limsupₛ g :=
- limsupₛ_le_limsupₛ hf hg fun a ha => h ha
-#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_le
+ limsSup f ≤ limsSup g :=
+ limsSup_le_limsSup hf hg fun a ha => h ha
+#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_le
-/- warning: filter.Liminf_le_Liminf_of_le -> Filter.liminfₛ_le_liminfₛ_of_le is a dubious translation:
+/- warning: filter.Liminf_le_Liminf_of_le -> Filter.limsInf_le_limsInf_of_le is a dubious translation:
lean 3 declaration is
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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd 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+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_leₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsInf.{u1} α _inst_1 f) (Filter.limsInf.{u1} α _inst_1 g))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-theorem liminfₛ_le_liminfₛ_of_le {f g : Filter α} (h : g ≤ f)
+theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
(hf : f.IsBounded (· ≥ ·) := by
run_tac
is_bounded_default)
(hg : g.IsCobounded (· ≥ ·) := by
run_tac
is_bounded_default) :
- liminfₛ f ≤ liminfₛ g :=
- liminfₛ_le_liminfₛ hf hg fun a ha => h ha
-#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_le
+ limsInf f ≤ limsInf g :=
+ limsInf_le_limsInf hf hg fun a ha => h ha
+#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_le
/- warning: filter.limsup_le_limsup_of_le -> Filter.limsup_le_limsup_of_le is a dubious translation:
lean 3 declaration is
@@ -871,7 +871,7 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
run_tac
is_bounded_default) :
limsup u f ≤ limsup u g :=
- limsupₛ_le_limsupₛ_of_le (map_mono h) hf hg
+ limsSup_le_limsSup_of_le (map_mono h) hf hg
#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_le
/- warning: filter.liminf_le_liminf_of_le -> Filter.liminf_le_liminf_of_le is a dubious translation:
@@ -891,28 +891,28 @@ theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g :
run_tac
is_bounded_default) :
liminf u f ≤ liminf u g :=
- liminfₛ_le_liminfₛ_of_le (map_mono h) hf hg
+ limsInf_le_limsInf_of_le (map_mono h) hf hg
#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_le
-/- warning: filter.Limsup_principal -> Filter.limsupₛ_principal is a dubious translation:
+/- warning: filter.Limsup_principal -> Filter.limsSup_principal is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsupₛ.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsupₛ.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_principal Filter.limsupₛ_principalₓ'. -/
-theorem limsupₛ_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsupₛ (𝓟 s) = supₛ s :=
- by simp [Limsup] <;> exact cinfₛ_upper_bounds_eq_csupₛ h hs
-#align filter.Limsup_principal Filter.limsupₛ_principal
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α _inst_1 (Filter.principal.{u1} α s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_principal Filter.limsSup_principalₓ'. -/
+theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsSup (𝓟 s) = sSup s :=
+ by simp [Limsup] <;> exact csInf_upper_bounds_eq_csSup h hs
+#align filter.Limsup_principal Filter.limsSup_principal
-/- warning: filter.Liminf_principal -> Filter.liminfₛ_principal is a dubious translation:
+/- warning: filter.Liminf_principal -> Filter.limsInf_principal is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.liminfₛ.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsInf.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.liminfₛ.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_principal Filter.liminfₛ_principalₓ'. -/
-theorem liminfₛ_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : liminfₛ (𝓟 s) = infₛ s :=
- @limsupₛ_principal αᵒᵈ _ s h hs
-#align filter.Liminf_principal Filter.liminfₛ_principal
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (Filter.limsInf.{u1} α _inst_1 (Filter.principal.{u1} α s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_principal Filter.limsInf_principalₓ'. -/
+theorem limsInf_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : limsInf (𝓟 s) = sInf s :=
+ @limsSup_principal αᵒᵈ _ s h hs
+#align filter.Liminf_principal Filter.limsInf_principal
#print Filter.limsup_congr /-
theorem limsup_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
@@ -954,7 +954,7 @@ theorem liminf_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter
#print Filter.limsup_const /-
theorem limsup_const {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : limsup (fun x => b) f = b := by
- simpa only [limsup_eq, eventually_const] using cinfₛ_Ici
+ simpa only [limsup_eq, eventually_const] using csInf_Ici
#align filter.limsup_const Filter.limsup_const
-/
@@ -971,49 +971,49 @@ section CompleteLattice
variable [CompleteLattice α]
-/- warning: filter.Limsup_bot -> Filter.limsupₛ_bot is a dubious translation:
+/- warning: filter.Limsup_bot -> Filter.limsSup_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_bot Filter.limsupₛ_botₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_bot Filter.limsSup_botₓ'. -/
@[simp]
-theorem limsupₛ_bot : limsupₛ (⊥ : Filter α) = ⊥ :=
- bot_unique <| infₛ_le <| by simp
-#align filter.Limsup_bot Filter.limsupₛ_bot
+theorem limsSup_bot : limsSup (⊥ : Filter α) = ⊥ :=
+ bot_unique <| sInf_le <| by simp
+#align filter.Limsup_bot Filter.limsSup_bot
-/- warning: filter.Liminf_bot -> Filter.liminfₛ_bot is a dubious translation:
+/- warning: filter.Liminf_bot -> Filter.limsInf_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_bot Filter.liminfₛ_botₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_bot Filter.limsInf_botₓ'. -/
@[simp]
-theorem liminfₛ_bot : liminfₛ (⊥ : Filter α) = ⊤ :=
- top_unique <| le_supₛ <| by simp
-#align filter.Liminf_bot Filter.liminfₛ_bot
+theorem limsInf_bot : limsInf (⊥ : Filter α) = ⊤ :=
+ top_unique <| le_sSup <| by simp
+#align filter.Liminf_bot Filter.limsInf_bot
-/- warning: filter.Limsup_top -> Filter.limsupₛ_top is a dubious translation:
+/- warning: filter.Limsup_top -> Filter.limsSup_top is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_top Filter.limsupₛ_topₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_top Filter.limsSup_topₓ'. -/
@[simp]
-theorem limsupₛ_top : limsupₛ (⊤ : Filter α) = ⊤ :=
- top_unique <| le_infₛ <| by simp [eq_univ_iff_forall] <;> exact fun b hb => top_unique <| hb _
-#align filter.Limsup_top Filter.limsupₛ_top
+theorem limsSup_top : limsSup (⊤ : Filter α) = ⊤ :=
+ top_unique <| le_sInf <| by simp [eq_univ_iff_forall] <;> exact fun b hb => top_unique <| hb _
+#align filter.Limsup_top Filter.limsSup_top
-/- warning: filter.Liminf_top -> Filter.liminfₛ_top is a dubious translation:
+/- warning: filter.Liminf_top -> Filter.limsInf_top is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.hasTop.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_top Filter.liminfₛ_topₓ'. -/
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (Top.top.{u1} (Filter.{u1} α) (Filter.instTopFilter.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_top Filter.limsInf_topₓ'. -/
@[simp]
-theorem liminfₛ_top : liminfₛ (⊤ : Filter α) = ⊥ :=
- bot_unique <| supₛ_le <| by simp [eq_univ_iff_forall] <;> exact fun b hb => bot_unique <| hb _
-#align filter.Liminf_top Filter.liminfₛ_top
+theorem limsInf_top : limsInf (⊤ : Filter α) = ⊥ :=
+ bot_unique <| sSup_le <| by simp [eq_univ_iff_forall] <;> exact fun b hb => bot_unique <| hb _
+#align filter.Liminf_top Filter.limsInf_top
/- warning: filter.blimsup_false -> Filter.blimsup_false is a dubious translation:
lean 3 declaration is
@@ -1047,7 +1047,7 @@ Case conversion may be inaccurate. Consider using '#align filter.limsup_const_bo
theorem limsup_const_bot {f : Filter β} : limsup (fun x : β => (⊥ : α)) f = (⊥ : α) :=
by
rw [limsup_eq, eq_bot_iff]
- exact infₛ_le (eventually_of_forall fun x => le_rfl)
+ exact sInf_le (eventually_of_forall fun x => le_rfl)
#align filter.limsup_const_bot Filter.limsup_const_bot
/- warning: filter.liminf_const_top -> Filter.liminf_const_top is a dubious translation:
@@ -1061,123 +1061,123 @@ theorem liminf_const_top {f : Filter β} : liminf (fun x : β => (⊤ : α)) f =
@limsup_const_bot αᵒᵈ β _ _
#align filter.liminf_const_top Filter.liminf_const_top
-/- warning: filter.has_basis.Limsup_eq_infi_Sup -> Filter.HasBasis.limsupₛ_eq_infᵢ_supₛ is a dubious translation:
+/- warning: filter.has_basis.Limsup_eq_infi_Sup -> Filter.HasBasis.limsSup_eq_iInf_sSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, u2} α ι f p s) -> (Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, u2} α ι f p s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, u2} α ι f p s) -> (Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsupₛ_eq_infᵢ_supₛₓ'. -/
-theorem HasBasis.limsupₛ_eq_infᵢ_supₛ {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
- limsupₛ f = ⨅ (i) (hi : p i), supₛ (s i) :=
- le_antisymm (le_infᵢ₂ fun i hi => infₛ_le <| h.eventually_iff.2 ⟨i, hi, fun x => le_supₛ⟩)
- (le_infₛ fun a ha =>
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, u2} α ι f p s) -> (Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSupₓ'. -/
+theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
+ limsSup f = ⨅ (i) (hi : p i), sSup (s i) :=
+ le_antisymm (le_iInf₂ fun i hi => sInf_le <| h.eventually_iff.2 ⟨i, hi, fun x => le_sSup⟩)
+ (le_sInf fun a ha =>
let ⟨i, hi, ha⟩ := h.eventually_iff.1 ha
- infᵢ₂_le_of_le _ hi <| supₛ_le ha)
-#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsupₛ_eq_infᵢ_supₛ
+ iInf₂_le_of_le _ hi <| sSup_le ha)
+#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSup
-/- warning: filter.has_basis.Liminf_eq_supr_Inf -> Filter.HasBasis.liminfₛ_eq_supᵢ_infₛ is a dubious translation:
+/- warning: filter.has_basis.Liminf_eq_supr_Inf -> Filter.HasBasis.limsInf_eq_iSup_sInf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, succ u2} α ι f p s) -> (Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
+ forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u1} α)} {f : Filter.{u1} α}, (Filter.HasBasis.{u1, succ u2} α ι f p s) -> (Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (s i)))))
but is expected to have type
- forall {α : Type.{u2}} {ι : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {s : ι -> (Set.{u2} α)} {f : Filter.{u2} α}, (Filter.HasBasis.{u2, succ u1} α ι f p s) -> (Eq.{succ u2} α (Filter.liminfₛ.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) f) (supᵢ.{u2, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) ι (fun (i : ι) => supᵢ.{u2, 0} α (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (p i) (fun (hi : p i) => InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (s i)))))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.liminfₛ_eq_supᵢ_infₛₓ'. -/
-theorem HasBasis.liminfₛ_eq_supᵢ_infₛ {p : ι → Prop} {s : ι → Set α} {f : Filter α}
- (h : f.HasBasis p s) : liminfₛ f = ⨆ (i) (hi : p i), infₛ (s i) :=
- @HasBasis.limsupₛ_eq_infᵢ_supₛ αᵒᵈ _ _ _ _ _ h
-#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.liminfₛ_eq_supᵢ_infₛ
+ forall {α : Type.{u2}} {ι : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {s : ι -> (Set.{u2} α)} {f : Filter.{u2} α}, (Filter.HasBasis.{u2, succ u1} α ι f p s) -> (Eq.{succ u2} α (Filter.limsInf.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) f) (iSup.{u2, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) ι (fun (i : ι) => iSup.{u2, 0} α (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (p i) (fun (hi : p i) => InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (s i)))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInfₓ'. -/
+theorem HasBasis.limsInf_eq_iSup_sInf {p : ι → Prop} {s : ι → Set α} {f : Filter α}
+ (h : f.HasBasis p s) : limsInf f = ⨆ (i) (hi : p i), sInf (s i) :=
+ @HasBasis.limsSup_eq_iInf_sSup αᵒᵈ _ _ _ _ _ h
+#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInf
-/- warning: filter.Limsup_eq_infi_Sup -> Filter.limsupₛ_eq_infᵢ_supₛ is a dubious translation:
+/- warning: filter.Limsup_eq_infi_Sup -> Filter.limsSup_eq_iInf_sSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (infᵢ.{u1, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) => SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iInf.{u1, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) => SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsupₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (infᵢ.{u1, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) => SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
-Case conversion may be inaccurate. Consider using '#align filter.Limsup_eq_infi_Sup Filter.limsupₛ_eq_infᵢ_supₛₓ'. -/
-theorem limsupₛ_eq_infᵢ_supₛ {f : Filter α} : limsupₛ f = ⨅ s ∈ f, supₛ s :=
- f.basis_sets.limsupₛ_eq_infᵢ_supₛ
-#align filter.Limsup_eq_infi_Sup Filter.limsupₛ_eq_infᵢ_supₛ
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iInf.{u1, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) => SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+Case conversion may be inaccurate. Consider using '#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSupₓ'. -/
+theorem limsSup_eq_iInf_sSup {f : Filter α} : limsSup f = ⨅ s ∈ f, sSup s :=
+ f.basis_sets.limsSup_eq_iInf_sSup
+#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSup
-/- warning: filter.Liminf_eq_supr_Inf -> Filter.liminfₛ_eq_supᵢ_infₛ is a dubious translation:
+/- warning: filter.Liminf_eq_supr_Inf -> Filter.limsInf_eq_iSup_sInf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (supᵢ.{u1, succ u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) => InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iSup.{u1, succ u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) => InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.liminfₛ.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (supᵢ.{u1, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) => InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
-Case conversion may be inaccurate. Consider using '#align filter.Liminf_eq_supr_Inf Filter.liminfₛ_eq_supᵢ_infₛₓ'. -/
-theorem liminfₛ_eq_supᵢ_infₛ {f : Filter α} : liminfₛ f = ⨆ s ∈ f, infₛ s :=
- @limsupₛ_eq_infᵢ_supₛ αᵒᵈ _ _
-#align filter.Liminf_eq_supr_Inf Filter.liminfₛ_eq_supᵢ_infₛ
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u1} α}, Eq.{succ u1} α (Filter.limsInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) f) (iSup.{u1, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) => InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+Case conversion may be inaccurate. Consider using '#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInfₓ'. -/
+theorem limsInf_eq_iSup_sInf {f : Filter α} : limsInf f = ⨆ s ∈ f, sInf s :=
+ @limsSup_eq_iInf_sSup αᵒᵈ _ _
+#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInf
-/- warning: filter.limsup_le_supr -> Filter.limsup_le_supᵢ is a dubious translation:
+/- warning: filter.limsup_le_supr -> Filter.limsup_le_iSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_le_supr Filter.limsup_le_supᵢₓ'. -/
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_le_supr Filter.limsup_le_iSupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-theorem limsup_le_supᵢ {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
- limsupₛ_le_of_le
+theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
+ limsSup_le_of_le
(by
run_tac
is_bounded_default)
- (eventually_of_forall (le_supᵢ u))
-#align filter.limsup_le_supr Filter.limsup_le_supᵢ
+ (eventually_of_forall (le_iSup u))
+#align filter.limsup_le_supr Filter.limsup_le_iSup
-/- warning: filter.infi_le_liminf -> Filter.infᵢ_le_liminf is a dubious translation:
+/- warning: filter.infi_le_liminf -> Filter.iInf_le_liminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
-Case conversion may be inaccurate. Consider using '#align filter.infi_le_liminf Filter.infᵢ_le_liminfₓ'. -/
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
+Case conversion may be inaccurate. Consider using '#align filter.infi_le_liminf Filter.iInf_le_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-theorem infᵢ_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
+theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
le_liminf_of_le
(by
run_tac
is_bounded_default)
- (eventually_of_forall (infᵢ_le u))
-#align filter.infi_le_liminf Filter.infᵢ_le_liminf
+ (eventually_of_forall (iInf_le u))
+#align filter.infi_le_liminf Filter.iInf_le_liminf
-/- warning: filter.limsup_eq_infi_supr -> Filter.limsup_eq_infᵢ_supᵢ is a dubious translation:
+/- warning: filter.limsup_eq_infi_supr -> Filter.limsup_eq_iInf_iSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => u a)))))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => u a)))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => u a)))))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr Filter.limsup_eq_infᵢ_supᵢₓ'. -/
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => u a)))))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSupₓ'. -/
/-- In a complete lattice, the limsup of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
-theorem limsup_eq_infᵢ_supᵢ {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
- (f.basis_sets.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, id]
-#align filter.limsup_eq_infi_supr Filter.limsup_eq_infᵢ_supᵢ
+theorem limsup_eq_iInf_iSup {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
+ (f.basis_sets.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
+#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSup
-/- warning: filter.limsup_eq_infi_supr_of_nat -> Filter.limsup_eq_infᵢ_supᵢ_of_nat is a dubious translation:
+/- warning: filter.limsup_eq_infi_supr_of_nat -> Filter.limsup_eq_iInf_iSup_of_nat is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_infᵢ_supᵢ_of_natₓ'. -/
-theorem limsup_eq_infᵢ_supᵢ_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
- (atTop_basis.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, infᵢ_const] <;> rfl
-#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_infᵢ_supᵢ_of_nat
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_iInf_iSup_of_natₓ'. -/
+theorem limsup_eq_iInf_iSup_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
+ (atTop_basis.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, iInf_const] <;> rfl
+#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_iInf_iSup_of_nat
-/- warning: filter.limsup_eq_infi_supr_of_nat' -> Filter.limsup_eq_infᵢ_supᵢ_of_nat' is a dubious translation:
+/- warning: filter.limsup_eq_infi_supr_of_nat' -> Filter.limsup_eq_iInf_iSup_of_nat' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n))))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_infᵢ_supᵢ_of_nat'ₓ'. -/
-theorem limsup_eq_infᵢ_supᵢ_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
- simp only [limsup_eq_infi_supr_of_nat, supᵢ_ge_eq_supᵢ_nat_add]
-#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_infᵢ_supᵢ_of_nat'
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n))))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'ₓ'. -/
+theorem limsup_eq_iInf_iSup_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
+ simp only [limsup_eq_infi_supr_of_nat, iSup_ge_eq_iSup_nat_add]
+#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'
-/- warning: filter.has_basis.limsup_eq_infi_supr -> Filter.HasBasis.limsup_eq_infᵢ_supᵢ is a dubious translation:
+/- warning: filter.has_basis.limsup_eq_infi_supr -> Filter.HasBasis.limsup_eq_iInf_iSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u2} β)} {f : Filter.{u2} β} {u : β -> α}, (Filter.HasBasis.{u2, succ u3} β ι f p s) -> (Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) => u a))))))
+ forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u2} β)} {f : Filter.{u2} β} {u : β -> α}, (Filter.HasBasis.{u2, succ u3} β ι f p s) -> (Eq.{succ u1} α (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) => u a))))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u3} β)} {f : Filter.{u3} β} {u : β -> α}, (Filter.HasBasis.{u3, succ u2} β ι f p s) -> (Eq.{succ u1} α (Filter.limsup.{u1, u3} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) => u a))))))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_infᵢ_supᵢₓ'. -/
-theorem HasBasis.limsup_eq_infᵢ_supᵢ {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
+ forall {α : Type.{u1}} {β : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u3} β)} {f : Filter.{u3} β} {u : β -> α}, (Filter.HasBasis.{u3, succ u2} β ι f p s) -> (Eq.{succ u1} α (Filter.limsup.{u1, u3} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) => u a))))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSupₓ'. -/
+theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : limsup u f = ⨅ (i) (hi : p i), ⨆ a ∈ s i, u a :=
- (h.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, id]
-#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_infᵢ_supᵢ
+ (h.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
+#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSup
/- warning: filter.blimsup_congr' -> Filter.blimsup_congr' is a dubious translation:
lean 3 declaration is
@@ -1207,147 +1207,147 @@ theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
@blimsup_congr' αᵒᵈ β _ _ _ _ _ h
#align filter.bliminf_congr' Filter.bliminf_congr'
-/- warning: filter.blimsup_eq_infi_bsupr -> Filter.blimsup_eq_infᵢ_bsupᵢ is a dubious translation:
+/- warning: filter.blimsup_eq_infi_bsupr -> Filter.blimsup_eq_iInf_biSup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) (fun (hb : And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) => u b)))))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) (fun (hb : And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) => u b)))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) (fun (hb : And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) => u b)))))
-Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_infᵢ_bsupᵢₓ'. -/
-theorem blimsup_eq_infᵢ_bsupᵢ {f : Filter β} {p : β → Prop} {u : β → α} :
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) (fun (hb : And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) => u b)))))
+Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSupₓ'. -/
+theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
blimsup u f p = ⨅ s ∈ f, ⨆ (b) (hb : p b ∧ b ∈ s), u b :=
by
- refine' le_antisymm (infₛ_le_infₛ _) (infi_le_iff.mpr fun a ha => le_Inf_iff.mpr fun a' ha' => _)
+ refine' le_antisymm (sInf_le_sInf _) (infi_le_iff.mpr fun a ha => le_Inf_iff.mpr fun a' ha' => _)
· rintro - ⟨s, rfl⟩
- simp only [mem_set_of_eq, le_infᵢ_iff]
+ simp only [mem_set_of_eq, le_iInf_iff]
conv =>
congr
ext
rw [Imp.swap]
refine'
eventually_imp_distrib_left.mpr fun h => eventually_iff_exists_mem.2 ⟨s, h, fun x h₁ h₂ => _⟩
- exact @le_supᵢ₂ α β (fun b => p b ∧ b ∈ s) _ (fun b hb => u b) x ⟨h₂, h₁⟩
+ exact @le_iSup₂ α β (fun b => p b ∧ b ∈ s) _ (fun b hb => u b) x ⟨h₂, h₁⟩
· obtain ⟨s, hs, hs'⟩ := eventually_iff_exists_mem.mp ha'
simp_rw [Imp.swap] at hs'
- exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [supᵢ₂_le_iff, and_imp] )
-#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_infᵢ_bsupᵢ
+ exact (le_infi_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp] )
+#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
-/- warning: filter.blimsup_eq_infi_bsupr_of_nat -> Filter.blimsup_eq_infᵢ_bsupᵢ_of_nat is a dubious translation:
+/- warning: filter.blimsup_eq_infi_bsupr_of_nat -> Filter.blimsup_eq_iInf_biSup_of_nat is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) p) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat Nat.hasLe i j)) (fun (hj : And (p j) (LE.le.{0} Nat Nat.hasLe i j)) => u j))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) p) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat Nat.hasLe i j)) (fun (hj : And (p j) (LE.le.{0} Nat Nat.hasLe i j)) => u j))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) p) (infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat instLENat i j)) (fun (hj : And (p j) (LE.le.{0} Nat instLENat i j)) => u j))))
-Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_infᵢ_bsupᵢ_of_natₓ'. -/
-theorem blimsup_eq_infᵢ_bsupᵢ_of_nat {p : ℕ → Prop} {u : ℕ → α} :
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) p) (iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat instLENat i j)) (fun (hj : And (p j) (LE.le.{0} Nat instLENat i j)) => u j))))
+Case conversion may be inaccurate. Consider using '#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_natₓ'. -/
+theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (hj : p j ∧ i ≤ j), u j := by
- simp only [blimsup_eq_limsup_subtype, mem_preimage, mem_Ici, Function.comp_apply, cinfᵢ_pos,
- supᵢ_subtype, (at_top_basis.comap (coe : { x | p x } → ℕ)).limsup_eq_infᵢ_supᵢ, mem_set_of_eq,
- Subtype.coe_mk, supᵢ_and]
-#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_infᵢ_bsupᵢ_of_nat
+ simp only [blimsup_eq_limsup_subtype, mem_preimage, mem_Ici, Function.comp_apply, ciInf_pos,
+ iSup_subtype, (at_top_basis.comap (coe : { x | p x } → ℕ)).limsup_eq_iInf_iSup, mem_set_of_eq,
+ Subtype.coe_mk, iSup_and]
+#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
-/- warning: filter.liminf_eq_supr_infi -> Filter.liminf_eq_supᵢ_infᵢ is a dubious translation:
+/- warning: filter.liminf_eq_supr_infi -> Filter.liminf_eq_iSup_iInf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => u a)))))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => u a)))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => u a)))))
-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi Filter.liminf_eq_supᵢ_infᵢₓ'. -/
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => u a)))))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInfₓ'. -/
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
-theorem liminf_eq_supᵢ_infᵢ {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
- @limsup_eq_infᵢ_supᵢ αᵒᵈ β _ _ _
-#align filter.liminf_eq_supr_infi Filter.liminf_eq_supᵢ_infᵢ
+theorem liminf_eq_iSup_iInf {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
+ @limsup_eq_iInf_iSup αᵒᵈ β _ _ _
+#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInf
-/- warning: filter.liminf_eq_supr_infi_of_nat -> Filter.liminf_eq_supᵢ_infᵢ_of_nat is a dubious translation:
+/- warning: filter.liminf_eq_supr_infi_of_nat -> Filter.liminf_eq_iSup_iInf_of_nat is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))))
-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_supᵢ_infᵢ_of_natₓ'. -/
-theorem liminf_eq_supᵢ_infᵢ_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
- @limsup_eq_infᵢ_supᵢ_of_nat αᵒᵈ _ u
-#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_supᵢ_infᵢ_of_nat
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_iSup_iInf_of_natₓ'. -/
+theorem liminf_eq_iSup_iInf_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
+ @limsup_eq_iInf_iSup_of_nat αᵒᵈ _ u
+#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_iSup_iInf_of_nat
-/- warning: filter.liminf_eq_supr_infi_of_nat' -> Filter.liminf_eq_supᵢ_infᵢ_of_nat' is a dubious translation:
+/- warning: filter.liminf_eq_supr_infi_of_nat' -> Filter.liminf_eq_iSup_iInf_of_nat' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n))))
-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_supᵢ_infᵢ_of_nat'ₓ'. -/
-theorem liminf_eq_supᵢ_infᵢ_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
- @limsup_eq_infᵢ_supᵢ_of_nat' αᵒᵈ _ _
-#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_supᵢ_infᵢ_of_nat'
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {u : Nat -> α}, Eq.{succ u1} α (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n))))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'ₓ'. -/
+theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
+ @limsup_eq_iInf_iSup_of_nat' αᵒᵈ _ _
+#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'
-/- warning: filter.has_basis.liminf_eq_supr_infi -> Filter.HasBasis.liminf_eq_supᵢ_infᵢ is a dubious translation:
+/- warning: filter.has_basis.liminf_eq_supr_infi -> Filter.HasBasis.liminf_eq_iSup_iInf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u2} β)} {f : Filter.{u2} β} {u : β -> α}, (Filter.HasBasis.{u2, succ u3} β ι f p s) -> (Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) => u a))))))
+ forall {α : Type.{u1}} {β : Type.{u2}} {ι : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u2} β)} {f : Filter.{u2} β} {u : β -> α}, (Filter.HasBasis.{u2, succ u3} β ι f p s) -> (Eq.{succ u1} α (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a (s i)) => u a))))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u3} β)} {f : Filter.{u3} β} {u : β -> α}, (Filter.HasBasis.{u3, succ u2} β ι f p s) -> (Eq.{succ u1} α (Filter.liminf.{u1, u3} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) => u a))))))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_supᵢ_infᵢₓ'. -/
-theorem HasBasis.liminf_eq_supᵢ_infᵢ {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
+ forall {α : Type.{u1}} {β : Type.{u3}} {ι : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {s : ι -> (Set.{u3} β)} {f : Filter.{u3} β} {u : β -> α}, (Filter.HasBasis.{u3, succ u2} β ι f p s) -> (Eq.{succ u1} α (Filter.liminf.{u1, u3} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (p i) (fun (hi : p i) => iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a (s i)) => u a))))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInfₓ'. -/
+theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : liminf u f = ⨆ (i) (hi : p i), ⨅ a ∈ s i, u a :=
- @HasBasis.limsup_eq_infᵢ_supᵢ αᵒᵈ _ _ _ _ _ _ _ h
-#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_supᵢ_infᵢ
+ @HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
+#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
-/- warning: filter.bliminf_eq_supr_binfi -> Filter.bliminf_eq_supᵢ_binfᵢ is a dubious translation:
+/- warning: filter.bliminf_eq_supr_binfi -> Filter.bliminf_eq_iSup_biInf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) (fun (hb : And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) => u b)))))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) s f) => iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) (fun (hb : And (p b) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b s)) => u b)))))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) (fun (hb : And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) => u b)))))
-Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_supᵢ_binfᵢₓ'. -/
-theorem bliminf_eq_supᵢ_binfᵢ {f : Filter β} {p : β → Prop} {u : β → α} :
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Set.{u2} β) (fun (s : Set.{u2} β) => iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) (fun (H : Membership.mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (instMembershipSetFilter.{u2} β) s f) => iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (b : β) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) (fun (hb : And (p b) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b s)) => u b)))))
+Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInfₓ'. -/
+theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
bliminf u f p = ⨆ s ∈ f, ⨅ (b) (hb : p b ∧ b ∈ s), u b :=
- @blimsup_eq_infᵢ_bsupᵢ αᵒᵈ β _ f p u
-#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_supᵢ_binfᵢ
+ @blimsup_eq_iInf_biSup αᵒᵈ β _ f p u
+#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInf
-/- warning: filter.bliminf_eq_supr_binfi_of_nat -> Filter.bliminf_eq_supᵢ_binfᵢ_of_nat is a dubious translation:
+/- warning: filter.bliminf_eq_supr_binfi_of_nat -> Filter.bliminf_eq_iSup_biInf_of_nat is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) p) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat Nat.hasLe i j)) (fun (hj : And (p j) (LE.le.{0} Nat Nat.hasLe i j)) => u j))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) p) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat Nat.hasLe i j)) (fun (hj : And (p j) (LE.le.{0} Nat Nat.hasLe i j)) => u j))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) p) (supᵢ.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat instLENat i j)) (fun (hj : And (p j) (LE.le.{0} Nat instLENat i j)) => u j))))
-Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_supᵢ_binfᵢ_of_natₓ'. -/
-theorem bliminf_eq_supᵢ_binfᵢ_of_nat {p : ℕ → Prop} {u : ℕ → α} :
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Nat -> Prop} {u : Nat -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) p) (iSup.{u1, 1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) Nat (fun (j : Nat) => iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (And (p j) (LE.le.{0} Nat instLENat i j)) (fun (hj : And (p j) (LE.le.{0} Nat instLENat i j)) => u j))))
+Case conversion may be inaccurate. Consider using '#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_natₓ'. -/
+theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
bliminf u atTop p = ⨆ i, ⨅ (j) (hj : p j ∧ i ≤ j), u j :=
- @blimsup_eq_infᵢ_bsupᵢ_of_nat αᵒᵈ _ p u
-#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_supᵢ_binfᵢ_of_nat
+ @blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
+#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
-/- warning: filter.limsup_eq_Inf_Sup -> Filter.limsup_eq_infₛ_supₛ is a dubious translation:
+/- warning: filter.limsup_eq_Inf_Sup -> Filter.limsup_eq_sInf_sSup is a dubious translation:
lean 3 declaration is
- forall {ι : Type.{u1}} {R : Type.{u2}} (F : Filter.{u1} ι) [_inst_2 : CompleteLattice.{u2} R] (a : ι -> R), Eq.{succ u2} R (Filter.limsup.{u2, u1} R ι (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2) a F) (InfSet.infₛ.{u2} R (ConditionallyCompleteLattice.toHasInf.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} (Set.{u1} ι) R (fun (I : Set.{u1} ι) => SupSet.supₛ.{u2} R (ConditionallyCompleteLattice.toHasSup.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} ι R a I)) (Filter.sets.{u1} ι F)))
+ forall {ι : Type.{u1}} {R : Type.{u2}} (F : Filter.{u1} ι) [_inst_2 : CompleteLattice.{u2} R] (a : ι -> R), Eq.{succ u2} R (Filter.limsup.{u2, u1} R ι (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2) a F) (InfSet.sInf.{u2} R (ConditionallyCompleteLattice.toHasInf.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} (Set.{u1} ι) R (fun (I : Set.{u1} ι) => SupSet.sSup.{u2} R (ConditionallyCompleteLattice.toHasSup.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} ι R a I)) (Filter.sets.{u1} ι F)))
but is expected to have type
- forall {ι : Type.{u2}} {R : Type.{u1}} (F : Filter.{u2} ι) [_inst_2 : CompleteLattice.{u1} R] (a : ι -> R), Eq.{succ u1} R (Filter.limsup.{u1, u2} R ι (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2) a F) (InfSet.infₛ.{u1} R (ConditionallyCompleteLattice.toInfSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} (Set.{u2} ι) R (fun (I : Set.{u2} ι) => SupSet.supₛ.{u1} R (ConditionallyCompleteLattice.toSupSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} ι R a I)) (Filter.sets.{u2} ι F)))
-Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_infₛ_supₛₓ'. -/
-theorem limsup_eq_infₛ_supₛ {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
- limsup a F = infₛ ((fun I => supₛ (a '' I)) '' F.sets) :=
+ forall {ι : Type.{u2}} {R : Type.{u1}} (F : Filter.{u2} ι) [_inst_2 : CompleteLattice.{u1} R] (a : ι -> R), Eq.{succ u1} R (Filter.limsup.{u1, u2} R ι (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2) a F) (InfSet.sInf.{u1} R (ConditionallyCompleteLattice.toInfSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} (Set.{u2} ι) R (fun (I : Set.{u2} ι) => SupSet.sSup.{u1} R (ConditionallyCompleteLattice.toSupSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} ι R a I)) (Filter.sets.{u2} ι F)))
+Case conversion may be inaccurate. Consider using '#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSupₓ'. -/
+theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+ limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) :=
by
refine' le_antisymm _ _
· rw [limsup_eq]
- refine' infₛ_le_infₛ fun x hx => _
+ refine' sInf_le_sInf fun x hx => _
rcases(mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
filter_upwards [I_mem_F]with i hi
- exact hI ▸ le_supₛ (mem_image_of_mem _ hi)
+ exact hI ▸ le_sSup (mem_image_of_mem _ hi)
· refine'
le_Inf_iff.mpr fun b hb =>
- infₛ_le_of_le (mem_image_of_mem _ <| filter.mem_sets.mpr hb) <| supₛ_le _
+ sInf_le_of_le (mem_image_of_mem _ <| filter.mem_sets.mpr hb) <| sSup_le _
rintro _ ⟨_, h, rfl⟩
exact h
-#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_infₛ_supₛ
+#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSup
-/- warning: filter.liminf_eq_Sup_Inf -> Filter.liminf_eq_supₛ_infₛ is a dubious translation:
+/- warning: filter.liminf_eq_Sup_Inf -> Filter.liminf_eq_sSup_sInf is a dubious translation:
lean 3 declaration is
- forall {ι : Type.{u1}} {R : Type.{u2}} (F : Filter.{u1} ι) [_inst_2 : CompleteLattice.{u2} R] (a : ι -> R), Eq.{succ u2} R (Filter.liminf.{u2, u1} R ι (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2) a F) (SupSet.supₛ.{u2} R (ConditionallyCompleteLattice.toHasSup.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} (Set.{u1} ι) R (fun (I : Set.{u1} ι) => InfSet.infₛ.{u2} R (ConditionallyCompleteLattice.toHasInf.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} ι R a I)) (Filter.sets.{u1} ι F)))
+ forall {ι : Type.{u1}} {R : Type.{u2}} (F : Filter.{u1} ι) [_inst_2 : CompleteLattice.{u2} R] (a : ι -> R), Eq.{succ u2} R (Filter.liminf.{u2, u1} R ι (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2) a F) (SupSet.sSup.{u2} R (ConditionallyCompleteLattice.toHasSup.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} (Set.{u1} ι) R (fun (I : Set.{u1} ι) => InfSet.sInf.{u2} R (ConditionallyCompleteLattice.toHasInf.{u2} R (CompleteLattice.toConditionallyCompleteLattice.{u2} R _inst_2)) (Set.image.{u1, u2} ι R a I)) (Filter.sets.{u1} ι F)))
but is expected to have type
- forall {ι : Type.{u2}} {R : Type.{u1}} (F : Filter.{u2} ι) [_inst_2 : CompleteLattice.{u1} R] (a : ι -> R), Eq.{succ u1} R (Filter.liminf.{u1, u2} R ι (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2) a F) (SupSet.supₛ.{u1} R (ConditionallyCompleteLattice.toSupSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} (Set.{u2} ι) R (fun (I : Set.{u2} ι) => InfSet.infₛ.{u1} R (ConditionallyCompleteLattice.toInfSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} ι R a I)) (Filter.sets.{u2} ι F)))
-Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_supₛ_infₛₓ'. -/
-theorem liminf_eq_supₛ_infₛ {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
- liminf a F = supₛ ((fun I => infₛ (a '' I)) '' F.sets) :=
- @Filter.limsup_eq_infₛ_supₛ ι (OrderDual R) _ _ a
-#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_supₛ_infₛ
+ forall {ι : Type.{u2}} {R : Type.{u1}} (F : Filter.{u2} ι) [_inst_2 : CompleteLattice.{u1} R] (a : ι -> R), Eq.{succ u1} R (Filter.liminf.{u1, u2} R ι (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2) a F) (SupSet.sSup.{u1} R (ConditionallyCompleteLattice.toSupSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} (Set.{u2} ι) R (fun (I : Set.{u2} ι) => InfSet.sInf.{u1} R (ConditionallyCompleteLattice.toInfSet.{u1} R (CompleteLattice.toConditionallyCompleteLattice.{u1} R _inst_2)) (Set.image.{u2, u1} ι R a I)) (Filter.sets.{u2} ι F)))
+Case conversion may be inaccurate. Consider using '#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInfₓ'. -/
+theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+ liminf a F = sSup ((fun I => sInf (a '' I)) '' F.sets) :=
+ @Filter.limsup_eq_sInf_sSup ι (OrderDual R) _ _ a
+#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInf
#print Filter.liminf_nat_add /-
@[simp]
theorem liminf_nat_add (f : ℕ → α) (k : ℕ) : liminf (fun i => f (i + k)) atTop = liminf f atTop :=
by
simp_rw [liminf_eq_supr_infi_of_nat]
- exact supᵢ_infᵢ_ge_nat_add f k
+ exact iSup_iInf_ge_nat_add f k
#align filter.liminf_nat_add Filter.liminf_nat_add
-/
@@ -1368,7 +1368,7 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x :=
by
rw [liminf_eq]
- refine' supₛ_le fun b hb => _
+ refine' sSup_le fun b hb => _
have hbx : ∃ᶠ a in f, b ≤ x := by
revert h
rw [← not_imp_not, not_frequently, not_frequently]
@@ -1391,7 +1391,7 @@ theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
Case conversion may be inaccurate. Consider using '#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterateₓ'. -/
/-- If `f : α → α` is a morphism of complete lattices, then the limsup of its iterates of any
`a : α` is a fixed point. -/
@@ -1399,20 +1399,20 @@ Case conversion may be inaccurate. Consider using '#align filter.complete_lattic
theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (a : α) :
f (limsup (fun n => (f^[n]) a) atTop) = limsup (fun n => (f^[n]) a) atTop :=
by
- rw [limsup_eq_infi_supr_of_nat', map_infᵢ]
+ rw [limsup_eq_infi_supr_of_nat', map_iInf]
simp_rw [_root_.map_supr, ← Function.comp_apply f, ← Function.iterate_succ' f, ← Nat.add_succ]
- conv_rhs => rw [infᵢ_split _ ((· < ·) (0 : ℕ))]
- simp only [not_lt, le_zero_iff, infᵢ_infᵢ_eq_left, add_zero, infᵢ_nat_gt_zero_eq, left_eq_inf]
- refine' (infᵢ_le (fun i => ⨆ j, (f^[j + (i + 1)]) a) 0).trans _
- simp only [zero_add, Function.comp_apply, supᵢ_le_iff]
- exact fun i => le_supᵢ (fun i => (f^[i]) a) (i + 1)
+ conv_rhs => rw [iInf_split _ ((· < ·) (0 : ℕ))]
+ simp only [not_lt, le_zero_iff, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
+ refine' (iInf_le (fun i => ⨆ j, (f^[j + (i + 1)]) a) 0).trans _
+ simp only [zero_add, Function.comp_apply, iSup_le_iff]
+ exact fun i => le_iSup (fun i => (f^[i]) a) (i + 1)
#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterate
/- warning: filter.complete_lattice_hom.apply_liminf_iterate -> Filter.CompleteLatticeHom.apply_liminf_iterate is a dubious translation:
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (sInfHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.tosInfHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
Case conversion may be inaccurate. Consider using '#align filter.complete_lattice_hom.apply_liminf_iterate Filter.CompleteLatticeHom.apply_liminf_iterateₓ'. -/
/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
`a : α` is a fixed point. -/
@@ -1430,7 +1430,7 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_mono Filter.blimsup_monoₓ'. -/
theorem blimsup_mono (h : ∀ x, p x → q x) : blimsup u f p ≤ blimsup u f q :=
- infₛ_le_infₛ fun a ha => ha.mono <| by tauto
+ sInf_le_sInf fun a ha => ha.mono <| by tauto
#align filter.blimsup_mono Filter.blimsup_mono
/- warning: filter.bliminf_antitone -> Filter.bliminf_antitone is a dubious translation:
@@ -1440,12 +1440,12 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, (forall (x : β), (p x) -> (q x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_antitone Filter.bliminf_antitoneₓ'. -/
theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u f p :=
- supₛ_le_supₛ fun a ha => ha.mono <| by tauto
+ sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
#print Filter.mono_blimsup' /-
theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
- infₛ_le_infₛ fun a ha => (ha.And h).mono fun x hx hx' => (hx.2 hx').trans (hx.1 hx')
+ sInf_le_sInf fun a ha => (ha.And h).mono fun x hx hx' => (hx.2 hx').trans (hx.1 hx')
#align filter.mono_blimsup' Filter.mono_blimsup'
-/
@@ -1461,7 +1461,7 @@ theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsu
#print Filter.mono_bliminf' /-
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
- supₛ_le_supₛ fun a ha => (ha.And h).mono fun x hx hx' => (hx.1 hx').trans (hx.2 hx')
+ sSup_le_sSup fun a ha => (ha.And h).mono fun x hx hx' => (hx.1 hx').trans (hx.2 hx')
#align filter.mono_bliminf' Filter.mono_bliminf'
-/
@@ -1482,7 +1482,7 @@ but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filterₓ'. -/
theorem bliminf_antitone_filter (h : f ≤ g) : bliminf u g p ≤ bliminf u f p :=
- supₛ_le_supₛ fun a ha => ha.filter_mono h
+ sSup_le_sSup fun a ha => ha.filter_mono h
#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filter
/- warning: filter.blimsup_monotone_filter -> Filter.blimsup_monotone_filter is a dubious translation:
@@ -1492,7 +1492,7 @@ but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {g : Filter.{u2} β} {p : β -> Prop} {u : β -> α}, (LE.le.{u2} (Filter.{u2} β) (Preorder.toLE.{u2} (Filter.{u2} β) (PartialOrder.toPreorder.{u2} (Filter.{u2} β) (Filter.instPartialOrderFilter.{u2} β))) f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u g p))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filterₓ'. -/
theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p :=
- infₛ_le_infₛ fun a ha => ha.filter_mono h
+ sInf_le_sInf fun a ha => ha.filter_mono h
#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filter
/- warning: filter.blimsup_and_le_inf -> Filter.blimsup_and_le_inf is a dubious translation:
@@ -1545,7 +1545,7 @@ theorem bliminf_or_le_inf : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f p
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.toInfₛHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.toInfₛHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e) u) f p)
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.tosInfHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α (fun (_x : α) => γ) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ (CompleteLattice.toInfSet.{u2} α _inst_1) (CompleteLattice.toInfSet.{u3} γ _inst_2) (CompleteLatticeHomClass.tosInfHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIsoClass.toCompleteLatticeHomClass.{max u2 u3, u2, u3} (OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) α γ _inst_1 _inst_2 (OrderIso.instOrderIsoClassOrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))))) e) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsupₓ'. -/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
e (blimsup u f p) = blimsup (e ∘ u) f p :=
@@ -1570,25 +1570,25 @@ theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
/- warning: filter.Sup_hom.apply_blimsup_le -> Filter.SupHom.apply_blimsup_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : SupₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (SupₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : SupₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (SupₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (SupₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : SupₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (SupₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p)
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.blimsup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sSupHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sSupHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : SupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Preorder.toLE.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (PartialOrder.toPreorder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteSemilatticeInf.toPartialOrder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteLattice.toCompleteSemilatticeInf.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (SupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (SupₛHomClass.toFunLike.{max u2 u3, u2, u3} (SupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (SupₛHom.instSupₛHomClassSupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (SupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (SupₛHomClass.toFunLike.{max u2 u3, u2, u3} (SupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (SupₛHom.instSupₛHomClassSupₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p)
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Preorder.toLE.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (PartialOrder.toPreorder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteSemilatticeInf.toPartialOrder.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (CompleteLattice.toCompleteSemilatticeInf.{u3} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (sSupHomClass.toFunLike.{max u2 u3, u2, u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sSupHom.instSSupHomClassSSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.blimsup.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.309 : α) => γ) _x) (sSupHomClass.toFunLike.{max u2 u3, u2, u3} (sSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sSupHom.instSSupHomClassSSupHom.{u2, u3} α γ (ConditionallyCompleteLattice.toSupSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_leₓ'. -/
-theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : SupₛHom α γ) :
+theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
g (blimsup u f p) ≤ blimsup (g ∘ u) f p :=
by
simp only [blimsup_eq_infi_bsupr]
- refine' ((OrderHomClass.mono g).map_infᵢ₂_le _).trans _
+ refine' ((OrderHomClass.mono g).map_iInf₂_le _).trans _
simp only [_root_.map_supr]
#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_le
/- warning: filter.Inf_hom.le_apply_bliminf -> Filter.InfHom.le_apply_bliminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (InfₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (InfₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : sInfHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (sInfHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sInfHom.instSInfHomClassSInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (sInfHomClass.toFunLike.{max u2 u3, u2, u3} (sInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (sInfHom.instSInfHomClassSInfHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminfₓ'. -/
-theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : InfₛHom α γ) :
+theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : sInfHom α γ) :
bliminf (g ∘ u) f p ≤ g (bliminf u f p) :=
@SupHom.apply_blimsup_le αᵒᵈ β γᵒᵈ _ f p u _ g.dual
#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminf
@@ -1609,8 +1609,8 @@ Case conversion may be inaccurate. Consider using '#align filter.blimsup_or_eq_s
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q :=
by
refine' le_antisymm _ blimsup_sup_le_or
- simp only [blimsup_eq, infₛ_sup_eq, sup_infₛ_eq, le_infᵢ₂_iff, mem_set_of_eq]
- refine' fun a' ha' a ha => infₛ_le ((ha.And ha').mono fun b h hb => _)
+ simp only [blimsup_eq, sInf_sup_eq, sup_sInf_eq, le_iInf₂_iff, mem_set_of_eq]
+ refine' fun a' ha' a ha => sInf_le ((ha.And ha').mono fun b h hb => _)
exact Or.elim hb (fun hb => le_sup_of_le_left <| h.1 hb) fun hb => le_sup_of_le_right <| h.2 hb
#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_sup
@@ -1633,9 +1633,9 @@ but is expected to have type
Case conversion may be inaccurate. Consider using '#align filter.sup_limsup Filter.sup_limsupₓ'. -/
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f :=
by
- simp only [limsup_eq_infi_supr, supᵢ_sup_eq, sup_infᵢ₂_eq]
+ simp only [limsup_eq_infi_supr, iSup_sup_eq, sup_iInf₂_eq]
congr ; ext s; congr ; ext hs; congr
- exact (bsupᵢ_const (nonempty_of_mem hs)).symm
+ exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
/- warning: filter.inf_liminf -> Filter.inf_liminf is a dubious translation:
@@ -1657,8 +1657,8 @@ Case conversion may be inaccurate. Consider using '#align filter.sup_liminf Filt
theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :=
by
simp only [liminf_eq_supr_infi]
- rw [sup_comm, bsupᵢ_sup (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
- simp_rw [infᵢ₂_sup_eq, @sup_comm _ _ a]
+ rw [sup_comm, biSup_sup (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
+ simp_rw [iInf₂_sup_eq, @sup_comm _ _ a]
#align filter.sup_liminf Filter.sup_liminf
/- warning: filter.inf_limsup -> Filter.inf_limsup is a dubious translation:
@@ -1684,7 +1684,7 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteBooleanAlgebra.{u2} α] (f : Filter.{u1} β) (u : β -> α), Eq.{succ u2} α (HasCompl.compl.{u2} α (BooleanAlgebra.toHasCompl.{u2} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u2} α _inst_1)) (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} α _inst_1)))) u f)) (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} α _inst_1)))) (Function.comp.{succ u1, succ u2, succ u2} β α α (HasCompl.compl.{u2} α (BooleanAlgebra.toHasCompl.{u2} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u2} α _inst_1))) u) f)
Case conversion may be inaccurate. Consider using '#align filter.limsup_compl Filter.limsup_complₓ'. -/
theorem limsup_compl : limsup u fᶜ = liminf (compl ∘ u) f := by
- simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_infᵢ, compl_supᵢ]
+ simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.limsup_compl Filter.limsup_compl
/- warning: filter.liminf_compl -> Filter.liminf_compl is a dubious translation:
@@ -1694,7 +1694,7 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteBooleanAlgebra.{u2} α] (f : Filter.{u1} β) (u : β -> α), Eq.{succ u2} α (HasCompl.compl.{u2} α (BooleanAlgebra.toHasCompl.{u2} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u2} α _inst_1)) (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} α _inst_1)))) u f)) (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} α _inst_1)))) (Function.comp.{succ u1, succ u2, succ u2} β α α (HasCompl.compl.{u2} α (BooleanAlgebra.toHasCompl.{u2} α (CompleteBooleanAlgebra.toBooleanAlgebra.{u2} α _inst_1))) u) f)
Case conversion may be inaccurate. Consider using '#align filter.liminf_compl Filter.liminf_complₓ'. -/
theorem liminf_compl : liminf u fᶜ = limsup (compl ∘ u) f := by
- simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_infᵢ, compl_supᵢ]
+ simp only [limsup_eq_infi_supr, liminf_eq_supr_infi, compl_iInf, compl_iSup]
#align filter.liminf_compl Filter.liminf_compl
/- warning: filter.limsup_sdiff -> Filter.limsup_sdiff is a dubious translation:
@@ -1706,8 +1706,8 @@ Case conversion may be inaccurate. Consider using '#align filter.limsup_sdiff Fi
theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f :=
by
simp only [limsup_eq_infi_supr, sdiff_eq]
- rw [binfᵢ_inf (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
- simp_rw [inf_comm, inf_supᵢ₂_eq, inf_comm]
+ rw [biInf_inf (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
+ simp_rw [inf_comm, inf_iSup₂_eq, inf_comm]
#align filter.limsup_sdiff Filter.limsup_sdiff
/- warning: filter.liminf_sdiff -> Filter.liminf_sdiff is a dubious translation:
@@ -1775,7 +1775,7 @@ Case conversion may be inaccurate. Consider using '#align filter.cofinite.blimin
theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x ∉ s n }.Finite } :=
by
rw [← compl_inj_iff]
- simpa only [bliminf_eq_supr_binfi, compl_infᵢ, compl_supᵢ, ← blimsup_eq_infi_bsupr,
+ simpa only [bliminf_eq_supr_binfi, compl_iInf, compl_iSup, ← blimsup_eq_infi_bsupr,
cofinite.blimsup_set_eq]
#align filter.cofinite.bliminf_set_eq Filter.cofinite.bliminf_set_eq
@@ -1840,28 +1840,28 @@ end SetLattice
section ConditionallyCompleteLinearOrder
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.frequently_lt_of_lt_limsupₛ /-
-theorem frequently_lt_of_lt_limsupₛ {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
+#print Filter.frequently_lt_of_lt_limsSup /-
+theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
is_bounded_default)
- (h : a < limsupₛ f) : ∃ᶠ n in f, a < n :=
+ (h : a < limsSup f) : ∃ᶠ n in f, a < n :=
by
contrapose! h
simp only [not_frequently, not_lt] at h
exact Limsup_le_of_le hf h
-#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsupₛ
+#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
-/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
-#print Filter.frequently_lt_of_liminfₛ_lt /-
-theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
+#print Filter.frequently_lt_of_limsInf_lt /-
+theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by
run_tac
is_bounded_default)
- (h : liminfₛ f < a) : ∃ᶠ n in f, n < a :=
- @frequently_lt_of_lt_limsupₛ (OrderDual α) f _ a hf h
-#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_liminfₛ_lt
+ (h : limsInf f < a) : ∃ᶠ n in f, n < a :=
+ @frequently_lt_of_lt_limsSup (OrderDual α) f _ a hf h
+#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
-/
/- warning: filter.eventually_lt_of_lt_liminf -> Filter.eventually_lt_of_lt_liminf is a dubious translation:
@@ -1879,7 +1879,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
∀ᶠ a in f, b < u a :=
by
obtain ⟨c, hc, hbc⟩ : ∃ (c : β)(hc : c ∈ { c : β | ∀ᶠ n : α in f, c ≤ u n }), b < c :=
- exists_lt_of_lt_csupₛ hu h
+ exists_lt_of_lt_csSup hu h
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -654,7 +654,7 @@ warning: filter.limsup_le_of_le -> Filter.limsupₛ_le_of_le is a dubious transl
lean 3 declaration is
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but is expected to have type
- forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4416 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4414 x._@.Mathlib.Order.LiminfLimsup._hyg.4416) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4380) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
+ forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsupₛ_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsupₛ_le_of_le {f : Filter β} {u : β → α} {a}
@@ -820,7 +820,7 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6063 x._@.Mathlib.Order.LiminfLimsup._hyg.6065) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6035) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6106 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6104 x._@.Mathlib.Order.LiminfLimsup._hyg.6106) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6076) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -839,7 +839,7 @@ theorem limsupₛ_le_limsupₛ_of_le {f g : Filter α} (h : f ≤ g)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6188 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6186 x._@.Mathlib.Order.LiminfLimsup._hyg.6188) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6158) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6229 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6227 x._@.Mathlib.Order.LiminfLimsup._hyg.6229) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6199) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -858,7 +858,7 @@ theorem liminfₛ_le_liminfₛ_of_le {f g : Filter α} (h : g ≤ f)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.limsup.{u2, u1} β α _inst_2 u f) (Filter.limsup.{u2, u1} β α _inst_2 u g)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6319 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6317 x._@.Mathlib.Order.LiminfLimsup._hyg.6319) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6289) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6361 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6359 x._@.Mathlib.Order.LiminfLimsup._hyg.6361) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6331) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6315 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6315 x._@.Mathlib.Order.LiminfLimsup._hyg.6317) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6287) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6357 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6357 x._@.Mathlib.Order.LiminfLimsup._hyg.6359) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6329) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -878,7 +878,7 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.liminf.{u2, u1} β α _inst_2 u f) (Filter.liminf.{u2, u1} β α _inst_2 u g)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6445 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6443 x._@.Mathlib.Order.LiminfLimsup._hyg.6445) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6415) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6487 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6485 x._@.Mathlib.Order.LiminfLimsup._hyg.6487) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6457) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6441 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6441 x._@.Mathlib.Order.LiminfLimsup._hyg.6443) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6413) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6483 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6483 x._@.Mathlib.Order.LiminfLimsup._hyg.6485) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6455) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -1868,7 +1868,7 @@ theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLine
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13601 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13603 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13601 x._@.Mathlib.Order.LiminfLimsup._hyg.13603) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13573) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13591 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13593 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13591 x._@.Mathlib.Order.LiminfLimsup._hyg.13593) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13563) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1887,7 +1887,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u a) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13772 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13774 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13772 x._@.Mathlib.Order.LiminfLimsup._hyg.13774) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13744) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13760 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13762 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13760 x._@.Mathlib.Order.LiminfLimsup._hyg.13762) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13732) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1903,7 +1903,7 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13884 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13886 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13884 x._@.Mathlib.Order.LiminfLimsup._hyg.13886) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13856) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13872 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13874 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13872 x._@.Mathlib.Order.LiminfLimsup._hyg.13874) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13844) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1922,7 +1922,7 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14019 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14021 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14019 x._@.Mathlib.Order.LiminfLimsup._hyg.14021) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13991) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14005 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14007 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14005 x._@.Mathlib.Order.LiminfLimsup._hyg.14007) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13977) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1938,7 +1938,7 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14092 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14094 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14092 x._@.Mathlib.Order.LiminfLimsup._hyg.14094) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14064) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14078 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14080 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14078 x._@.Mathlib.Order.LiminfLimsup._hyg.14080) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14050) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1957,7 +1957,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14209 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14211 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14209 x._@.Mathlib.Order.LiminfLimsup._hyg.14211) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14181) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14195 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14197 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14195 x._@.Mathlib.Order.LiminfLimsup._hyg.14197) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14167) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1981,7 +1981,7 @@ open Filter
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14306 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14308 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14306 x._@.Mathlib.Order.LiminfLimsup._hyg.14308) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14330 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14332 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14330 x._@.Mathlib.Order.LiminfLimsup._hyg.14332) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14292 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14294 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14292 x._@.Mathlib.Order.LiminfLimsup._hyg.14294) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14316 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14318 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14316 x._@.Mathlib.Order.LiminfLimsup._hyg.14318) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_compₓ'. -/
theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
@@ -1997,7 +1997,7 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14489 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14491 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14489 x._@.Mathlib.Order.LiminfLimsup._hyg.14491) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14513 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14515 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14513 x._@.Mathlib.Order.LiminfLimsup._hyg.14515) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14475 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14477 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14475 x._@.Mathlib.Order.LiminfLimsup._hyg.14477) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14499 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14501 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14499 x._@.Mathlib.Order.LiminfLimsup._hyg.14501) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_compₓ'. -/
theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
@@ -2009,7 +2009,7 @@ theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14572 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14574 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14572 x._@.Mathlib.Order.LiminfLimsup._hyg.14574) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14596 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14598 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14596 x._@.Mathlib.Order.LiminfLimsup._hyg.14598) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14558 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14560 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14558 x._@.Mathlib.Order.LiminfLimsup._hyg.14560) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14582 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14584 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14582 x._@.Mathlib.Order.LiminfLimsup._hyg.14584) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_compₓ'. -/
theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
@@ -2021,7 +2021,7 @@ theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14655 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14657 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14655 x._@.Mathlib.Order.LiminfLimsup._hyg.14657) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14679 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14681 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14679 x._@.Mathlib.Order.LiminfLimsup._hyg.14681) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14641 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14643 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14641 x._@.Mathlib.Order.LiminfLimsup._hyg.14643) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14665 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14667 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14665 x._@.Mathlib.Order.LiminfLimsup._hyg.14667) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_compₓ'. -/
theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
@@ -2033,7 +2033,7 @@ theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f v) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) (l (Filter.limsup.{u2, u1} β α _inst_1 v f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14753 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14755 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14753 x._@.Mathlib.Order.LiminfLimsup._hyg.14755) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14725) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14802 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14804 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14802 x._@.Mathlib.Order.LiminfLimsup._hyg.14804) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14774) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14739 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14741 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14739 x._@.Mathlib.Order.LiminfLimsup._hyg.14741) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14711) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14788 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14790 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14788 x._@.Mathlib.Order.LiminfLimsup._hyg.14790) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14760) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2058,7 +2058,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str 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(OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat 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(bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd 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but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15050) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14928 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14930 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14928 x._@.Mathlib.Order.LiminfLimsup._hyg.14930) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14900) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14970 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14972 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14970 x._@.Mathlib.Order.LiminfLimsup._hyg.14972) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14942) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15012 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15014 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15012 x._@.Mathlib.Order.LiminfLimsup._hyg.15014) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14984) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15062 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15064 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15062 x._@.Mathlib.Order.LiminfLimsup._hyg.15064) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15034) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2094,7 +2094,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) 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but is expected to have type
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(ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15387) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15465 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15467 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15465 x._@.Mathlib.Order.LiminfLimsup._hyg.15467) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15437) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15313 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15315 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15313 x._@.Mathlib.Order.LiminfLimsup._hyg.15315) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15285) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15355 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15357 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15355 x._@.Mathlib.Order.LiminfLimsup._hyg.15357) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15327) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15397 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15399 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15397 x._@.Mathlib.Order.LiminfLimsup._hyg.15399) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15369) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15447 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15449 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15447 x._@.Mathlib.Order.LiminfLimsup._hyg.15449) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15419) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba
@@ -371,7 +371,7 @@ theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBo
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -383,7 +383,7 @@ theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -1561,7 +1561,7 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p)) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (OrderIso.{u1, u3} α γ (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))) (fun (_x : RelIso.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) => α -> γ) (RelIso.hasCoeToFun.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))))) e) u) f p)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => γ) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α γ) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α γ) α γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α γ)) (RelEmbedding.toEmbedding.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α γ) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α γ) α γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α γ)) (RelEmbedding.toEmbedding.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e))) u) f p)
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (e : OrderIso.{u2, u3} α γ (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2))))), Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p)) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) u) f p)
Case conversion may be inaccurate. Consider using '#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminfₓ'. -/
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
e (bliminf u f p) = bliminf (e ∘ u) f p :=
@@ -1868,7 +1868,7 @@ theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLine
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13637 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13639 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13637 x._@.Mathlib.Order.LiminfLimsup._hyg.13639) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13609) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13601 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13603 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13601 x._@.Mathlib.Order.LiminfLimsup._hyg.13603) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13573) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1887,7 +1887,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u a) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13808 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13810 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13808 x._@.Mathlib.Order.LiminfLimsup._hyg.13810) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13780) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13772 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13774 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13772 x._@.Mathlib.Order.LiminfLimsup._hyg.13774) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13744) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1903,7 +1903,7 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13920 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13922 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13920 x._@.Mathlib.Order.LiminfLimsup._hyg.13922) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13892) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13884 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13886 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13884 x._@.Mathlib.Order.LiminfLimsup._hyg.13886) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13856) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1922,7 +1922,7 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14055 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14057 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14055 x._@.Mathlib.Order.LiminfLimsup._hyg.14057) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14027) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14019 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14021 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14019 x._@.Mathlib.Order.LiminfLimsup._hyg.14021) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13991) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1938,7 +1938,7 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14128 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14130 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14128 x._@.Mathlib.Order.LiminfLimsup._hyg.14130) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14100) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14092 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14094 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14092 x._@.Mathlib.Order.LiminfLimsup._hyg.14094) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14064) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1957,7 +1957,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14245 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14247 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14245 x._@.Mathlib.Order.LiminfLimsup._hyg.14247) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14217) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14209 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14211 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14209 x._@.Mathlib.Order.LiminfLimsup._hyg.14211) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14181) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1981,7 +1981,7 @@ open Filter
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14342 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14344 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14342 x._@.Mathlib.Order.LiminfLimsup._hyg.14344) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14366 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14368 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14366 x._@.Mathlib.Order.LiminfLimsup._hyg.14368) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14306 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14308 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14306 x._@.Mathlib.Order.LiminfLimsup._hyg.14308) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14330 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14332 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14330 x._@.Mathlib.Order.LiminfLimsup._hyg.14332) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_compₓ'. -/
theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
@@ -1997,7 +1997,7 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14525 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14527 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14525 x._@.Mathlib.Order.LiminfLimsup._hyg.14527) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14549 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14551 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14549 x._@.Mathlib.Order.LiminfLimsup._hyg.14551) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14489 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14491 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14489 x._@.Mathlib.Order.LiminfLimsup._hyg.14491) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14513 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14515 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14513 x._@.Mathlib.Order.LiminfLimsup._hyg.14515) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_compₓ'. -/
theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
@@ -2009,7 +2009,7 @@ theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14608 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14610 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14608 x._@.Mathlib.Order.LiminfLimsup._hyg.14610) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14632 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14634 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14632 x._@.Mathlib.Order.LiminfLimsup._hyg.14634) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14572 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14574 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14572 x._@.Mathlib.Order.LiminfLimsup._hyg.14574) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14596 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14598 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14596 x._@.Mathlib.Order.LiminfLimsup._hyg.14598) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_compₓ'. -/
theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
@@ -2021,7 +2021,7 @@ theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14691 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14693 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14691 x._@.Mathlib.Order.LiminfLimsup._hyg.14693) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14715 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14717 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14715 x._@.Mathlib.Order.LiminfLimsup._hyg.14717) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14655 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14657 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14655 x._@.Mathlib.Order.LiminfLimsup._hyg.14657) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14679 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14681 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14679 x._@.Mathlib.Order.LiminfLimsup._hyg.14681) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_compₓ'. -/
theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
@@ -2033,7 +2033,7 @@ theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) (l (Filter.limsup.{u2, u1} β α _inst_1 v f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14789 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14791 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14789 x._@.Mathlib.Order.LiminfLimsup._hyg.14791) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14761) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14838 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14840 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14838 x._@.Mathlib.Order.LiminfLimsup._hyg.14840) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14810) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14753 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14755 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14753 x._@.Mathlib.Order.LiminfLimsup._hyg.14755) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14725) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14802 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14804 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14802 x._@.Mathlib.Order.LiminfLimsup._hyg.14804) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14774) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2058,7 +2058,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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but is expected to have type
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(PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15036) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15114 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15116 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15114 x._@.Mathlib.Order.LiminfLimsup._hyg.15116) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15086) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14944 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14946 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14944 x._@.Mathlib.Order.LiminfLimsup._hyg.14946) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14916) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14986 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14988 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14986 x._@.Mathlib.Order.LiminfLimsup._hyg.14988) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14958) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15028 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15030 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15028 x._@.Mathlib.Order.LiminfLimsup._hyg.15030) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15000) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15078 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15080 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15078 x._@.Mathlib.Order.LiminfLimsup._hyg.15080) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15050) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2094,7 +2094,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) 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but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15423) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15501 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15503 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15501 x._@.Mathlib.Order.LiminfLimsup._hyg.15503) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15473) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15331 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15333 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15331 x._@.Mathlib.Order.LiminfLimsup._hyg.15333) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15303) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15373 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15375 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15373 x._@.Mathlib.Order.LiminfLimsup._hyg.15375) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15345) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15415 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15417 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15415 x._@.Mathlib.Order.LiminfLimsup._hyg.15417) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15387) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15465 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15467 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15465 x._@.Mathlib.Order.LiminfLimsup._hyg.15467) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15437) -> (Eq.{succ u3} γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u2 u3, u2, u3} (RelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) g (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -371,7 +371,7 @@ theorem isBounded_ge_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsBo
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2484 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2486 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2484 x._@.Mathlib.Order.LiminfLimsup._hyg.2486) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2459 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2461 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2459 x._@.Mathlib.Order.LiminfLimsup._hyg.2461) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2485 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2487 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2485 x._@.Mathlib.Order.LiminfLimsup._hyg.2487) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -383,7 +383,7 @@ theorem OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e : α ≃o
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u3} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u3} β γ (GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2)) l (fun (x : γ) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) e (u x))) (Filter.IsBoundedUnder.{u1, u3} α γ (GE.ge.{u1} α (Preorder.toLE.{u1} α _inst_1)) l u)
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2545 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2547 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2545 x._@.Mathlib.Order.LiminfLimsup._hyg.2547) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2570 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2570 x._@.Mathlib.Order.LiminfLimsup._hyg.2572) l u)
+ forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : Preorder.{u3} α] [_inst_2 : Preorder.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) {l : Filter.{u1} γ} {u : γ -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} β γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2546 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.2548 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.LiminfLimsup._hyg.2546 x._@.Mathlib.Order.LiminfLimsup._hyg.2548) l (fun (x : γ) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (u x))) (Filter.IsBoundedUnder.{u3, u1} α γ (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2572 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2574 : α) => GE.ge.{u3} α (Preorder.toLE.{u3} α _inst_1) x._@.Mathlib.Order.LiminfLimsup._hyg.2572 x._@.Mathlib.Order.LiminfLimsup._hyg.2574) l u)
Case conversion may be inaccurate. Consider using '#align order_iso.is_bounded_under_ge_comp OrderIso.isBoundedUnder_ge_compₓ'. -/
@[simp]
theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o β) {l : Filter γ}
@@ -395,7 +395,7 @@ theorem OrderIso.isBoundedUnder_ge_comp [Preorder α] [Preorder β] (e : α ≃o
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2609 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2611 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2609 x._@.Mathlib.Order.LiminfLimsup._hyg.2611) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2636 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2638 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2636 x._@.Mathlib.Order.LiminfLimsup._hyg.2638) l u)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2611 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2613 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2611 x._@.Mathlib.Order.LiminfLimsup._hyg.2613) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2638 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2640 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2638 x._@.Mathlib.Order.LiminfLimsup._hyg.2640) l u)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_inv Filter.isBoundedUnder_le_invₓ'. -/
@[simp, to_additive]
theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
@@ -408,7 +408,7 @@ theorem isBoundedUnder_le_inv [OrderedCommGroup α] {l : Filter β} {u : β →
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OrderedCommGroup.{u1} α] {l : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l (fun (x : β) => Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) (u x))) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)))) l u)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2679 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2681 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2679 x._@.Mathlib.Order.LiminfLimsup._hyg.2681) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2706 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2708 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2706 x._@.Mathlib.Order.LiminfLimsup._hyg.2708) l u)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OrderedCommGroup.{u2} α] {l : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2681 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2683 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2681 x._@.Mathlib.Order.LiminfLimsup._hyg.2683) l (fun (x : β) => Inv.inv.{u2} α (InvOneClass.toInv.{u2} α (DivInvOneMonoid.toInvOneClass.{u2} α (DivisionMonoid.toDivInvOneMonoid.{u2} α (DivisionCommMonoid.toDivisionMonoid.{u2} α (CommGroup.toDivisionCommMonoid.{u2} α (OrderedCommGroup.toCommGroup.{u2} α _inst_1)))))) (u x))) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2708 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2710 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedCommGroup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2708 x._@.Mathlib.Order.LiminfLimsup._hyg.2710) l u)
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inv Filter.isBoundedUnder_ge_invₓ'. -/
@[simp, to_additive]
theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β → α} :
@@ -421,7 +421,7 @@ theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β →
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2751 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2753 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2751 x._@.Mathlib.Order.LiminfLimsup._hyg.2753) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2769 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2771 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2769 x._@.Mathlib.Order.LiminfLimsup._hyg.2771) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2786 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2788 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2786 x._@.Mathlib.Order.LiminfLimsup._hyg.2788) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2753 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2755 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2753 x._@.Mathlib.Order.LiminfLimsup._hyg.2755) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2771 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2773 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2771 x._@.Mathlib.Order.LiminfLimsup._hyg.2773) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2788 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2790 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2788 x._@.Mathlib.Order.LiminfLimsup._hyg.2790) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.sup Filter.IsBoundedUnder.supₓ'. -/
theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≤ ·) u →
@@ -434,7 +434,7 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2983 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2983 x._@.Mathlib.Order.LiminfLimsup._hyg.2985) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3012 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3012 x._@.Mathlib.Order.LiminfLimsup._hyg.3014) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3029 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3029 x._@.Mathlib.Order.LiminfLimsup._hyg.3031) f v))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2987 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2985 x._@.Mathlib.Order.LiminfLimsup._hyg.2987) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3016 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3014 x._@.Mathlib.Order.LiminfLimsup._hyg.3016) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3033 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3031 x._@.Mathlib.Order.LiminfLimsup._hyg.3033) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_supₓ'. -/
@[simp]
theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
@@ -450,7 +450,7 @@ theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β →
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3097 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3097 x._@.Mathlib.Order.LiminfLimsup._hyg.3099) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3115 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3115 x._@.Mathlib.Order.LiminfLimsup._hyg.3117) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3132 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3132 x._@.Mathlib.Order.LiminfLimsup._hyg.3134) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3101 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3099 x._@.Mathlib.Order.LiminfLimsup._hyg.3101) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3119 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3117 x._@.Mathlib.Order.LiminfLimsup._hyg.3119) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3136 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3134 x._@.Mathlib.Order.LiminfLimsup._hyg.3136) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.inf Filter.IsBoundedUnder.infₓ'. -/
theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≥ ·) u →
@@ -462,7 +462,7 @@ theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α}
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3186 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3186 x._@.Mathlib.Order.LiminfLimsup._hyg.3188) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3215 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3215 x._@.Mathlib.Order.LiminfLimsup._hyg.3217) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3232 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3232 x._@.Mathlib.Order.LiminfLimsup._hyg.3234) f v))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3190 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3188 x._@.Mathlib.Order.LiminfLimsup._hyg.3190) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3219 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3217 x._@.Mathlib.Order.LiminfLimsup._hyg.3219) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3236 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3234 x._@.Mathlib.Order.LiminfLimsup._hyg.3236) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_infₓ'. -/
@[simp]
theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
@@ -475,7 +475,7 @@ theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β →
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f (fun (a : β) => Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (u a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3273 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3273 x._@.Mathlib.Order.LiminfLimsup._hyg.3275) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3300 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3300 x._@.Mathlib.Order.LiminfLimsup._hyg.3302) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3317 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3317 x._@.Mathlib.Order.LiminfLimsup._hyg.3319) f u))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3277 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3275 x._@.Mathlib.Order.LiminfLimsup._hyg.3277) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3304 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3302 x._@.Mathlib.Order.LiminfLimsup._hyg.3304) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3321 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3319 x._@.Mathlib.Order.LiminfLimsup._hyg.3321) f u))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_abs Filter.isBoundedUnder_le_absₓ'. -/
theorem isBoundedUnder_le_abs [LinearOrderedAddCommGroup α] {f : Filter β} {u : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => |u a|) ↔
@@ -654,7 +654,7 @@ warning: filter.limsup_le_of_le -> Filter.limsupₛ_le_of_le is a dubious transl
lean 3 declaration is
forall {α : Type.{u_1}} {β : Type.{u_2}} [_inst_1 : ConditionallyCompleteLattice.{u_1} α] {f : Filter.{u_2} β} {u : β -> α} {a : α}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u_1, u_2} α β (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u_2} β (fun (n : β) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (u n) a) f) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α _inst_1))))) (Filter.limsup.{u_1, u_2} α β _inst_1 u f) a)
but is expected to have type
- forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
+ forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4416 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4414 x._@.Mathlib.Order.LiminfLimsup._hyg.4416) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4380) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsupₛ_le_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsupₛ_le_of_le {f : Filter β} {u : β → α} {a}
@@ -820,7 +820,7 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6063 x._@.Mathlib.Order.LiminfLimsup._hyg.6065) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6035) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6106 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6104 x._@.Mathlib.Order.LiminfLimsup._hyg.6106) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6076) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -839,7 +839,7 @@ theorem limsupₛ_le_limsupₛ_of_le {f g : Filter α} (h : f ≤ g)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (autoParamₓ.{0} (Filter.IsBounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd 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Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCobounded.{u1} α (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) g) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
+ forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6188 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6186 x._@.Mathlib.Order.LiminfLimsup._hyg.6188) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6158) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6229 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6227 x._@.Mathlib.Order.LiminfLimsup._hyg.6229) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6199) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -858,7 +858,7 @@ theorem liminfₛ_le_liminfₛ_of_le {f g : Filter α} (h : g ≤ f)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f g) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat 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(String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat 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(Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat 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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6315 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6315 x._@.Mathlib.Order.LiminfLimsup._hyg.6317) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6287) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6357 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6357 x._@.Mathlib.Order.LiminfLimsup._hyg.6359) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6329) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6319 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6317 x._@.Mathlib.Order.LiminfLimsup._hyg.6319) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6289) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6361 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6359 x._@.Mathlib.Order.LiminfLimsup._hyg.6361) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6331) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -878,7 +878,7 @@ theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (forall {u : α -> β}, (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) g u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Filter.liminf.{u2, u1} β α _inst_2 u f) (Filter.liminf.{u2, u1} β α _inst_2 u g)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6441 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6441 x._@.Mathlib.Order.LiminfLimsup._hyg.6443) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6413) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6483 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6483 x._@.Mathlib.Order.LiminfLimsup._hyg.6485) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6455) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6445 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6443 x._@.Mathlib.Order.LiminfLimsup._hyg.6445) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6415) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6487 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6485 x._@.Mathlib.Order.LiminfLimsup._hyg.6487) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6457) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -1391,7 +1391,7 @@ theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.limsup.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
Case conversion may be inaccurate. Consider using '#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterateₓ'. -/
/-- If `f : α → α` is a morphism of complete lattices, then the limsup of its iterates of any
`a : α` is a fixed point. -/
@@ -1412,7 +1412,7 @@ theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (coeFn.{succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (CompleteLatticeHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+ forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (a : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) a) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (Filter.liminf.{u1, 0} α Nat (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) (fun (n : Nat) => Nat.iterate.{succ u1} α (FunLike.coe.{succ u1, succ u1, succ u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => α) _x) (InfₛHomClass.toFunLike.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLattice.toInfSet.{u1} α _inst_1) (CompleteLatticeHomClass.toInfₛHomClass.{u1, u1, u1} (CompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (CompleteLatticeHom.instCompleteLatticeHomClassCompleteLatticeHom.{u1, u1} α α _inst_1 _inst_1))) f) n a) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
Case conversion may be inaccurate. Consider using '#align filter.complete_lattice_hom.apply_liminf_iterate Filter.CompleteLatticeHom.apply_liminf_iterateₓ'. -/
/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
`a : α` is a fixed point. -/
@@ -1586,7 +1586,7 @@ theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : SupₛHom α γ) :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u2, succ u1, succ u3} β α γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (InfₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g) u) f p) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) (fun (_x : InfₛHom.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) => α -> γ) (InfₛHom.hasCoeToFun.{u1, u3} α γ (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) (ConditionallyCompleteLattice.toHasInf.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) g (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.372 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
+ forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {u : β -> α} [_inst_2 : CompleteLattice.{u3} γ] (g : InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))), LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (CompleteSemilatticeInf.toPartialOrder.{u3} γ (CompleteLattice.toCompleteSemilatticeInf.{u3} γ _inst_2)))) (Filter.bliminf.{u3, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2) (Function.comp.{succ u1, succ u2, succ u3} β α γ (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g) u) f p) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.CompleteLattice._hyg.374 : α) => γ) _x) (InfₛHomClass.toFunLike.{max u2 u3, u2, u3} (InfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2))) α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)) (InfₛHom.instInfₛHomClassInfₛHom.{u2, u3} α γ (ConditionallyCompleteLattice.toInfSet.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)) (ConditionallyCompleteLattice.toInfSet.{u3} γ (CompleteLattice.toConditionallyCompleteLattice.{u3} γ _inst_2)))) g (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p))
Case conversion may be inaccurate. Consider using '#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminfₓ'. -/
theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : InfₛHom α γ) :
bliminf (g ∘ u) f p ≤ g (bliminf u f p) :=
@@ -1868,7 +1868,7 @@ theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLine
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u a)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13616 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13618 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13616 x._@.Mathlib.Order.LiminfLimsup._hyg.13618) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13588) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13637 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13639 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13637 x._@.Mathlib.Order.LiminfLimsup._hyg.13639) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13609) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1887,7 +1887,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {f : Filter.{u1} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {u : α -> β} {b : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u a) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13787 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13789 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13787 x._@.Mathlib.Order.LiminfLimsup._hyg.13789) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13759) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13808 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13810 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13808 x._@.Mathlib.Order.LiminfLimsup._hyg.13810) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13780) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
@@ -1903,7 +1903,7 @@ theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearO
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13899 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13901 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13899 x._@.Mathlib.Order.LiminfLimsup._hyg.13901) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13871) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13920 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13922 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13920 x._@.Mathlib.Order.LiminfLimsup._hyg.13922) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13892) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1922,7 +1922,7 @@ theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (Filter.Frequently.{u1} α (fun (x : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14034 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14036 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14034 x._@.Mathlib.Order.LiminfLimsup._hyg.14036) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14006) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14055 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14057 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14055 x._@.Mathlib.Order.LiminfLimsup._hyg.14057) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14027) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1938,7 +1938,7 @@ theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (Filter.limsup.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f)) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) b (u x)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14107 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14109 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14107 x._@.Mathlib.Order.LiminfLimsup._hyg.14109) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14079) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14128 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14130 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14128 x._@.Mathlib.Order.LiminfLimsup._hyg.14130) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14100) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1957,7 +1957,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : Filter.{u1} α} {u : α -> β} {b : β}, (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (Filter.liminf.{u2, u1} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) u f) b) -> (Filter.Frequently.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (u x) b) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14224 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14226 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14224 x._@.Mathlib.Order.LiminfLimsup._hyg.14226) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14196) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14245 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14247 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14245 x._@.Mathlib.Order.LiminfLimsup._hyg.14247) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14217) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
@@ -1981,7 +1981,7 @@ open Filter
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14321 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14323 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14321 x._@.Mathlib.Order.LiminfLimsup._hyg.14323) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14345 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14347 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14345 x._@.Mathlib.Order.LiminfLimsup._hyg.14347) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14342 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14344 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14342 x._@.Mathlib.Order.LiminfLimsup._hyg.14344) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14366 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14368 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14366 x._@.Mathlib.Order.LiminfLimsup._hyg.14368) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_compₓ'. -/
theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
@@ -1997,7 +1997,7 @@ theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14504 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14506 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14504 x._@.Mathlib.Order.LiminfLimsup._hyg.14506) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14528 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14530 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14528 x._@.Mathlib.Order.LiminfLimsup._hyg.14530) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Monotone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14525 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14527 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14525 x._@.Mathlib.Order.LiminfLimsup._hyg.14527) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14549 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14551 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14549 x._@.Mathlib.Order.LiminfLimsup._hyg.14551) l f))
Case conversion may be inaccurate. Consider using '#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_compₓ'. -/
theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
@@ -2009,7 +2009,7 @@ theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMaxOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atTop.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14587 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14589 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14587 x._@.Mathlib.Order.LiminfLimsup._hyg.14589) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14611 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14613 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14611 x._@.Mathlib.Order.LiminfLimsup._hyg.14613) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMaxOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atBot.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atTop.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14608 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14610 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14608 x._@.Mathlib.Order.LiminfLimsup._hyg.14610) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14632 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14634 : β) => GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14632 x._@.Mathlib.Order.LiminfLimsup._hyg.14634) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_compₓ'. -/
theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
@@ -2021,7 +2021,7 @@ theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Nonempty.{succ u2} β] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : NoMinOrder.{u3} γ (Preorder.toLT.{u3} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))) _inst_3 g) -> (Filter.Tendsto.{u2, u3} β γ g (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))))) (Filter.atBot.{u3} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u3, u1} γ α (GE.ge.{u3} γ (Preorder.toLE.{u3} γ _inst_3)) l (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) l f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14670 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14672 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14670 x._@.Mathlib.Order.LiminfLimsup._hyg.14672) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14694 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14696 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14694 x._@.Mathlib.Order.LiminfLimsup._hyg.14696) l f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Nonempty.{succ u3} β] [_inst_2 : LinearOrder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_4 : NoMinOrder.{u2} γ (Preorder.toLT.{u2} γ _inst_3)] {g : β -> γ} {f : α -> β} {l : Filter.{u1} α}, (Antitone.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2))))) _inst_3 g) -> (Filter.Tendsto.{u3, u2} β γ g (Filter.atTop.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) (Filter.atBot.{u2} γ _inst_3)) -> (Iff (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14691 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14693 : γ) => GE.ge.{u2} γ (Preorder.toLE.{u2} γ _inst_3) x._@.Mathlib.Order.LiminfLimsup._hyg.14691 x._@.Mathlib.Order.LiminfLimsup._hyg.14693) l (Function.comp.{succ u1, succ u3, succ u2} α β γ g f)) (Filter.IsBoundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14715 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14717 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (DistribLattice.toLattice.{u3} β (instDistribLattice.{u3} β _inst_2)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14715 x._@.Mathlib.Order.LiminfLimsup._hyg.14717) l f))
Case conversion may be inaccurate. Consider using '#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_compₓ'. -/
theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
@@ -2033,7 +2033,7 @@ theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))) l u) -> (autoParamₓ.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))) f (fun (x : α) => l (v x))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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(OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) (l (Filter.limsup.{u2, u1} β α _inst_1 v f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14768 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14770 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14768 x._@.Mathlib.Order.LiminfLimsup._hyg.14770) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14740) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14817 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14819 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14817 x._@.Mathlib.Order.LiminfLimsup._hyg.14819) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14789) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14789 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14791 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14789 x._@.Mathlib.Order.LiminfLimsup._hyg.14791) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14761) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14838 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14840 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14838 x._@.Mathlib.Order.LiminfLimsup._hyg.14840) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14810) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2058,7 +2058,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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but is expected to have type
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(PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15015) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15092 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15094 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15092 x._@.Mathlib.Order.LiminfLimsup._hyg.15094) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15064) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14980 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14982 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14980 x._@.Mathlib.Order.LiminfLimsup._hyg.14982) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14952) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15022 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15024 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15022 x._@.Mathlib.Order.LiminfLimsup._hyg.15024) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14994) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15064 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15066 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15064 x._@.Mathlib.Order.LiminfLimsup._hyg.15066) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15036) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15114 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15116 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15114 x._@.Mathlib.Order.LiminfLimsup._hyg.15116) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15086) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -2094,7 +2094,7 @@ theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [Conditiona
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (autoParamₓ.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1)))))) f u) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 115 (OfNat.mk.{0} Nat 115 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 95 (OfNat.mk.{0} Nat 95 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 98 (OfNat.mk.{0} Nat 98 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 111 (OfNat.mk.{0} Nat 111 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 110 (OfNat.mk.{0} Nat 110 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 100 (OfNat.mk.{0} Nat 100 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat 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(OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 97 (OfNat.mk.{0} Nat 97 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 117 (OfNat.mk.{0} Nat 117 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne 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but is expected to have type
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x._@.Mathlib.Order.LiminfLimsup._hyg.15341) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15311) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15381 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15383 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15381 x._@.Mathlib.Order.LiminfLimsup._hyg.15383) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15353) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15423 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15425 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15423 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(PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15395) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15472 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15474 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15472 x._@.Mathlib.Order.LiminfLimsup._hyg.15474) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β 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(EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15367 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15369 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15367 x._@.Mathlib.Order.LiminfLimsup._hyg.15369) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15339) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15409 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15411 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15409 x._@.Mathlib.Order.LiminfLimsup._hyg.15411) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15381) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15451 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15453 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15451 x._@.Mathlib.Order.LiminfLimsup._hyg.15453) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15423) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15501 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15503 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15501 x._@.Mathlib.Order.LiminfLimsup._hyg.15503) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15473) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -627,7 +627,7 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
#align filter.bliminf_eq_liminf_subtype Filter.bliminf_eq_liminf_subtype
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.limsupₛ_le_of_le /-
theorem limsupₛ_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by
@@ -638,7 +638,7 @@ theorem limsupₛ_le_of_le {f : Filter α} {a}
#align filter.Limsup_le_of_le Filter.limsupₛ_le_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_liminfₛ_of_le /-
theorem le_liminfₛ_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by
@@ -656,7 +656,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u_1}} [β : ConditionallyCompleteLattice.{u_1} α] {_inst_1 : Filter.{u_1} α} {f : α}, (autoParam.{0} (Filter.IsCobounded.{u_1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.4412 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.4414 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) x._@.Mathlib.Order.LiminfLimsup._hyg.4412 x._@.Mathlib.Order.LiminfLimsup._hyg.4414) _inst_1) _auto._@.Mathlib.Order.LiminfLimsup._hyg.4378) -> (Filter.Eventually.{u_1} α (fun (n : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) n f) _inst_1) -> (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (ConditionallyCompleteLattice.toLattice.{u_1} α β))))) (Filter.limsupₛ.{u_1} α β _inst_1) f)
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_of_le Filter.limsupₛ_le_of_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsupₛ_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by
run_tac
@@ -665,7 +665,7 @@ theorem limsupₛ_le_of_le {f : Filter β} {u : β → α} {a}
cinfₛ_le hf h
#align filter.limsup_le_of_le Filter.limsupₛ_le_of_le
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_liminf_of_le /-
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≥ ·) u := by
@@ -676,7 +676,7 @@ theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
#align filter.le_liminf_of_le Filter.le_liminf_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_limsupₛ_of_le /-
theorem le_limsupₛ_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by
@@ -687,7 +687,7 @@ theorem le_limsupₛ_of_le {f : Filter α} {a}
#align filter.le_Limsup_of_le Filter.le_limsupₛ_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminfₛ_le_of_le /-
theorem liminfₛ_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by
@@ -698,7 +698,7 @@ theorem liminfₛ_le_of_le {f : Filter α} {a}
#align filter.Liminf_le_of_le Filter.liminfₛ_le_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.le_limsup_of_le /-
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≤ ·) u := by
@@ -709,7 +709,7 @@ theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
#align filter.le_limsup_of_le Filter.le_limsup_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminf_le_of_le /-
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
@@ -720,8 +720,8 @@ theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
#align filter.liminf_le_of_le Filter.liminf_le_of_le
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminfₛ_le_limsupₛ /-
theorem liminfₛ_le_limsupₛ {f : Filter α} [NeBot f]
(h₁ : f.IsBounded (· ≤ ·) := by
@@ -739,8 +739,8 @@ theorem liminfₛ_le_limsupₛ {f : Filter α} [NeBot f]
#align filter.Liminf_le_Limsup Filter.liminfₛ_le_limsupₛ
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminf_le_limsup /-
theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
(h : f.IsBoundedUnder (· ≤ ·) u := by
@@ -754,8 +754,8 @@ theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
#align filter.liminf_le_limsup Filter.liminf_le_limsup
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.limsupₛ_le_limsupₛ /-
theorem limsupₛ_le_limsupₛ {f g : Filter α}
(hf : f.IsCobounded (· ≤ ·) := by
@@ -769,8 +769,8 @@ theorem limsupₛ_le_limsupₛ {f g : Filter α}
#align filter.Limsup_le_Limsup Filter.limsupₛ_le_limsupₛ
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminfₛ_le_liminfₛ /-
theorem liminfₛ_le_liminfₛ {f g : Filter α}
(hf : f.IsBounded (· ≥ ·) := by
@@ -784,8 +784,8 @@ theorem liminfₛ_le_liminfₛ {f g : Filter α}
#align filter.Liminf_le_Liminf Filter.liminfₛ_le_liminfₛ
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.limsup_le_limsup /-
theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : u ≤ᶠ[f] v)
@@ -800,8 +800,8 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
#align filter.limsup_le_limsup Filter.limsup_le_limsup
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.liminf_le_liminf /-
theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a ≤ v a)
@@ -822,8 +822,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f g) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6061 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6063 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6061 x._@.Mathlib.Order.LiminfLimsup._hyg.6063) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6033) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6102 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6104 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6102 x._@.Mathlib.Order.LiminfLimsup._hyg.6104) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6074) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.limsupₛ.{u1} α _inst_1 f) (Filter.limsupₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsupₛ_le_limsupₛ_of_le {f g : Filter α} (h : f ≤ g)
(hf : f.IsCobounded (· ≤ ·) := by
run_tac
@@ -841,8 +841,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (autoParam.{0} (Filter.IsBounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6184 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6186 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6184 x._@.Mathlib.Order.LiminfLimsup._hyg.6186) f) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6156) -> (autoParam.{0} (Filter.IsCobounded.{u1} α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6225 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.6227 : α) => GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6225 x._@.Mathlib.Order.LiminfLimsup._hyg.6227) g) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6197) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Filter.liminfₛ.{u1} α _inst_1 f) (Filter.liminfₛ.{u1} α _inst_1 g))
Case conversion may be inaccurate. Consider using '#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminfₛ_le_liminfₛ_of_le {f g : Filter α} (h : g ≤ f)
(hf : f.IsBounded (· ≥ ·) := by
run_tac
@@ -860,8 +860,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) f g) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6315 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6317 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6315 x._@.Mathlib.Order.LiminfLimsup._hyg.6317) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6287) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6357 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6359 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6357 x._@.Mathlib.Order.LiminfLimsup._hyg.6359) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6329) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.limsup.{u1, u2} β α _inst_2 u f) (Filter.limsup.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : f ≤ g)
{u : α → β}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -880,8 +880,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : Filter.{u2} α} {g : Filter.{u2} α}, (LE.le.{u2} (Filter.{u2} α) (Preorder.toLE.{u2} (Filter.{u2} α) (PartialOrder.toPreorder.{u2} (Filter.{u2} α) (Filter.instPartialOrderFilter.{u2} α))) g f) -> (forall {u : α -> β}, (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6441 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6443 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6441 x._@.Mathlib.Order.LiminfLimsup._hyg.6443) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6413) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.6483 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.6485 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.6483 x._@.Mathlib.Order.LiminfLimsup._hyg.6485) g u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.6455) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Filter.liminf.{u1, u2} β α _inst_2 u f) (Filter.liminf.{u1, u2} β α _inst_2 u g)))
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : g ≤ f)
{u : α → β}
(hf : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1112,7 +1112,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n))
Case conversion may be inaccurate. Consider using '#align filter.limsup_le_supr Filter.limsup_le_supᵢₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
theorem limsup_le_supᵢ {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
limsupₛ_le_of_le
(by
@@ -1127,7 +1127,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)) β (fun (n : β) => u n)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f)
Case conversion may be inaccurate. Consider using '#align filter.infi_le_liminf Filter.infᵢ_le_liminfₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
theorem infᵢ_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
le_liminf_of_le
(by
@@ -1839,7 +1839,7 @@ end SetLattice
section ConditionallyCompleteLinearOrder
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.frequently_lt_of_lt_limsupₛ /-
theorem frequently_lt_of_lt_limsupₛ {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by
@@ -1853,7 +1853,7 @@ theorem frequently_lt_of_lt_limsupₛ {f : Filter α} [ConditionallyCompleteLine
#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsupₛ
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
#print Filter.frequently_lt_of_liminfₛ_lt /-
theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by
@@ -1870,7 +1870,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13616 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13618 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13616 x._@.Mathlib.Order.LiminfLimsup._hyg.13618) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13588) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u a)) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminfₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : b < liminf u f)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1889,7 +1889,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} {f : Filter.{u2} α} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {u : α -> β} {b : β}, (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13787 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13789 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13787 x._@.Mathlib.Order.LiminfLimsup._hyg.13789) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13759) -> (Filter.Eventually.{u2} α (fun (a : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u a) b) f)
Case conversion may be inaccurate. Consider using '#align filter.eventually_lt_of_limsup_lt Filter.eventually_lt_of_limsup_ltₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem eventually_lt_of_limsup_lt {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : limsup u f < b)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -1905,7 +1905,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.13899 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.13901 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.13899 x._@.Mathlib.Order.LiminfLimsup._hyg.13901) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.13871) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f))
Case conversion may be inaccurate. Consider using '#align filter.le_limsup_of_frequently_le Filter.le_limsup_of_frequently_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem le_limsup_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, b ≤ u x)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -1924,7 +1924,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (Filter.Frequently.{u2} α (fun (x : α) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f) -> (autoParam.{0} (Filter.IsBoundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14034 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14036 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14034 x._@.Mathlib.Order.LiminfLimsup._hyg.14036) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14006) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b)
Case conversion may be inaccurate. Consider using '#align filter.liminf_le_of_frequently_le Filter.liminf_le_of_frequently_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem liminf_le_of_frequently_le {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β} (hu_le : ∃ᶠ x in f, u x ≤ b)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
@@ -1940,7 +1940,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14107 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14109 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14107 x._@.Mathlib.Order.LiminfLimsup._hyg.14109) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14079) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (Filter.limsup.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f)) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) b (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsupₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
(hu : f.IsCoboundedUnder (· ≤ ·) u := by
@@ -1959,7 +1959,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {f : Filter.{u2} α} {u : α -> β} {b : β}, (autoParam.{0} (Filter.IsCoboundedUnder.{u1, u2} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14224 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14226 : β) => GE.ge.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14224 x._@.Mathlib.Order.LiminfLimsup._hyg.14226) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14196) -> (LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (Filter.liminf.{u1, u2} β α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) u f) b) -> (Filter.Frequently.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (u x) b) f)
Case conversion may be inaccurate. Consider using '#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_ltₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β] {f : Filter α}
{u : α → β} {b : β}
(hu : f.IsCoboundedUnder (· ≥ ·) u := by
@@ -2035,8 +2035,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} β] [_inst_2 : ConditionallyCompleteLattice.{u2} γ] {f : Filter.{u1} α} {v : α -> β} {l : β -> γ} {u : γ -> β}, (GaloisConnection.{u3, u2} β γ (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2)))) l u) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14768 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.14770 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14768 x._@.Mathlib.Order.LiminfLimsup._hyg.14770) f (fun (x : α) => l (v x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14740) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14817 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14819 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeInf.toPartialOrder.{u3} β (Lattice.toSemilatticeInf.{u3} β (ConditionallyCompleteLattice.toLattice.{u3} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14817 x._@.Mathlib.Order.LiminfLimsup._hyg.14819) f v) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14789) -> (LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_2))))) (l (Filter.limsup.{u3, u1} β α _inst_1 v f)) (Filter.limsup.{u2, u1} γ α _inst_2 (fun (x : α) => l (v x)) f))
Case conversion may be inaccurate. Consider using '#align galois_connection.l_limsup_le GaloisConnection.l_limsup_leₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
[ConditionallyCompleteLattice γ] {f : Filter α} {v : α → β} {l : β → γ} {u : γ → β}
(gc : GaloisConnection l u)
@@ -2060,10 +2060,10 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.14959 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.14961 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.14959 x._@.Mathlib.Order.LiminfLimsup._hyg.14961) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14931) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15001 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15003 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15001 x._@.Mathlib.Order.LiminfLimsup._hyg.15003) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.14973) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15043 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15045 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15043 x._@.Mathlib.Order.LiminfLimsup._hyg.15045) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15015) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15092 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15094 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15092 x._@.Mathlib.Order.LiminfLimsup._hyg.15094) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15064) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.limsup.{u2, u1} β α _inst_1 u f)) (Filter.limsup.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.limsup_apply OrderIso.limsup_applyₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [ConditionallyCompleteLattice γ]
{f : Filter α} {u : α → β} (g : β ≃o γ)
(hu : f.IsBoundedUnder (· ≤ ·) u := by
@@ -2096,10 +2096,10 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : ConditionallyCompleteLattice.{u3} γ] {f : Filter.{u1} α} {u : α -> β} (g : OrderIso.{u2, u3} β γ (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2)))))), (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15339 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15341 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15339 x._@.Mathlib.Order.LiminfLimsup._hyg.15341) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15311) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u2, u1} β α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15381 : β) (x._@.Mathlib.Order.LiminfLimsup._hyg.15383 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15381 x._@.Mathlib.Order.LiminfLimsup._hyg.15383) f u) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15353) -> (autoParam.{0} (Filter.IsBoundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15423 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15425 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15423 x._@.Mathlib.Order.LiminfLimsup._hyg.15425) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15395) -> (autoParam.{0} (Filter.IsCoboundedUnder.{u3, u1} γ α (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.15472 : γ) (x._@.Mathlib.Order.LiminfLimsup._hyg.15474 : γ) => GE.ge.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.LiminfLimsup._hyg.15472 x._@.Mathlib.Order.LiminfLimsup._hyg.15474) f (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x))) _auto._@.Mathlib.Order.LiminfLimsup._hyg.15444) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (Filter.liminf.{u2, u1} β α _inst_1 u f)) (Filter.liminf.{u3, u1} γ α _inst_2 (fun (x : α) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} β γ) β γ (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} β γ)) (RelEmbedding.toEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : γ) => LE.le.{u3} γ (Preorder.toLE.{u3} γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) g)) (u x)) f))
Case conversion may be inaccurate. Consider using '#align order_iso.liminf_apply OrderIso.liminf_applyₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
theorem OrderIso.liminf_apply {γ} [ConditionallyCompleteLattice β] [ConditionallyCompleteLattice γ]
{f : Filter α} {u : α → β} (g : β ≃o γ)
(hu : f.IsBoundedUnder (· ≥ ·) u := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -118,9 +118,9 @@ theorem isBounded_principal (s : Set α) : IsBounded r (𝓟 s) ↔ ∃ t, ∀ x
/- warning: filter.is_bounded_sup -> Filter.isBounded_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (HasSup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) f g))
+ forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))))) f g))
but is expected to have type
- forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (HasSup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toHasSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) f g))
+ forall {α : Type.{u1}} {r : α -> α -> Prop} {f : Filter.{u1} α} {g : Filter.{u1} α} [_inst_1 : IsTrans.{u1} α r], (forall (b₁ : α) (b₂ : α), Exists.{succ u1} α (fun (b : α) => And (r b₁ b) (r b₂ b))) -> (Filter.IsBounded.{u1} α r f) -> (Filter.IsBounded.{u1} α r g) -> (Filter.IsBounded.{u1} α r (Sup.sup.{u1} (Filter.{u1} α) (SemilatticeSup.toSup.{u1} (Filter.{u1} α) (Lattice.toSemilatticeSup.{u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toLattice.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))))) f g))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_sup Filter.isBounded_supₓ'. -/
theorem isBounded_sup [IsTrans α r] (hr : ∀ b₁ b₂, ∃ b, r b₁ b ∧ r b₂ b) :
IsBounded r f → IsBounded r g → IsBounded r (f ⊔ g)
@@ -419,9 +419,9 @@ theorem isBoundedUnder_ge_inv [OrderedCommGroup α] {l : Filter β} {u : β →
/- warning: filter.is_bounded_under.sup -> Filter.IsBoundedUnder.sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2751 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2753 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2751 x._@.Mathlib.Order.LiminfLimsup._hyg.2753) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2769 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2771 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2769 x._@.Mathlib.Order.LiminfLimsup._hyg.2771) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2786 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2788 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2786 x._@.Mathlib.Order.LiminfLimsup._hyg.2788) f (fun (a : β) => HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2751 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2753 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2751 x._@.Mathlib.Order.LiminfLimsup._hyg.2753) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2769 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2771 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2769 x._@.Mathlib.Order.LiminfLimsup._hyg.2771) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2786 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2788 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2786 x._@.Mathlib.Order.LiminfLimsup._hyg.2788) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.sup Filter.IsBoundedUnder.supₓ'. -/
theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≤ ·) u →
@@ -432,9 +432,9 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
/- warning: filter.is_bounded_under_le_sup -> Filter.isBoundedUnder_le_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeSup.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2983 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2983 x._@.Mathlib.Order.LiminfLimsup._hyg.2985) f (fun (a : β) => HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3012 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3012 x._@.Mathlib.Order.LiminfLimsup._hyg.3014) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3029 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3029 x._@.Mathlib.Order.LiminfLimsup._hyg.3031) f v))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeSup.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.2983 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.2985 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.2983 x._@.Mathlib.Order.LiminfLimsup._hyg.2985) f (fun (a : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3012 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3014 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3012 x._@.Mathlib.Order.LiminfLimsup._hyg.3014) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3029 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3031 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeSup.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3029 x._@.Mathlib.Order.LiminfLimsup._hyg.3031) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_sup Filter.isBoundedUnder_le_supₓ'. -/
@[simp]
theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β → α} :
@@ -448,9 +448,9 @@ theorem isBoundedUnder_le_sup [SemilatticeSup α] {f : Filter β} {u v : β →
/- warning: filter.is_bounded_under.inf -> Filter.IsBoundedUnder.inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v) -> (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3097 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3097 x._@.Mathlib.Order.LiminfLimsup._hyg.3099) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3115 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3115 x._@.Mathlib.Order.LiminfLimsup._hyg.3117) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3132 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3132 x._@.Mathlib.Order.LiminfLimsup._hyg.3134) f (fun (a : β) => HasInf.inf.{u2} α (SemilatticeInf.toHasInf.{u2} α _inst_1) (u a) (v a)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3097 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3099 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3097 x._@.Mathlib.Order.LiminfLimsup._hyg.3099) f u) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3115 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3117 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3115 x._@.Mathlib.Order.LiminfLimsup._hyg.3117) f v) -> (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3132 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3134 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3132 x._@.Mathlib.Order.LiminfLimsup._hyg.3134) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a)))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under.inf Filter.IsBoundedUnder.infₓ'. -/
theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
f.IsBoundedUnder (· ≥ ·) u →
@@ -460,9 +460,9 @@ theorem IsBoundedUnder.inf [SemilatticeInf α] {f : Filter β} {u v : β → α}
/- warning: filter.is_bounded_under_ge_inf -> Filter.isBoundedUnder_ge_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SemilatticeInf.{u1} α] {f : Filter.{u2} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f (fun (a : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) f v))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3186 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3186 x._@.Mathlib.Order.LiminfLimsup._hyg.3188) f (fun (a : β) => HasInf.inf.{u2} α (SemilatticeInf.toHasInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3215 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3215 x._@.Mathlib.Order.LiminfLimsup._hyg.3217) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3232 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3232 x._@.Mathlib.Order.LiminfLimsup._hyg.3234) f v))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SemilatticeInf.{u2} α] {f : Filter.{u1} β} {u : β -> α} {v : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3186 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3188 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3186 x._@.Mathlib.Order.LiminfLimsup._hyg.3188) f (fun (a : β) => Inf.inf.{u2} α (SemilatticeInf.toInf.{u2} α _inst_1) (u a) (v a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3215 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3217 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3215 x._@.Mathlib.Order.LiminfLimsup._hyg.3217) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3232 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3234 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α _inst_1))) x._@.Mathlib.Order.LiminfLimsup._hyg.3232 x._@.Mathlib.Order.LiminfLimsup._hyg.3234) f v))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_ge_inf Filter.isBoundedUnder_ge_infₓ'. -/
@[simp]
theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β → α} :
@@ -475,7 +475,7 @@ theorem isBoundedUnder_ge_inf [SemilatticeInf α] {f : Filter β} {u v : β →
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {f : Filter.{u2} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f (fun (a : β) => Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (u a))) (And (Filter.IsBoundedUnder.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u) (Filter.IsBoundedUnder.{u1, u2} α β (GE.ge.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) f u))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3273 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3273 x._@.Mathlib.Order.LiminfLimsup._hyg.3275) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3300 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3300 x._@.Mathlib.Order.LiminfLimsup._hyg.3302) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3317 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3317 x._@.Mathlib.Order.LiminfLimsup._hyg.3319) f u))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u2} α] {f : Filter.{u1} β} {u : β -> α}, Iff (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3273 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3275 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3273 x._@.Mathlib.Order.LiminfLimsup._hyg.3275) f (fun (a : β) => Abs.abs.{u2} α (Neg.toHasAbs.{u2} α (NegZeroClass.toNeg.{u2} α (SubNegZeroMonoid.toNegZeroClass.{u2} α (SubtractionMonoid.toSubNegZeroMonoid.{u2} α (SubtractionCommMonoid.toSubtractionMonoid.{u2} α (AddCommGroup.toDivisionAddCommMonoid.{u2} α (OrderedAddCommGroup.toAddCommGroup.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1))))))) (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α (LinearOrderedAddCommGroup.toLinearOrder.{u2} α _inst_1)))))) (u a))) (And (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3300 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3300 x._@.Mathlib.Order.LiminfLimsup._hyg.3302) f u) (Filter.IsBoundedUnder.{u2, u1} α β (fun (x._@.Mathlib.Order.LiminfLimsup._hyg.3317 : α) (x._@.Mathlib.Order.LiminfLimsup._hyg.3319 : α) => GE.ge.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (OrderedAddCommGroup.toPartialOrder.{u2} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} α _inst_1)))) x._@.Mathlib.Order.LiminfLimsup._hyg.3317 x._@.Mathlib.Order.LiminfLimsup._hyg.3319) f u))
Case conversion may be inaccurate. Consider using '#align filter.is_bounded_under_le_abs Filter.isBoundedUnder_le_absₓ'. -/
theorem isBoundedUnder_le_abs [LinearOrderedAddCommGroup α] {f : Filter β} {u : β → α} :
(f.IsBoundedUnder (· ≤ ·) fun a => |u a|) ↔
@@ -1497,9 +1497,9 @@ theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p
/- warning: filter.blimsup_and_le_inf -> Filter.blimsup_and_le_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_and_le_inf Filter.blimsup_and_le_infₓ'. -/
@[simp]
theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p ⊓ blimsup u f q :=
@@ -1508,9 +1508,9 @@ theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f
/- warning: filter.bliminf_sup_le_and -> Filter.bliminf_sup_le_and is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => And (p x) (q x)))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_sup_le_and Filter.bliminf_sup_le_andₓ'. -/
@[simp]
theorem bliminf_sup_le_and : bliminf u f p ⊔ bliminf u f q ≤ bliminf u f fun x => p x ∧ q x :=
@@ -1519,9 +1519,9 @@ theorem bliminf_sup_le_and : bliminf u f p ⊔ bliminf u f q ≤ bliminf u f fun
/- warning: filter.blimsup_sup_le_or -> Filter.blimsup_sup_le_or is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q)) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1)))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q)) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x)))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_sup_le_or Filter.blimsup_sup_le_orₓ'. -/
/-- See also `filter.blimsup_or_eq_sup`. -/
@[simp]
@@ -1531,9 +1531,9 @@ theorem blimsup_sup_le_or : blimsup u f p ⊔ blimsup u f q ≤ blimsup u f fun
/- warning: filter.bliminf_or_le_inf -> Filter.bliminf_or_le_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1)))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_1) u f q))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α _inst_1) u f q))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_or_le_inf Filter.bliminf_or_le_infₓ'. -/
/-- See also `filter.bliminf_or_eq_inf`. -/
@[simp]
@@ -1601,9 +1601,9 @@ variable [CompleteDistribLattice α] {f : Filter β} {p q : β → Prop} {u : β
/- warning: filter.blimsup_or_eq_sup -> Filter.blimsup_or_eq_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f p) (Filter.blimsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f q))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f q))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u2} α (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f p) (Filter.blimsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f q))
Case conversion may be inaccurate. Consider using '#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_supₓ'. -/
@[simp]
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q :=
@@ -1616,35 +1616,43 @@ theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p
/- warning: filter.bliminf_or_eq_inf -> Filter.bliminf_or_eq_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f q))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u1} α (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f p) (Filter.bliminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f q))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f q))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {p : β -> Prop} {q : β -> Prop} {u : β -> α}, Eq.{succ u2} α (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f (fun (x : β) => Or (p x) (q x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f p) (Filter.bliminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f q))
Case conversion may be inaccurate. Consider using '#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_infₓ'. -/
@[simp]
theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p ⊓ bliminf u f q :=
@blimsup_or_eq_sup αᵒᵈ β _ f p q u
#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_inf
-#print Filter.sup_limsup /-
+/- warning: filter.sup_limsup -> Filter.sup_limsup is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} [_inst_2 : Filter.NeBot.{u2} β f] (a : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} [_inst_2 : Filter.NeBot.{u2} β f] (a : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
+Case conversion may be inaccurate. Consider using '#align filter.sup_limsup Filter.sup_limsupₓ'. -/
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f :=
by
simp only [limsup_eq_infi_supr, supᵢ_sup_eq, sup_infᵢ₂_eq]
congr ; ext s; congr ; ext hs; congr
exact (bsupᵢ_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
--/
-#print Filter.inf_liminf /-
+/- warning: filter.inf_liminf -> Filter.inf_liminf is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} [_inst_2 : Filter.NeBot.{u2} β f] (a : α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} [_inst_2 : Filter.NeBot.{u2} β f] (a : α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))))) a (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))))) a (u x)) f)
+Case conversion may be inaccurate. Consider using '#align filter.inf_liminf Filter.inf_liminfₓ'. -/
theorem inf_liminf [NeBot f] (a : α) : a ⊓ liminf u f = liminf (fun x => a ⊓ u x) f :=
@sup_limsup αᵒᵈ β _ f _ _ _
#align filter.inf_liminf Filter.inf_liminf
--/
/- warning: filter.sup_liminf -> Filter.sup_liminf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} (a : α), Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} (a : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.liminf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} (a : α), Eq.{succ u2} α (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) a (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f)) (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) (fun (x : β) => HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) a (u x)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} (a : α), Eq.{succ u2} α (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) a (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f)) (Filter.liminf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) (fun (x : β) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1)))))) a (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.sup_liminf Filter.sup_liminfₓ'. -/
theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :=
by
@@ -1655,9 +1663,9 @@ theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f :
/- warning: filter.inf_limsup -> Filter.inf_limsup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} (a : α), Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteDistribLattice.{u1} α] {f : Filter.{u2} β} {u : β -> α} (a : α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) u f)) (Filter.limsup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1))) (fun (x : β) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (Order.Coframe.toCompleteLattice.{u1} α (CompleteDistribLattice.toCoframe.{u1} α _inst_1)))))) a (u x)) f)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} (a : α), Eq.{succ u2} α (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) a (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f)) (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) (fun (x : β) => HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) a (u x)) f)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteDistribLattice.{u2} α] {f : Filter.{u1} β} {u : β -> α} (a : α), Eq.{succ u2} α (Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) a (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) u f)) (Filter.limsup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))) (fun (x : β) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (Order.Coframe.toCompleteLattice.{u2} α (CompleteDistribLattice.toCoframe.{u2} α _inst_1))))) a (u x)) f)
Case conversion may be inaccurate. Consider using '#align filter.inf_limsup Filter.inf_limsupₓ'. -/
theorem inf_limsup (a : α) : a ⊓ limsup u f = limsup (fun x => a ⊓ u x) f :=
@sup_liminf αᵒᵈ β _ f _ _
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.
@@ -208,7 +208,7 @@ def IsCoboundedUnder (r : α → α → Prop) (f : Filter β) (u : β → α) :=
/-- To check that a filter is frequently bounded, it suffices to have a witness
which bounds `f` at some point for every admissible set.
-This is only an implication, as the other direction is wrong for the trivial filter.-/
+This is only an implication, as the other direction is wrong for the trivial filter. -/
theorem IsCobounded.mk [IsTrans α r] (a : α) (h : ∀ s ∈ f, ∃ x ∈ s, r a x) : f.IsCobounded r :=
⟨a, fun _ s =>
let ⟨_, h₁, h₂⟩ := h _ s
@@ -1050,7 +1050,7 @@ theorem bliminf_or_le_inf_aux_right : (bliminf u f fun x => p x ∨ q x) ≤ bli
bliminf_or_le_inf.trans inf_le_right
/- Porting note: Replaced `e` with `DFunLike.coe e` to override the strange
- coercion to `↑(RelIso.toRelEmbedding e).toEmbedding`.-/
+ coercion to `↑(RelIso.toRelEmbedding e).toEmbedding`. -/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
DFunLike.coe e (blimsup u f p) = blimsup ((DFunLike.coe e) ∘ u) f p := by
simp only [blimsup_eq, map_sInf, Function.comp_apply]
LinearOrderedCommGroupWithZero
(#11716)
Reconstitute the file Algebra.Order.Monoid.WithZero
from three files:
Algebra.Order.Monoid.WithZero.Defs
Algebra.Order.Monoid.WithZero.Basic
Algebra.Order.WithZero
Avoid importing it in many files. Most uses were just to get le_zero_iff
to work on Nat
.
Before
After
@@ -946,7 +946,7 @@ theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (
simp_rw [_root_.map_iSup, ← Function.comp_apply (f := f), ← Function.iterate_succ' f,
← Nat.add_succ]
conv_rhs => rw [iInf_split _ (0 < ·)]
- simp only [not_lt, le_zero_iff, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
+ simp only [not_lt, Nat.le_zero, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
refine' (iInf_le (fun i => ⨆ j, f^[j + (i + 1)] a) 0).trans _
simp only [zero_add, Function.comp_apply, iSup_le_iff]
exact fun i => le_iSup (fun i => f^[i] a) (i + 1)
filter_upwards
(#11208)
This is presumably not exhaustive, but covers about a hundred instances.
Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.
@@ -1123,7 +1123,7 @@ lemma limsup_piecewise {s : Set β} [DecidablePred (· ∈ s)] {v} :
limsup (s.piecewise u v) f = blimsup u f (· ∈ s) ⊔ blimsup v f (· ∉ s) := by
rw [← blimsup_sup_not (p := (· ∈ s))]
refine congr_arg₂ _ (blimsup_congr ?_) (blimsup_congr ?_) <;>
- refine eventually_of_forall fun _ h ↦ ?_ <;> simp [h]
+ filter_upwards with _ h using by simp [h]
lemma liminf_piecewise {s : Set β} [DecidablePred (· ∈ s)] {v} :
liminf (s.piecewise u v) f = bliminf u f (· ∈ s) ⊓ bliminf v f (· ∉ s) :=
ball
and bex
from lemma names (#10816)
ball
for "bounded forall" and bex
for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem
and exists_mem
in the few Set
lemma names that mention them.
Also deprecate ball_image_of_ball
, mem_image_elim
, mem_image_elim_on
since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image
semi-implicit), have obscure names and are completely unused.
@@ -165,7 +165,7 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [Preorder β] [IsDirected β (
rcases hf with ⟨b, hb⟩
haveI : Nonempty β := ⟨b⟩
rw [← image_univ, ← union_compl_self { x | f x ≤ b }, image_union, bddAbove_union]
- exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).bddAbove⟩
+ exact ⟨⟨b, forall_mem_image.2 fun x => id⟩, (hb.image f).bddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
theorem IsBoundedUnder.bddBelow_range_of_cofinite [Preorder β] [IsDirected β (· ≥ ·)] {f : α → β}
Those lemmas have historically been very annoying to use in rw
since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.
Downstream code broken by this change can fix it by adding appropriately many _
s.
Also marks CauSeq.ext
@[ext]
.
Order.BoundedOrder
top_sup_eq
sup_top_eq
bot_sup_eq
sup_bot_eq
top_inf_eq
inf_top_eq
bot_inf_eq
inf_bot_eq
Order.Lattice
sup_idem
sup_comm
sup_assoc
sup_left_idem
sup_right_idem
inf_idem
inf_comm
inf_assoc
inf_left_idem
inf_right_idem
sup_inf_left
sup_inf_right
inf_sup_left
inf_sup_right
Order.MinMax
max_min_distrib_left
max_min_distrib_right
min_max_distrib_left
min_max_distrib_right
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -1170,7 +1170,7 @@ theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f :=
#align filter.limsup_sdiff Filter.limsup_sdiff
theorem liminf_sdiff [NeBot f] (a : α) : liminf u f \ a = liminf (fun b => u b \ a) f := by
- simp only [sdiff_eq, inf_comm (b := aᶜ), inf_liminf]
+ simp only [sdiff_eq, inf_comm _ aᶜ, inf_liminf]
#align filter.liminf_sdiff Filter.liminf_sdiff
theorem sdiff_limsup [NeBot f] (a : α) : a \ limsup u f = liminf (fun b => a \ u b) f := by
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -1332,7 +1332,7 @@ set_option linter.uppercaseLean3 false in
section Classical
-open Classical
+open scoped Classical
/-- Given an indexed family of sets `s j` over `j : Subtype p` and a function `f`, then
`liminf_reparam j` is equal to `j` if `f` is bounded below on `s j`, and otherwise to some
@@ -1344,11 +1344,11 @@ noncomputable def liminf_reparam
(f : ι → α) (s : ι' → Set ι) (p : ι' → Prop) [Countable (Subtype p)] [Nonempty (Subtype p)]
(j : Subtype p) : Subtype p :=
let m : Set (Subtype p) := {j | BddBelow (range (fun (i : s j) ↦ f i))}
- let g : ℕ → Subtype p := choose (exists_surjective_nat _)
+ let g : ℕ → Subtype p := (exists_surjective_nat _).choose
have Z : ∃ n, g n ∈ m ∨ ∀ j, j ∉ m := by
by_cases H : ∃ j, j ∈ m
· rcases H with ⟨j, hj⟩
- rcases choose_spec (exists_surjective_nat (Subtype p)) j with ⟨n, rfl⟩
+ rcases (exists_surjective_nat (Subtype p)).choose_spec j with ⟨n, rfl⟩
exact ⟨n, Or.inl hj⟩
· push_neg at H
exact ⟨0, Or.inr H⟩
@@ -1385,8 +1385,8 @@ theorem HasBasis.liminf_eq_ciSup_ciInf {v : Filter ι}
by_cases Hj : j ∈ m
· simpa only [liminf_reparam, if_pos Hj] using Hj
· simp only [liminf_reparam, if_neg Hj]
- have Z : ∃ n, choose (exists_surjective_nat (Subtype p)) n ∈ m ∨ ∀ j, j ∉ m := by
- rcases choose_spec (exists_surjective_nat (Subtype p)) j0 with ⟨n, rfl⟩
+ have Z : ∃ n, (exists_surjective_nat (Subtype p)).choose n ∈ m ∨ ∀ j, j ∉ m := by
+ rcases (exists_surjective_nat (Subtype p)).choose_spec j0 with ⟨n, rfl⟩
exact ⟨n, Or.inl hj0⟩
rcases Nat.find_spec Z with hZ|hZ
· exact hZ
@@ -1373,7 +1373,7 @@ theorem HasBasis.liminf_eq_ciSup_ciInf {v : Filter ι}
· have : j = liminf_reparam f s p j := by simp only [liminf_reparam, hj, ite_true]
conv_lhs => rw [this]
apply subset_iUnion _ j
- · simp only [mem_setOf_eq, ← nonempty_iInter_Iic_iff, not_nonempty_iff_eq_empty] at hj
+ · simp only [m, mem_setOf_eq, ← nonempty_iInter_Iic_iff, not_nonempty_iff_eq_empty] at hj
simp only [hj, empty_subset]
· apply iUnion_subset (fun j ↦ ?_)
exact subset_iUnion (fun (k : Subtype p) ↦ (⋂ (i : s k), Iic (f i))) (liminf_reparam f s p j)
@@ -246,6 +246,26 @@ theorem IsBoundedUnder.isCoboundedUnder_ge {u : γ → α} {l : Filter γ} [Preo
(h : l.IsBoundedUnder (· ≤ ·) u) : l.IsCoboundedUnder (· ≥ ·) u :=
h.isCoboundedUnder_flip
+lemma isCoboundedUnder_le_of_eventually_le [Preorder α] (l : Filter ι) [NeBot l] {f : ι → α} {x : α}
+ (hf : ∀ᶠ i in l, x ≤ f i) :
+ IsCoboundedUnder (· ≤ ·) l f :=
+ IsBoundedUnder.isCoboundedUnder_le ⟨x, hf⟩
+
+lemma isCoboundedUnder_ge_of_eventually_le [Preorder α] (l : Filter ι) [NeBot l] {f : ι → α} {x : α}
+ (hf : ∀ᶠ i in l, f i ≤ x) :
+ IsCoboundedUnder (· ≥ ·) l f :=
+ IsBoundedUnder.isCoboundedUnder_ge ⟨x, hf⟩
+
+lemma isCoboundedUnder_le_of_le [Preorder α] (l : Filter ι) [NeBot l] {f : ι → α} {x : α}
+ (hf : ∀ i, x ≤ f i) :
+ IsCoboundedUnder (· ≤ ·) l f :=
+ isCoboundedUnder_le_of_eventually_le l (eventually_of_forall hf)
+
+lemma isCoboundedUnder_ge_of_le [Preorder α] (l : Filter ι) [NeBot l] {f : ι → α} {x : α}
+ (hf : ∀ i, f i ≤ x) :
+ IsCoboundedUnder (· ≥ ·) l f :=
+ isCoboundedUnder_ge_of_eventually_le l (eventually_of_forall hf)
+
theorem isCobounded_bot : IsCobounded r ⊥ ↔ ∃ b, ∀ x, r b x := by simp [IsCobounded]
#align filter.is_cobounded_bot Filter.isCobounded_bot
@@ -663,11 +663,13 @@ theorem liminf_congr {α : Type*} [ConditionallyCompleteLattice β] {f : Filter
limsup_congr (β := βᵒᵈ) h
#align filter.liminf_congr Filter.liminf_congr
+@[simp]
theorem limsup_const {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : limsup (fun _ => b) f = b := by
simpa only [limsup_eq, eventually_const] using csInf_Ici
#align filter.limsup_const Filter.limsup_const
+@[simp]
theorem liminf_const {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : liminf (fun _ => b) f = b :=
limsup_const (β := βᵒᵈ) b
@@ -756,12 +758,14 @@ theorem bliminf_false {f : Filter β} {u : β → α} : (bliminf u f fun _ => Fa
#align filter.bliminf_false Filter.bliminf_false
/-- Same as limsup_const applied to `⊥` but without the `NeBot f` assumption -/
+@[simp]
theorem limsup_const_bot {f : Filter β} : limsup (fun _ : β => (⊥ : α)) f = (⊥ : α) := by
rw [limsup_eq, eq_bot_iff]
exact sInf_le (eventually_of_forall fun _ => le_rfl)
#align filter.limsup_const_bot Filter.limsup_const_bot
/-- Same as limsup_const applied to `⊤` but without the `NeBot f` assumption -/
+@[simp]
theorem liminf_const_top {f : Filter β} : liminf (fun _ : β => (⊤ : α)) f = (⊤ : α) :=
limsup_const_bot (α := αᵒᵈ)
#align filter.liminf_const_top Filter.liminf_const_top
FunLike
to DFunLike
(#9785)
This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.
This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:
sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@@ -1025,10 +1025,10 @@ theorem bliminf_or_le_inf_aux_left : (bliminf u f fun x => p x ∨ q x) ≤ blim
theorem bliminf_or_le_inf_aux_right : (bliminf u f fun x => p x ∨ q x) ≤ bliminf u f q :=
bliminf_or_le_inf.trans inf_le_right
-/- Porting note: Replaced `e` with `FunLike.coe e` to override the strange
+/- Porting note: Replaced `e` with `DFunLike.coe e` to override the strange
coercion to `↑(RelIso.toRelEmbedding e).toEmbedding`.-/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
- FunLike.coe e (blimsup u f p) = blimsup ((FunLike.coe e) ∘ u) f p := by
+ DFunLike.coe e (blimsup u f p) = blimsup ((DFunLike.coe e) ∘ u) f p := by
simp only [blimsup_eq, map_sInf, Function.comp_apply]
congr
ext c
cases'
(#9171)
I literally went through and regex'd some uses of cases'
, replacing them with rcases
; this is meant to be a low effort PR as I hope that tools can do this in the future.
rcases
is an easier replacement than cases
, though with better tools we could in future do a second pass converting simple rcases
added here (and existing ones) to cases
.
@@ -823,7 +823,7 @@ theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
simp only [blimsup_eq]
congr with a
refine' eventually_congr (h.mono fun b hb => _)
- cases' eq_or_ne (u b) ⊥ with hu hu; · simp [hu]
+ rcases eq_or_ne (u b) ⊥ with hu | hu; · simp [hu]
rw [hb hu]
#align filter.blimsup_congr' Filter.blimsup_congr'
@@ -459,6 +459,12 @@ theorem bliminf_eq : bliminf u f p = sSup { a | ∀ᶠ x in f, p x → a ≤ u x
rfl
#align filter.bliminf_eq Filter.bliminf_eq
+lemma liminf_comp (u : β → α) (v : γ → β) (f : Filter γ) :
+ liminf (u ∘ v) f = liminf u (map v f) := rfl
+
+lemma limsup_comp (u : β → α) (v : γ → β) (f : Filter γ) :
+ limsup (u ∘ v) f = limsup u (map v f) := rfl
+
end
@[simp]
(· op ·) a
by (a op ·)
(#8843)
I used the regex \(\(· (.) ·\) (.)\)
, replacing with ($2 $1 ·)
.
@@ -915,7 +915,7 @@ theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (
rw [limsup_eq_iInf_iSup_of_nat', map_iInf]
simp_rw [_root_.map_iSup, ← Function.comp_apply (f := f), ← Function.iterate_succ' f,
← Nat.add_succ]
- conv_rhs => rw [iInf_split _ ((· < ·) (0 : ℕ))]
+ conv_rhs => rw [iInf_split _ (0 < ·)]
simp only [not_lt, le_zero_iff, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
refine' (iInf_le (fun i => ⨆ j, f^[j + (i + 1)] a) 0).trans _
simp only [zero_add, Function.comp_apply, iSup_le_iff]
@@ -1164,7 +1164,7 @@ lemma mem_liminf_iff_eventually_mem : (a ∈ liminf s 𝓕) ↔ (∀ᶠ i in
using ⟨fun ⟨S, hS, hS'⟩ ↦ mem_of_superset hS (by tauto), fun h ↦ ⟨{i | a ∈ s i}, h, by tauto⟩⟩
lemma mem_limsup_iff_frequently_mem : (a ∈ limsup s 𝓕) ↔ (∃ᶠ i in 𝓕, a ∈ s i) := by
- simp only [Filter.Frequently, iff_not_comm, ←mem_compl_iff, limsup_compl, comp_apply,
+ simp only [Filter.Frequently, iff_not_comm, ← mem_compl_iff, limsup_compl, comp_apply,
mem_liminf_iff_eventually_mem]
theorem cofinite.blimsup_set_eq :
Add two simple lemmas identifying "liminf" of a family of sets along a filter as "things which are eventually members", and "limsup" as "things which are frequently members".
@@ -1157,7 +1157,15 @@ end CompleteBooleanAlgebra
section SetLattice
-variable {p : ι → Prop} {s : ι → Set α}
+variable {p : ι → Prop} {s : ι → Set α} {𝓕 : Filter ι} {a : α}
+
+lemma mem_liminf_iff_eventually_mem : (a ∈ liminf s 𝓕) ↔ (∀ᶠ i in 𝓕, a ∈ s i) := by
+ simpa only [liminf_eq_iSup_iInf, iSup_eq_iUnion, iInf_eq_iInter, mem_iUnion, mem_iInter]
+ using ⟨fun ⟨S, hS, hS'⟩ ↦ mem_of_superset hS (by tauto), fun h ↦ ⟨{i | a ∈ s i}, h, by tauto⟩⟩
+
+lemma mem_limsup_iff_frequently_mem : (a ∈ limsup s 𝓕) ↔ (∃ᶠ i in 𝓕, a ∈ s i) := by
+ simp only [Filter.Frequently, iff_not_comm, ←mem_compl_iff, limsup_compl, comp_apply,
+ mem_liminf_iff_eventually_mem]
theorem cofinite.blimsup_set_eq :
blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } := by
@@ -624,8 +624,9 @@ theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g :
limsInf_le_limsInf_of_le (map_mono h) hf hg
#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_le
-theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsSup (𝓟 s) = sSup s :=
- by simp only [limsSup, eventually_principal]; exact csInf_upper_bounds_eq_csSup h hs
+theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) :
+ limsSup (𝓟 s) = sSup s := by
+ simp only [limsSup, eventually_principal]; exact csInf_upper_bounds_eq_csSup h hs
set_option linter.uppercaseLean3 false in
#align filter.Limsup_principal Filter.limsSup_principal
blimsup_eq_limsup
and bliminf_eq_liminf
limsup_nat_add
and liminf_nat_add
to a ConditionallyCompleteLattice
.Filter.HasBasis.blimsup_eq_iInf_iSup
.limsup_sup_filter
, liminf_sup_filter
, blimsup_sup_not
,
bliminf_inf_not
, blimsup_not_sup
, bliminf_not_inf
,
limsup_piecewise
, and liminf_piecewise
.essSup_piecewise
.ℝ≥0∞
in essSup_indicator_eq_essSup_restrict
.
This allows us to drop assumptions 0 ≤ᵐ[_] f
and μ s ≠ 0
.snormEssSup_piecewise_le
(now
snormEssSup_piecewise
) and snorm_top_piecewise_le
(now
snorm_top_piecewise
).@@ -471,16 +471,17 @@ theorem bliminf_true (f : Filter β) (u : β → α) : (bliminf u f fun _ => Tru
simp [bliminf_eq, liminf_eq]
#align filter.bliminf_true Filter.bliminf_true
+lemma blimsup_eq_limsup {f : Filter β} {u : β → α} {p : β → Prop} :
+ blimsup u f p = limsup u (f ⊓ 𝓟 {x | p x}) := by
+ simp only [blimsup_eq, limsup_eq, eventually_inf_principal, mem_setOf_eq]
+
+lemma bliminf_eq_liminf {f : Filter β} {u : β → α} {p : β → Prop} :
+ bliminf u f p = liminf u (f ⊓ 𝓟 {x | p x}) :=
+ blimsup_eq_limsup (α := αᵒᵈ)
+
theorem blimsup_eq_limsup_subtype {f : Filter β} {u : β → α} {p : β → Prop} :
blimsup u f p = limsup (u ∘ ((↑) : { x | p x } → β)) (comap (↑) f) := by
- simp only [blimsup_eq, limsup_eq, Function.comp_apply, eventually_comap, SetCoe.forall,
- Subtype.coe_mk, mem_setOf_eq]
- congr
- ext a
- simp_rw [Subtype.forall]
- exact eventually_congr (
- eventually_of_forall
- fun x => ⟨fun hx y hy hxy => hxy.symm ▸ hx (hxy ▸ hy), fun hx hx' => hx x hx' rfl⟩)
+ rw [blimsup_eq_limsup, limsup, limsup, ← map_map, map_comap_setCoe_val]
#align filter.blimsup_eq_limsup_subtype Filter.blimsup_eq_limsup_subtype
theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Prop} :
@@ -642,13 +643,7 @@ theorem limsup_congr {α : Type*} [ConditionallyCompleteLattice β] {f : Filter
theorem blimsup_congr {f : Filter β} {u v : β → α} {p : β → Prop} (h : ∀ᶠ a in f, p a → u a = v a) :
blimsup u f p = blimsup v f p := by
- rw [blimsup_eq]
- congr with b
- refine' eventually_congr (h.mono fun x hx => ⟨fun h₁ h₂ => _, fun h₁ h₂ => _⟩)
- · rw [← hx h₂]
- exact h₁ h₂
- · rw [hx h₂]
- exact h₁ h₂
+ simpa only [blimsup_eq_limsup] using limsup_congr <| eventually_inf_principal.2 h
#align filter.blimsup_congr Filter.blimsup_congr
theorem bliminf_congr {f : Filter β} {u v : β → α} {p : β → Prop} (h : ∀ᶠ a in f, p a → u a = v a) :
@@ -683,11 +678,7 @@ theorem HasBasis.liminf_eq_sSup_iUnion_iInter {ι ι' : Type*} {f : ι → α} {
theorem HasBasis.liminf_eq_sSup_univ_of_empty {f : ι → α} {v : Filter ι}
{p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) (i : ι') (hi : p i) (h'i : s i = ∅) :
liminf f v = sSup univ := by
- simp_rw [liminf_eq, hv.eventually_iff]
- congr
- ext x
- simp only [mem_setOf_eq, mem_univ, iff_true]
- exact ⟨i, by simp [hi, h'i]⟩
+ simp [hv.eq_bot_iff.2 ⟨i, hi, h'i⟩, liminf_eq]
theorem HasBasis.limsup_eq_sInf_iUnion_iInter {ι ι' : Type*} {f : ι → α} {v : Filter ι}
{p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) :
@@ -699,6 +690,20 @@ theorem HasBasis.limsup_eq_sInf_univ_of_empty {f : ι → α} {v : Filter ι}
limsup f v = sInf univ :=
HasBasis.liminf_eq_sSup_univ_of_empty (α := αᵒᵈ) hv i hi h'i
+-- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
+@[simp, nolint simpNF]
+theorem liminf_nat_add (f : ℕ → α) (k : ℕ) :
+ liminf (fun i => f (i + k)) atTop = liminf f atTop := by
+ change liminf (f ∘ (· + k)) atTop = liminf f atTop
+ rw [liminf, liminf, ← map_map, map_add_atTop_eq_nat]
+#align filter.liminf_nat_add Filter.liminf_nat_add
+
+-- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
+@[simp, nolint simpNF]
+theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k)) atTop = limsup f atTop :=
+ @liminf_nat_add αᵒᵈ _ f k
+#align filter.limsup_nat_add Filter.limsup_nat_add
+
end ConditionallyCompleteLattice
section CompleteLattice
@@ -809,8 +814,7 @@ theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f :
theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊥ → (p x ↔ q x)) : blimsup u f p = blimsup u f q := by
simp only [blimsup_eq]
- congr
- ext a
+ congr with a
refine' eventually_congr (h.mono fun b hb => _)
cases' eq_or_ne (u b) ⊥ with hu hu; · simp [hu]
rw [hb hu]
@@ -821,29 +825,20 @@ theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
blimsup_congr' (α := αᵒᵈ) h
#align filter.bliminf_congr' Filter.bliminf_congr'
+lemma HasBasis.blimsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
+ (hf : f.HasBasis p s) {q : β → Prop} :
+ blimsup u f q = ⨅ (i) (_ : p i), ⨆ a ∈ s i, ⨆ (_ : q a), u a := by
+ simp only [blimsup_eq_limsup, (hf.inf_principal _).limsup_eq_iInf_iSup, mem_inter_iff, iSup_and,
+ mem_setOf_eq]
+
theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
blimsup u f p = ⨅ s ∈ f, ⨆ (b) (_ : p b ∧ b ∈ s), u b := by
- refine' le_antisymm (sInf_le_sInf _) (iInf_le_iff.mpr fun a ha => le_sInf_iff.mpr fun a' ha' => _)
- · rintro - ⟨s, rfl⟩
- simp only [mem_setOf_eq, le_iInf_iff]
- conv =>
- congr
- ext
- rw [Imp.swap]
- refine'
- eventually_imp_distrib_left.mpr fun h => eventually_iff_exists_mem.2 ⟨s, h, fun x h₁ h₂ => _⟩
- exact @le_iSup₂ α β (fun b => p b ∧ b ∈ s) _ (fun b _ => u b) x ⟨h₂, h₁⟩
- · obtain ⟨s, hs, hs'⟩ := eventually_iff_exists_mem.mp ha'
- have : ∀ (y : β), p y → y ∈ s → u y ≤ a' := fun y ↦ by rw [Imp.swap]; exact hs' y
- exact (le_iInf_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp] )
+ simp only [f.basis_sets.blimsup_eq_iInf_iSup, iSup_and', id, and_comm]
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (_ : p j ∧ i ≤ j), u j := by
- -- Porting note: Making this into a single simp only does not work?
- simp only [blimsup_eq_limsup_subtype, Function.comp,
- (atTop_basis.comap ((↑) : { x | p x } → ℕ)).limsup_eq_iInf_iSup, iSup_subtype, iSup_and]
- simp only [mem_setOf_eq, mem_preimage, mem_Ici, not_le, iInf_pos]
+ simp only [atTop_basis.blimsup_eq_iInf_iSup, @and_comm (p _), iSup_and, mem_Ici, iInf_true]
#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
@@ -877,15 +872,13 @@ theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
theorem limsup_eq_sInf_sSup {ι R : Type*} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) := by
- refine' le_antisymm _ _
+ apply le_antisymm
· rw [limsup_eq]
refine' sInf_le_sInf fun x hx => _
rcases (mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
filter_upwards [I_mem_F] with i hi
exact hI ▸ le_sSup (mem_image_of_mem _ hi)
- · refine'
- le_sInf_iff.mpr fun b hb =>
- sInf_le_of_le (mem_image_of_mem _ <| Filter.mem_sets.mpr hb) <| sSup_le _
+ · refine le_sInf fun b hb => sInf_le_of_le (mem_image_of_mem _ hb) <| sSup_le ?_
rintro _ ⟨_, h, rfl⟩
exact h
set_option linter.uppercaseLean3 false in
@@ -897,20 +890,6 @@ theorem liminf_eq_sSup_sInf {ι R : Type*} (F : Filter ι) [CompleteLattice R] (
set_option linter.uppercaseLean3 false in
#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInf
--- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
-@[simp, nolint simpNF]
-theorem liminf_nat_add (f : ℕ → α) (k : ℕ) :
- liminf (fun i => f (i + k)) atTop = liminf f atTop := by
- simp_rw [liminf_eq_iSup_iInf_of_nat]
- exact iSup_iInf_ge_nat_add f k
-#align filter.liminf_nat_add Filter.liminf_nat_add
-
--- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
-@[simp, nolint simpNF]
-theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k)) atTop = limsup f atTop :=
- @liminf_nat_add αᵒᵈ _ f k
-#align filter.limsup_nat_add Filter.limsup_nat_add
-
theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x := by
rw [liminf_eq]
@@ -983,7 +962,6 @@ theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p
sInf_le_sInf fun _ ha => ha.filter_mono h
#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filter
-
-- @[simp] -- Porting note: simp_nf linter, lhs simplifies, added _aux versions below
theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p ⊓ blimsup u f q :=
le_inf (blimsup_mono <| by tauto) (blimsup_mono <| by tauto)
@@ -1074,12 +1052,19 @@ section CompleteDistribLattice
variable [CompleteDistribLattice α] {f : Filter β} {p q : β → Prop} {u : β → α}
+lemma limsup_sup_filter {g} : limsup u (f ⊔ g) = limsup u f ⊔ limsup u g := by
+ refine le_antisymm ?_
+ (sup_le (limsup_le_limsup_of_le le_sup_left) (limsup_le_limsup_of_le le_sup_right))
+ simp_rw [limsup_eq, sInf_sup_eq, sup_sInf_eq, mem_setOf_eq, le_iInf₂_iff]
+ intro a ha b hb
+ exact sInf_le ⟨ha.mono fun _ h ↦ h.trans le_sup_left, hb.mono fun _ h ↦ h.trans le_sup_right⟩
+
+lemma liminf_sup_filter {g} : liminf u (f ⊔ g) = liminf u f ⊓ liminf u g :=
+ limsup_sup_filter (α := αᵒᵈ)
+
@[simp]
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q := by
- refine' le_antisymm _ blimsup_sup_le_or
- simp only [blimsup_eq, sInf_sup_eq, sup_sInf_eq, le_iInf₂_iff, mem_setOf_eq]
- refine' fun a' ha' a ha => sInf_le ((ha.and ha').mono fun b h hb => _)
- exact Or.elim hb (fun hb => le_sup_of_le_left <| h.1 hb) fun hb => le_sup_of_le_right <| h.2 hb
+ simp only [blimsup_eq_limsup, ← limsup_sup_filter, ← inf_sup_left, sup_principal, setOf_or]
#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_sup
@[simp]
@@ -1087,6 +1072,32 @@ theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p
blimsup_or_eq_sup (α := αᵒᵈ)
#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_inf
+@[simp]
+lemma blimsup_sup_not : blimsup u f p ⊔ blimsup u f (¬p ·) = limsup u f := by
+ simp_rw [← blimsup_or_eq_sup, or_not, blimsup_true]
+
+@[simp]
+lemma bliminf_inf_not : bliminf u f p ⊓ bliminf u f (¬p ·) = liminf u f :=
+ blimsup_sup_not (α := αᵒᵈ)
+
+@[simp]
+lemma blimsup_not_sup : blimsup u f (¬p ·) ⊔ blimsup u f p = limsup u f := by
+ simpa only [not_not] using blimsup_sup_not (p := (¬p ·))
+
+@[simp]
+lemma bliminf_not_inf : bliminf u f (¬p ·) ⊓ bliminf u f p = liminf u f :=
+ blimsup_not_sup (α := αᵒᵈ)
+
+lemma limsup_piecewise {s : Set β} [DecidablePred (· ∈ s)] {v} :
+ limsup (s.piecewise u v) f = blimsup u f (· ∈ s) ⊔ blimsup v f (· ∉ s) := by
+ rw [← blimsup_sup_not (p := (· ∈ s))]
+ refine congr_arg₂ _ (blimsup_congr ?_) (blimsup_congr ?_) <;>
+ refine eventually_of_forall fun _ h ↦ ?_ <;> simp [h]
+
+lemma liminf_piecewise {s : Set β} [DecidablePred (· ∈ s)] {v} :
+ liminf (s.piecewise u v) f = bliminf u f (· ∈ s) ⊓ bliminf v f (· ∉ s) :=
+ limsup_piecewise (α := αᵒᵈ)
+
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f := by
simp only [limsup_eq_iInf_iSup, iSup_sup_eq, sup_iInf₂_eq]
congr; ext s; congr; ext hs; congr
rcases
, convert
and congrm
(#7725)
Replace rcases(
with rcases (
. Same thing for convert(
and congrm(
. No other change.
@@ -880,7 +880,7 @@ theorem limsup_eq_sInf_sSup {ι R : Type*} (F : Filter ι) [CompleteLattice R] (
refine' le_antisymm _ _
· rw [limsup_eq]
refine' sInf_le_sInf fun x hx => _
- rcases(mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
+ rcases (mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
filter_upwards [I_mem_F] with i hi
exact hI ▸ le_sSup (mem_image_of_mem _ hi)
· refine'
filter_upwards
(#7719)
mathport was forgetting a space in filter_upwards [...]with
instead of filter_upwards [...] with
.
@@ -342,7 +342,8 @@ theorem IsBoundedUnder.sup [SemilatticeSup α] {f : Filter β} {u v : β → α}
f.IsBoundedUnder (· ≤ ·) u →
f.IsBoundedUnder (· ≤ ·) v → f.IsBoundedUnder (· ≤ ·) fun a => u a ⊔ v a
| ⟨bu, (hu : ∀ᶠ x in f, u x ≤ bu)⟩, ⟨bv, (hv : ∀ᶠ x in f, v x ≤ bv)⟩ =>
- ⟨bu ⊔ bv, show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv by filter_upwards [hu, hv]with _ using sup_le_sup⟩
+ ⟨bu ⊔ bv, show ∀ᶠ x in f, u x ⊔ v x ≤ bu ⊔ bv
+ by filter_upwards [hu, hv] with _ using sup_le_sup⟩
#align filter.is_bounded_under.sup Filter.IsBoundedUnder.sup
@[simp]
@@ -880,7 +881,7 @@ theorem limsup_eq_sInf_sSup {ι R : Type*} (F : Filter ι) [CompleteLattice R] (
· rw [limsup_eq]
refine' sInf_le_sInf fun x hx => _
rcases(mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
- filter_upwards [I_mem_F]with i hi
+ filter_upwards [I_mem_F] with i hi
exact hI ▸ le_sSup (mem_image_of_mem _ hi)
· refine'
le_sInf_iff.mpr fun b hb =>
@@ -990,7 +990,7 @@ theorem blimsup_and_le_inf : (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f
@[simp]
theorem bliminf_sup_le_inf_aux_left :
- (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p :=
+ (blimsup u f fun x => p x ∧ q x) ≤ blimsup u f p :=
blimsup_and_le_inf.trans inf_le_left
@[simp]
Forward-ports https://github.com/leanprover-community/mathlib/pull/18628
@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.Hom.CompleteLattice
-#align_import order.liminf_limsup from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+#align_import order.liminf_limsup from "leanprover-community/mathlib"@"ffde2d8a6e689149e44fd95fa862c23a57f8c780"
/-!
# liminfs and limsups of functions and filters
@@ -160,7 +160,7 @@ theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f :
not_isBoundedUnder_of_tendsto_atTop (β := βᵒᵈ) hf
#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBot
-theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
+theorem IsBoundedUnder.bddAbove_range_of_cofinite [Preorder β] [IsDirected β (· ≤ ·)] {f : α → β}
(hf : IsBoundedUnder (· ≤ ·) cofinite f) : BddAbove (range f) := by
rcases hf with ⟨b, hb⟩
haveI : Nonempty β := ⟨b⟩
@@ -168,18 +168,18 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
exact ⟨⟨b, ball_image_iff.2 fun x => id⟩, (hb.image f).bddAbove⟩
#align filter.is_bounded_under.bdd_above_range_of_cofinite Filter.IsBoundedUnder.bddAbove_range_of_cofinite
-theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
+theorem IsBoundedUnder.bddBelow_range_of_cofinite [Preorder β] [IsDirected β (· ≥ ·)] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
IsBoundedUnder.bddAbove_range_of_cofinite (β := βᵒᵈ) hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
-theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
+theorem IsBoundedUnder.bddAbove_range [Preorder β] [IsDirected β (· ≤ ·)] {f : ℕ → β}
(hf : IsBoundedUnder (· ≤ ·) atTop f) : BddAbove (range f) := by
rw [← Nat.cofinite_eq_atTop] at hf
exact hf.bddAbove_range_of_cofinite
#align filter.is_bounded_under.bdd_above_range Filter.IsBoundedUnder.bddAbove_range
-theorem IsBoundedUnder.bddBelow_range [SemilatticeInf β] {f : ℕ → β}
+theorem IsBoundedUnder.bddBelow_range [Preorder β] [IsDirected β (· ≥ ·)] {f : ℕ → β}
(hf : IsBoundedUnder (· ≥ ·) atTop f) : BddBelow (range f) :=
IsBoundedUnder.bddAbove_range (β := βᵒᵈ) hf
#align filter.is_bounded_under.bdd_below_range Filter.IsBoundedUnder.bddBelow_range
@@ -264,6 +264,37 @@ theorem IsCobounded.mono (h : f ≤ g) : f.IsCobounded r → g.IsCobounded r
end Relation
+section Nonempty
+variable [Preorder α] [Nonempty α] {f : Filter β} {u : β → α}
+
+theorem isBounded_le_atBot : (atBot : Filter α).IsBounded (· ≤ ·) :=
+ ‹Nonempty α›.elim fun a => ⟨a, eventually_le_atBot _⟩
+#align filter.is_bounded_le_at_bot Filter.isBounded_le_atBot
+
+theorem isBounded_ge_atTop : (atTop : Filter α).IsBounded (· ≥ ·) :=
+ ‹Nonempty α›.elim fun a => ⟨a, eventually_ge_atTop _⟩
+#align filter.is_bounded_ge_at_top Filter.isBounded_ge_atTop
+
+theorem Tendsto.isBoundedUnder_le_atBot (h : Tendsto u f atBot) : f.IsBoundedUnder (· ≤ ·) u :=
+ isBounded_le_atBot.mono h
+#align filter.tendsto.is_bounded_under_le_at_bot Filter.Tendsto.isBoundedUnder_le_atBot
+
+theorem Tendsto.isBoundedUnder_ge_atTop (h : Tendsto u f atTop) : f.IsBoundedUnder (· ≥ ·) u :=
+ isBounded_ge_atTop.mono h
+#align filter.tendsto.is_bounded_under_ge_at_top Filter.Tendsto.isBoundedUnder_ge_atTop
+
+theorem bddAbove_range_of_tendsto_atTop_atBot [IsDirected α (· ≤ ·)] {u : ℕ → α}
+ (hx : Tendsto u atTop atBot) : BddAbove (Set.range u) :=
+ hx.isBoundedUnder_le_atBot.bddAbove_range
+#align filter.bdd_above_range_of_tendsto_at_top_at_bot Filter.bddAbove_range_of_tendsto_atTop_atBot
+
+theorem bddBelow_range_of_tendsto_atTop_atTop [IsDirected α (· ≥ ·)] {u : ℕ → α}
+ (hx : Tendsto u atTop atTop) : BddBelow (Set.range u) :=
+ hx.isBoundedUnder_ge_atTop.bddBelow_range
+#align filter.bdd_below_range_of_tendsto_at_top_at_top Filter.bddBelow_range_of_tendsto_atTop_atTop
+
+end Nonempty
+
theorem isCobounded_le_of_bot [Preorder α] [OrderBot α] {f : Filter α} : f.IsCobounded (· ≤ ·) :=
⟨⊥, fun _ _ => bot_le⟩
#align filter.is_cobounded_le_of_bot Filter.isCobounded_le_of_bot
@@ -1232,10 +1263,25 @@ theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β]
frequently_lt_of_lt_limsup (β := βᵒᵈ) hu h
#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_lt
+variable [ConditionallyCompleteLinearOrder α] {f : Filter α} {b : α}
+
+-- The linter erroneously claims that I'm not referring to `c`
+set_option linter.unusedVariables false in
+theorem lt_mem_sets_of_limsSup_lt (h : f.IsBounded (· ≤ ·)) (l : f.limsSup < b) :
+ ∀ᶠ a in f, a < b :=
+ let ⟨c, (h : ∀ᶠ a in f, a ≤ c), hcb⟩ := exists_lt_of_csInf_lt h l
+ mem_of_superset h fun _a => hcb.trans_le'
+set_option linter.uppercaseLean3 false in
+#align filter.lt_mem_sets_of_Limsup_lt Filter.lt_mem_sets_of_limsSup_lt
+
+theorem gt_mem_sets_of_limsInf_gt : f.IsBounded (· ≥ ·) → b < f.limsInf → ∀ᶠ a in f, b < a :=
+ @lt_mem_sets_of_limsSup_lt αᵒᵈ _ _ _
+set_option linter.uppercaseLean3 false in
+#align filter.gt_mem_sets_of_Liminf_gt Filter.gt_mem_sets_of_limsInf_gt
+
section Classical
open Classical
-variable [ConditionallyCompleteLinearOrder α]
/-- Given an indexed family of sets `s j` over `j : Subtype p` and a function `f`, then
`liminf_reparam j` is equal to `j` if `f` is bounded below on `s j`, and otherwise to some
Currently, we only have that sups and limsups are measurable in complete linear orders, which excludes the main case of the real line. With more complicated proofs, these measurability results can be extended to all conditionally complete linear orders, without any further assumption in the statements.
@@ -41,7 +41,7 @@ set_option autoImplicit true
open Filter Set Function
-variable {α β γ ι : Type*}
+variable {α β γ ι ι' : Type*}
namespace Filter
@@ -639,6 +639,34 @@ theorem liminf_const {α : Type*} [ConditionallyCompleteLattice β] {f : Filter
limsup_const (β := βᵒᵈ) b
#align filter.liminf_const Filter.liminf_const
+theorem HasBasis.liminf_eq_sSup_iUnion_iInter {ι ι' : Type*} {f : ι → α} {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) :
+ liminf f v = sSup (⋃ (j : Subtype p), ⋂ (i : s j), Iic (f i)) := by
+ simp_rw [liminf_eq, hv.eventually_iff]
+ congr
+ ext x
+ simp only [mem_setOf_eq, iInter_coe_set, mem_iUnion, mem_iInter, mem_Iic, Subtype.exists,
+ exists_prop]
+
+theorem HasBasis.liminf_eq_sSup_univ_of_empty {f : ι → α} {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) (i : ι') (hi : p i) (h'i : s i = ∅) :
+ liminf f v = sSup univ := by
+ simp_rw [liminf_eq, hv.eventually_iff]
+ congr
+ ext x
+ simp only [mem_setOf_eq, mem_univ, iff_true]
+ exact ⟨i, by simp [hi, h'i]⟩
+
+theorem HasBasis.limsup_eq_sInf_iUnion_iInter {ι ι' : Type*} {f : ι → α} {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) :
+ limsup f v = sInf (⋃ (j : Subtype p), ⋂ (i : s j), Ici (f i)) :=
+ HasBasis.liminf_eq_sSup_iUnion_iInter (α := αᵒᵈ) hv
+
+theorem HasBasis.limsup_eq_sInf_univ_of_empty {f : ι → α} {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} (hv : v.HasBasis p s) (i : ι') (hi : p i) (h'i : s i = ∅) :
+ limsup f v = sInf univ :=
+ HasBasis.liminf_eq_sSup_univ_of_empty (α := αᵒᵈ) hv i hi h'i
+
end ConditionallyCompleteLattice
section CompleteLattice
@@ -1204,6 +1232,127 @@ theorem frequently_lt_of_liminf_lt {α β} [ConditionallyCompleteLinearOrder β]
frequently_lt_of_lt_limsup (β := βᵒᵈ) hu h
#align filter.frequently_lt_of_liminf_lt Filter.frequently_lt_of_liminf_lt
+section Classical
+
+open Classical
+variable [ConditionallyCompleteLinearOrder α]
+
+/-- Given an indexed family of sets `s j` over `j : Subtype p` and a function `f`, then
+`liminf_reparam j` is equal to `j` if `f` is bounded below on `s j`, and otherwise to some
+index `k` such that `f` is bounded below on `s k` (if there exists one).
+To ensure good measurability behavior, this index `k` is chosen as the minimal suitable index.
+This function is used to write down a liminf in a measurable way,
+in `Filter.HasBasis.liminf_eq_ciSup_ciInf` and `Filter.HasBasis.liminf_eq_ite`. -/
+noncomputable def liminf_reparam
+ (f : ι → α) (s : ι' → Set ι) (p : ι' → Prop) [Countable (Subtype p)] [Nonempty (Subtype p)]
+ (j : Subtype p) : Subtype p :=
+ let m : Set (Subtype p) := {j | BddBelow (range (fun (i : s j) ↦ f i))}
+ let g : ℕ → Subtype p := choose (exists_surjective_nat _)
+ have Z : ∃ n, g n ∈ m ∨ ∀ j, j ∉ m := by
+ by_cases H : ∃ j, j ∈ m
+ · rcases H with ⟨j, hj⟩
+ rcases choose_spec (exists_surjective_nat (Subtype p)) j with ⟨n, rfl⟩
+ exact ⟨n, Or.inl hj⟩
+ · push_neg at H
+ exact ⟨0, Or.inr H⟩
+ if j ∈ m then j else g (Nat.find Z)
+
+/-- Writing a liminf as a supremum of infimum, in a (possibly non-complete) conditionally complete
+linear order. A reparametrization trick is needed to avoid taking the infimum of sets which are
+not bounded below. -/
+theorem HasBasis.liminf_eq_ciSup_ciInf {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} [Countable (Subtype p)] [Nonempty (Subtype p)]
+ (hv : v.HasBasis p s) {f : ι → α} (hs : ∀ (j : Subtype p), (s j).Nonempty)
+ (H : ∃ (j : Subtype p), BddBelow (range (fun (i : s j) ↦ f i))) :
+ liminf f v = ⨆ (j : Subtype p), ⨅ (i : s (liminf_reparam f s p j)), f i := by
+ rcases H with ⟨j0, hj0⟩
+ let m : Set (Subtype p) := {j | BddBelow (range (fun (i : s j) ↦ f i))}
+ have : ∀ (j : Subtype p), Nonempty (s j) := fun j ↦ Nonempty.coe_sort (hs j)
+ have A : ⋃ (j : Subtype p), ⋂ (i : s j), Iic (f i) =
+ ⋃ (j : Subtype p), ⋂ (i : s (liminf_reparam f s p j)), Iic (f i) := by
+ apply Subset.antisymm
+ · apply iUnion_subset (fun j ↦ ?_)
+ by_cases hj : j ∈ m
+ · have : j = liminf_reparam f s p j := by simp only [liminf_reparam, hj, ite_true]
+ conv_lhs => rw [this]
+ apply subset_iUnion _ j
+ · simp only [mem_setOf_eq, ← nonempty_iInter_Iic_iff, not_nonempty_iff_eq_empty] at hj
+ simp only [hj, empty_subset]
+ · apply iUnion_subset (fun j ↦ ?_)
+ exact subset_iUnion (fun (k : Subtype p) ↦ (⋂ (i : s k), Iic (f i))) (liminf_reparam f s p j)
+ have B : ∀ (j : Subtype p), ⋂ (i : s (liminf_reparam f s p j)), Iic (f i) =
+ Iic (⨅ (i : s (liminf_reparam f s p j)), f i) := by
+ intro j
+ apply (Iic_ciInf _).symm
+ change liminf_reparam f s p j ∈ m
+ by_cases Hj : j ∈ m
+ · simpa only [liminf_reparam, if_pos Hj] using Hj
+ · simp only [liminf_reparam, if_neg Hj]
+ have Z : ∃ n, choose (exists_surjective_nat (Subtype p)) n ∈ m ∨ ∀ j, j ∉ m := by
+ rcases choose_spec (exists_surjective_nat (Subtype p)) j0 with ⟨n, rfl⟩
+ exact ⟨n, Or.inl hj0⟩
+ rcases Nat.find_spec Z with hZ|hZ
+ · exact hZ
+ · exact (hZ j0 hj0).elim
+ simp_rw [hv.liminf_eq_sSup_iUnion_iInter, A, B, sSup_iUnion_Iic]
+
+/-- Writing a liminf as a supremum of infimum, in a (possibly non-complete) conditionally complete
+linear order. A reparametrization trick is needed to avoid taking the infimum of sets which are
+not bounded below. -/
+theorem HasBasis.liminf_eq_ite {v : Filter ι} {p : ι' → Prop} {s : ι' → Set ι}
+ [Countable (Subtype p)] [Nonempty (Subtype p)] (hv : v.HasBasis p s) (f : ι → α):
+ liminf f v = if ∃ (j : Subtype p), s j = ∅ then sSup univ else
+ if ∀ (j : Subtype p), ¬BddBelow (range (fun (i : s j) ↦ f i)) then sSup ∅
+ else ⨆ (j : Subtype p), ⨅ (i : s (liminf_reparam f s p j)), f i := by
+ by_cases H : ∃ (j : Subtype p), s j = ∅
+ · rw [if_pos H]
+ rcases H with ⟨j, hj⟩
+ simp [hv.liminf_eq_sSup_univ_of_empty j j.2 hj]
+ rw [if_neg H]
+ by_cases H' : ∀ (j : Subtype p), ¬BddBelow (range (fun (i : s j) ↦ f i))
+ · have A : ∀ (j : Subtype p), ⋂ (i : s j), Iic (f i) = ∅ := by
+ simp_rw [← not_nonempty_iff_eq_empty, nonempty_iInter_Iic_iff]
+ exact H'
+ simp_rw [if_pos H', hv.liminf_eq_sSup_iUnion_iInter, A, iUnion_empty]
+ rw [if_neg H']
+ apply hv.liminf_eq_ciSup_ciInf
+ · push_neg at H
+ simpa only [nonempty_iff_ne_empty] using H
+ · push_neg at H'
+ exact H'
+
+/-- Given an indexed family of sets `s j` and a function `f`, then `limsup_reparam j` is equal
+to `j` if `f` is bounded above on `s j`, and otherwise to some index `k` such that `f` is bounded
+above on `s k` (if there exists one). To ensure good measurability behavior, this index `k` is
+chosen as the minimal suitable index. This function is used to write down a limsup in a measurable
+way, in `Filter.HasBasis.limsup_eq_ciInf_ciSup` and `Filter.HasBasis.limsup_eq_ite`. -/
+noncomputable def limsup_reparam
+ (f : ι → α) (s : ι' → Set ι) (p : ι' → Prop) [Countable (Subtype p)] [Nonempty (Subtype p)]
+ (j : Subtype p) : Subtype p :=
+ liminf_reparam (α := αᵒᵈ) f s p j
+
+/-- Writing a limsup as an infimum of supremum, in a (possibly non-complete) conditionally complete
+linear order. A reparametrization trick is needed to avoid taking the supremum of sets which are
+not bounded above. -/
+theorem HasBasis.limsup_eq_ciInf_ciSup {v : Filter ι}
+ {p : ι' → Prop} {s : ι' → Set ι} [Countable (Subtype p)] [Nonempty (Subtype p)]
+ (hv : v.HasBasis p s) {f : ι → α} (hs : ∀ (j : Subtype p), (s j).Nonempty)
+ (H : ∃ (j : Subtype p), BddAbove (range (fun (i : s j) ↦ f i))) :
+ limsup f v = ⨅ (j : Subtype p), ⨆ (i : s (limsup_reparam f s p j)), f i :=
+ HasBasis.liminf_eq_ciSup_ciInf (α := αᵒᵈ) hv hs H
+
+/-- Writing a limsup as an infimum of supremum, in a (possibly non-complete) conditionally complete
+linear order. A reparametrization trick is needed to avoid taking the supremum of sets which are
+not bounded below. -/
+theorem HasBasis.limsup_eq_ite {v : Filter ι} {p : ι' → Prop} {s : ι' → Set ι}
+ [Countable (Subtype p)] [Nonempty (Subtype p)] (hv : v.HasBasis p s) (f : ι → α) :
+ limsup f v = if ∃ (j : Subtype p), s j = ∅ then sInf univ else
+ if ∀ (j : Subtype p), ¬BddAbove (range (fun (i : s j) ↦ f i)) then sInf ∅
+ else ⨅ (j : Subtype p), ⨆ (i : s (limsup_reparam f s p j)), f i :=
+ HasBasis.liminf_eq_ite (α := αᵒᵈ) hv f
+
+end Classical
+
end ConditionallyCompleteLinearOrder
end Filter
Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.
The intent of this PR is to make autoImplicit
opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true
in the few files that rely on it.
That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.
I claim that many of the uses of autoImplicit
in these files are accidental; situations such as:
variables
are in scope, but pasting the lemma in the wrong sectionHaving set_option autoImplicit false
as the default prevents these types of mistake being made in the 90% of files where autoImplicit
s are not used at all, and causes them to be caught by CI during review.
I think there were various points during the port where we encouraged porters to delete the universes u v
lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.
A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18
as the no:dontcare:yes
vote ratio.
While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true
has been placed locally within a section, rather than at the top of the file.
@@ -36,6 +36,8 @@ the definitions of Limsup and Liminf.
In complete lattices, however, it coincides with the `Inf Sup` definition.
-/
+set_option autoImplicit true
+
open Filter Set Function
@@ -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
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -39,7 +39,7 @@ In complete lattices, however, it coincides with the `Inf Sup` definition.
open Filter Set Function
-variable {α β γ ι : Type _}
+variable {α β γ ι : Type*}
namespace Filter
@@ -541,7 +541,7 @@ theorem limsInf_le_limsInf {f g : Filter α}
set_option linter.uppercaseLean3 false in
#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
-theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
+theorem limsup_le_limsup {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : u ≤ᶠ[f] v)
(hu : f.IsCoboundedUnder (· ≤ ·) u := by isBoundedDefault)
(hv : f.IsBoundedUnder (· ≤ ·) v := by isBoundedDefault) :
@@ -549,7 +549,7 @@ theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
limsSup_le_limsSup hu hv fun _ => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
-theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
+theorem liminf_le_liminf {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a ≤ v a)
(hu : f.IsBoundedUnder (· ≥ ·) u := by isBoundedDefault)
(hv : f.IsCoboundedUnder (· ≥ ·) v := by isBoundedDefault) :
@@ -599,7 +599,7 @@ theorem limsInf_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : lims
set_option linter.uppercaseLean3 false in
#align filter.Liminf_principal Filter.limsInf_principal
-theorem limsup_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
+theorem limsup_congr {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a = v a) : limsup u f = limsup v f := by
rw [limsup_eq]
congr with b
@@ -622,17 +622,17 @@ theorem bliminf_congr {f : Filter β} {u v : β → α} {p : β → Prop} (h :
blimsup_congr (α := αᵒᵈ) h
#align filter.bliminf_congr Filter.bliminf_congr
-theorem liminf_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
+theorem liminf_congr {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a = v a) : liminf u f = liminf v f :=
limsup_congr (β := βᵒᵈ) h
#align filter.liminf_congr Filter.liminf_congr
-theorem limsup_const {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
+theorem limsup_const {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : limsup (fun _ => b) f = b := by
simpa only [limsup_eq, eventually_const] using csInf_Ici
#align filter.limsup_const Filter.limsup_const
-theorem liminf_const {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
+theorem liminf_const {α : Type*} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : liminf (fun _ => b) f = b :=
limsup_const (β := βᵒᵈ) b
#align filter.liminf_const Filter.liminf_const
@@ -813,7 +813,7 @@ theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
@blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
-theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+theorem limsup_eq_sInf_sSup {ι R : Type*} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) := by
refine' le_antisymm _ _
· rw [limsup_eq]
@@ -829,7 +829,7 @@ theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R]
set_option linter.uppercaseLean3 false in
#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSup
-theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+theorem liminf_eq_sSup_sInf {ι R : Type*} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
liminf a F = sSup ((fun I => sInf (a '' I)) '' F.sets) :=
@Filter.limsup_eq_sInf_sSup ι (OrderDual R) _ _ a
set_option linter.uppercaseLean3 false in
Generalize some existing lemmas from CompleteLinearOrder
s to ConditionallyCompleteLinearOrder
s, adding the appropriate boundedness assumptions:
Monotone.map_limsSup_of_continuousAt
+ its 3 order-dual variantsMonotone.map_limsup_of_continuousAt
+ its 3 order-dual variantsMonotone.map_sSup_of_continuousAt'
+ its 3 order-dual variantsMonotone.map_iSup_of_continuousAt'
+ its 3 order-dual variantsFor the first two to work automatically still on CompleteLinearOrder
s, the existing macro tactic isBoundedDefault
about boundedness of filters is used. For the last two to work automatically still on CompleteLinearOrder
s, a similar new macro tactic bddDefault
about boundedness of sets is included in the PR.
Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>
@@ -343,8 +343,8 @@ theorem isBoundedUnder_le_abs [LinearOrderedAddCommGroup α] {f : Filter β} {u
/-- Filters are automatically bounded or cobounded in complete lattices. To use the same statements
in complete and conditionally complete lattices but let automation fill automatically the
-boundedness proofs in complete lattices, we use the tactic `isBounded_default` in the statements,
-in the form `(hf : f.IsBounded (≥) . isBoundedDefault)`. -/
+boundedness proofs in complete lattices, we use the tactic `isBoundedDefault` in the statements,
+in the form `(hf : f.IsBounded (≥) := by isBoundedDefault)`. -/
macro "isBoundedDefault" : tactic =>
`(tactic| first
@@ -787,7 +787,7 @@ theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
theorem liminf_eq_iSup_iInf {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
- @limsup_eq_iInf_iSup αᵒᵈ β _ _ _
+ limsup_eq_iInf_iSup (α := αᵒᵈ)
#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInf
theorem liminf_eq_iSup_iInf_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
@@ -800,7 +800,7 @@ theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n :
theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : liminf u f = ⨆ (i) (_ : p i), ⨅ a ∈ s i, u a :=
- @HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
+ HasBasis.limsup_eq_iInf_iSup (α := αᵒᵈ) h
#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
@@ -862,7 +862,7 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, x ≤ u a) : x ≤ limsup u f :=
- @liminf_le_of_frequently_le' _ βᵒᵈ _ _ _ _ h
+ liminf_le_of_frequently_le' (β := βᵒᵈ) h
#align filter.le_limsup_of_frequently_le' Filter.le_limsup_of_frequently_le'
/-- If `f : α → α` is a morphism of complete lattices, then the limsup of its iterates of any
@@ -37,9 +37,7 @@ In complete lattices, however, it coincides with the `Inf Sup` definition.
-/
-open Filter Set
-
-open Filter
+open Filter Set Function
variable {α β γ ι : Type _}
@@ -116,10 +114,34 @@ theorem isBoundedUnder_const [IsRefl α r] {l : Filter β} {a : α} : IsBoundedU
#align filter.is_bounded_under_const Filter.isBoundedUnder_const
theorem IsBounded.isBoundedUnder {q : β → β → Prop} {u : α → β}
- (hf : ∀ a₀ a₁, r a₀ a₁ → q (u a₀) (u a₁)) : f.IsBounded r → f.IsBoundedUnder q u
- | ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hf x b⟩
+ (hu : ∀ a₀ a₁, r a₀ a₁ → q (u a₀) (u a₁)) : f.IsBounded r → f.IsBoundedUnder q u
+ | ⟨b, h⟩ => ⟨u b, show ∀ᶠ x in f, q (u x) (u b) from h.mono fun x => hu x b⟩
#align filter.is_bounded.is_bounded_under Filter.IsBounded.isBoundedUnder
+theorem IsBoundedUnder.comp {l : Filter γ} {q : β → β → Prop} {u : γ → α} {v : α → β}
+ (hv : ∀ a₀ a₁, r a₀ a₁ → q (v a₀) (v a₁)) : l.IsBoundedUnder r u → l.IsBoundedUnder q (v ∘ u)
+ | ⟨a, h⟩ => ⟨v a, show ∀ᶠ x in map u l, q (v x) (v a) from h.mono fun x => hv x a⟩
+
+theorem _root_.Monotone.isBoundedUnder_le_comp [Preorder α] [Preorder β] {l : Filter γ} {u : γ → α}
+ {v : α → β} (hv : Monotone v) (hl : l.IsBoundedUnder (· ≤ ·) u) :
+ l.IsBoundedUnder (· ≤ ·) (v ∘ u) :=
+ hl.comp hv
+
+theorem _root_.Monotone.isBoundedUnder_ge_comp [Preorder α] [Preorder β] {l : Filter γ} {u : γ → α}
+ {v : α → β} (hv : Monotone v) (hl : l.IsBoundedUnder (· ≥ ·) u) :
+ l.IsBoundedUnder (· ≥ ·) (v ∘ u) :=
+ hl.comp (swap hv)
+
+theorem _root_.Antitone.isBoundedUnder_le_comp [Preorder α] [Preorder β] {l : Filter γ} {u : γ → α}
+ {v : α → β} (hv : Antitone v) (hl : l.IsBoundedUnder (· ≥ ·) u) :
+ l.IsBoundedUnder (· ≤ ·) (v ∘ u) :=
+ hl.comp (swap hv)
+
+theorem _root_.Antitone.isBoundedUnder_ge_comp [Preorder α] [Preorder β] {l : Filter γ} {u : γ → α}
+ {v : α → β} (hv : Antitone v) (hl : l.IsBoundedUnder (· ≤ ·) u) :
+ l.IsBoundedUnder (· ≥ ·) (v ∘ u) :=
+ hl.comp hv
+
theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f : α → β} {l : Filter α}
[l.NeBot] (hf : Tendsto f l atTop) : ¬IsBoundedUnder (· ≤ ·) l f := by
rintro ⟨b, hb⟩
@@ -210,6 +232,18 @@ theorem IsBounded.isCobounded_le [Preorder α] [NeBot f] (h : f.IsBounded (·
h.isCobounded_flip
#align filter.is_bounded.is_cobounded_le Filter.IsBounded.isCobounded_le
+theorem IsBoundedUnder.isCoboundedUnder_flip {l : Filter γ} [IsTrans α r] [NeBot l]
+ (h : l.IsBoundedUnder r u) : l.IsCoboundedUnder (flip r) u :=
+ h.isCobounded_flip
+
+theorem IsBoundedUnder.isCoboundedUnder_le {u : γ → α} {l : Filter γ} [Preorder α] [NeBot l]
+ (h : l.IsBoundedUnder (· ≥ ·) u) : l.IsCoboundedUnder (· ≤ ·) u :=
+ h.isCoboundedUnder_flip
+
+theorem IsBoundedUnder.isCoboundedUnder_ge {u : γ → α} {l : Filter γ} [Preorder α] [NeBot l]
+ (h : l.IsBoundedUnder (· ≤ ·) u) : l.IsCoboundedUnder (· ≥ ·) u :=
+ h.isCoboundedUnder_flip
+
theorem isCobounded_bot : IsCobounded r ⊥ ↔ ∃ b, ∀ x, r b x := by simp [IsCobounded]
#align filter.is_cobounded_bot Filter.isCobounded_bot
@@ -1176,32 +1210,32 @@ section Order
open Filter
-theorem Monotone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
+theorem Monotone.isBoundedUnder_le_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atTop atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f := by
refine' ⟨_, fun h => h.isBoundedUnder (α := β) hg⟩
rintro ⟨c, hc⟩; rw [eventually_map] at hc
obtain ⟨b, hb⟩ : ∃ b, ∀ a ≥ b, c < g a := eventually_atTop.1 (hg'.eventually_gt_atTop c)
exact ⟨b, hc.mono fun x hx => not_lt.1 fun h => (hb _ h.le).not_le hx⟩
-#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp
+#align monotone.is_bounded_under_le_comp Monotone.isBoundedUnder_le_comp_iff
-theorem Monotone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
+theorem Monotone.isBoundedUnder_ge_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Monotone g) (hg' : Tendsto g atBot atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
- hg.dual.isBoundedUnder_le_comp hg'
-#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp
+ hg.dual.isBoundedUnder_le_comp_iff hg'
+#align monotone.is_bounded_under_ge_comp Monotone.isBoundedUnder_ge_comp_iff
-theorem Antitone.isBoundedUnder_le_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
+theorem Antitone.isBoundedUnder_le_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMaxOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atBot atTop) :
IsBoundedUnder (· ≤ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≥ ·) l f :=
- hg.dual_right.isBoundedUnder_ge_comp hg'
-#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp
+ hg.dual_right.isBoundedUnder_ge_comp_iff hg'
+#align antitone.is_bounded_under_le_comp Antitone.isBoundedUnder_le_comp_iff
-theorem Antitone.isBoundedUnder_ge_comp [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
+theorem Antitone.isBoundedUnder_ge_comp_iff [Nonempty β] [LinearOrder β] [Preorder γ] [NoMinOrder γ]
{g : β → γ} {f : α → β} {l : Filter α} (hg : Antitone g) (hg' : Tendsto g atTop atBot) :
IsBoundedUnder (· ≥ ·) l (g ∘ f) ↔ IsBoundedUnder (· ≤ ·) l f :=
- hg.dual_right.isBoundedUnder_le_comp hg'
-#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp
+ hg.dual_right.isBoundedUnder_le_comp_iff hg'
+#align antitone.is_bounded_under_ge_comp Antitone.isBoundedUnder_ge_comp_iff
theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
[ConditionallyCompleteLattice γ] {f : Filter α} {v : α → β} {l : β → γ} {u : γ → β}
@@ -2,15 +2,12 @@
Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Johannes Hölzl, Rémy Degenne
-
-! This file was ported from Lean 3 source module order.liminf_limsup
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Filter.Cofinite
import Mathlib.Order.Hom.CompleteLattice
+#align_import order.liminf_limsup from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
/-!
# liminfs and limsups of functions and filters
@@ -136,7 +136,7 @@ theorem not_isBoundedUnder_of_tendsto_atTop [Preorder β] [NoMaxOrder β] {f :
theorem not_isBoundedUnder_of_tendsto_atBot [Preorder β] [NoMinOrder β] {f : α → β} {l : Filter α}
[l.NeBot] (hf : Tendsto f l atBot) : ¬IsBoundedUnder (· ≥ ·) l f :=
- not_isBoundedUnder_of_tendsto_atTop (β := βᵒᵈ) hf
+ not_isBoundedUnder_of_tendsto_atTop (β := βᵒᵈ) hf
#align filter.not_is_bounded_under_of_tendsto_at_bot Filter.not_isBoundedUnder_of_tendsto_atBot
theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α → β}
@@ -149,7 +149,7 @@ theorem IsBoundedUnder.bddAbove_range_of_cofinite [SemilatticeSup β] {f : α
theorem IsBoundedUnder.bddBelow_range_of_cofinite [SemilatticeInf β] {f : α → β}
(hf : IsBoundedUnder (· ≥ ·) cofinite f) : BddBelow (range f) :=
- IsBoundedUnder.bddAbove_range_of_cofinite (β := βᵒᵈ) hf
+ IsBoundedUnder.bddAbove_range_of_cofinite (β := βᵒᵈ) hf
#align filter.is_bounded_under.bdd_below_range_of_cofinite Filter.IsBoundedUnder.bddBelow_range_of_cofinite
theorem IsBoundedUnder.bddAbove_range [SemilatticeSup β] {f : ℕ → β}
@@ -725,7 +725,7 @@ theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊤ → (p x ↔ q x)) : bliminf u f p = bliminf u f q :=
- blimsup_congr' (α := αᵒᵈ) h
+ blimsup_congr' (α := αᵒᵈ) h
#align filter.bliminf_congr' Filter.bliminf_congr'
theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -996,7 +996,7 @@ theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f := by
simp only [limsup_eq_iInf_iSup, iSup_sup_eq, sup_iInf₂_eq]
- congr ; ext s; congr ; ext hs; congr
+ congr; ext s; congr; ext hs; congr
exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
@@ -690,7 +690,7 @@ theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u
limsup_le_of_le (by isBoundedDefault) (eventually_of_forall (le_iSup u))
#align filter.limsup_le_supr Filter.limsup_le_iSup
-theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
+theorem iInf_le_liminf {f : Filter β} {u : β → α} : ⨅ n, u n ≤ liminf u f :=
le_liminf_of_le (by isBoundedDefault) (eventually_of_forall (iInf_le u))
#align filter.infi_le_liminf Filter.iInf_le_liminf
@@ -1020,11 +1020,11 @@ section CompleteBooleanAlgebra
variable [CompleteBooleanAlgebra α] (f : Filter β) (u : β → α)
-theorem limsup_compl : limsup u fᶜ = liminf (compl ∘ u) f := by
+theorem limsup_compl : (limsup u f)ᶜ = liminf (compl ∘ u) f := by
simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Function.comp_apply]
#align filter.limsup_compl Filter.limsup_compl
-theorem liminf_compl : liminf u fᶜ = limsup (compl ∘ u) f := by
+theorem liminf_compl : (liminf u f)ᶜ = limsup (compl ∘ u) f := by
simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Function.comp_apply]
#align filter.liminf_compl Filter.liminf_compl
@@ -838,21 +838,21 @@ theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
`a : α` is a fixed point. -/
@[simp]
theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (a : α) :
- f (limsup (fun n => (f^[n]) a) atTop) = limsup (fun n => (f^[n]) a) atTop := by
+ f (limsup (fun n => f^[n] a) atTop) = limsup (fun n => f^[n] a) atTop := by
rw [limsup_eq_iInf_iSup_of_nat', map_iInf]
simp_rw [_root_.map_iSup, ← Function.comp_apply (f := f), ← Function.iterate_succ' f,
← Nat.add_succ]
conv_rhs => rw [iInf_split _ ((· < ·) (0 : ℕ))]
simp only [not_lt, le_zero_iff, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
- refine' (iInf_le (fun i => ⨆ j, (f^[j + (i + 1)]) a) 0).trans _
+ refine' (iInf_le (fun i => ⨆ j, f^[j + (i + 1)] a) 0).trans _
simp only [zero_add, Function.comp_apply, iSup_le_iff]
- exact fun i => le_iSup (fun i => (f^[i]) a) (i + 1)
+ exact fun i => le_iSup (fun i => f^[i] a) (i + 1)
#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterate
/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
`a : α` is a fixed point. -/
theorem CompleteLatticeHom.apply_liminf_iterate (f : CompleteLatticeHom α α) (a : α) :
- f (liminf (fun n => (f^[n]) a) atTop) = liminf (fun n => (f^[n]) a) atTop :=
+ f (liminf (fun n => f^[n] a) atTop) = liminf (fun n => f^[n] a) atTop :=
apply_limsup_iterate (CompleteLatticeHom.dual f) _
#align filter.complete_lattice_hom.apply_liminf_iterate Filter.CompleteLatticeHom.apply_liminf_iterate
Filter.eq_or_neBot
(#5230)
Also add Filter.limsup_bot
, Filter.liminf_bot
, and golf some proofs using new lemmas.
@@ -618,12 +618,16 @@ theorem limsSup_bot : limsSup (⊥ : Filter α) = ⊥ :=
set_option linter.uppercaseLean3 false in
#align filter.Limsup_bot Filter.limsSup_bot
+@[simp] theorem limsup_bot (f : β → α) : limsup f ⊥ = ⊥ := by simp [limsup]
+
@[simp]
theorem limsInf_bot : limsInf (⊥ : Filter α) = ⊤ :=
top_unique <| le_sSup <| by simp
set_option linter.uppercaseLean3 false in
#align filter.Liminf_bot Filter.limsInf_bot
+@[simp] theorem liminf_bot (f : β → α) : liminf f ⊥ = ⊤ := by simp [liminf]
+
@[simp]
theorem limsSup_top : limsSup (⊤ : Filter α) = ⊤ :=
top_unique <| le_sInf <| by simp [eq_univ_iff_forall]; exact fun b hb => top_unique <| hb _
at
and goals (#5387)
Changes are of the form
some_tactic at h⊢
-> some_tactic at h ⊢
some_tactic at h
-> some_tactic at h
@@ -1210,7 +1210,7 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
l (limsup v f) ≤ limsup (fun x => l (v x)) f := by
refine' le_limsSup_of_le hlv fun c hc => _
rw [Filter.eventually_map] at hc
- simp_rw [gc _ _] at hc⊢
+ simp_rw [gc _ _] at hc ⊢
exact limsSup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
@@ -26,7 +26,7 @@ For instance, in ℕ along a function `u`, this is `inf_n (sup_{k ≥ n} u k)` (
decreases with `n`, so this is in fact a limit.). There is however a difficulty: it is well possible
that `u` is not bounded on the whole space, only eventually (think of `limsup (fun x ↦ 1/x)` on ℝ.
Then there is no guarantee that the quantity above really decreases (the value of the `sup`
-beforehand isnot really well defined, as one can not use ∞), so that the Inf could be anything.
+beforehand is not really well defined, as one can not use ∞), so that the Inf could be anything.
So one can not use this `inf sup ...` definition in conditionally complete lattices, and one has
to use a less tractable definition.
@@ -658,7 +658,7 @@ theorem liminf_const_top {f : Filter β} : liminf (fun _ : β => (⊤ : α)) f =
#align filter.liminf_const_top Filter.liminf_const_top
theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
- limsSup f = ⨅ (i) (_hi : p i), sSup (s i) :=
+ limsSup f = ⨅ (i) (_ : p i), sSup (s i) :=
le_antisymm (le_iInf₂ fun i hi => sInf_le <| h.eventually_iff.2 ⟨i, hi, fun _ => le_sSup⟩)
(le_sInf fun _ ha =>
let ⟨_, hi, ha⟩ := h.eventually_iff.1 ha
@@ -667,7 +667,7 @@ set_option linter.uppercaseLean3 false in
#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSup
theorem HasBasis.limsInf_eq_iSup_sInf {p : ι → Prop} {s : ι → Set α} {f : Filter α}
- (h : f.HasBasis p s) : limsInf f = ⨆ (i) (_hi : p i), sInf (s i) :=
+ (h : f.HasBasis p s) : limsInf f = ⨆ (i) (_ : p i), sInf (s i) :=
HasBasis.limsSup_eq_iInf_sSup (α := αᵒᵈ) h
set_option linter.uppercaseLean3 false in
#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInf
@@ -705,7 +705,7 @@ theorem limsup_eq_iInf_iSup_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n :
#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'
theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
- (h : f.HasBasis p s) : limsup u f = ⨅ (i) (_hi : p i), ⨆ a ∈ s i, u a :=
+ (h : f.HasBasis p s) : limsup u f = ⨅ (i) (_ : p i), ⨆ a ∈ s i, u a :=
(h.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSup
@@ -725,7 +725,7 @@ theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
#align filter.bliminf_congr' Filter.bliminf_congr'
theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
- blimsup u f p = ⨅ s ∈ f, ⨆ (b) (_hb : p b ∧ b ∈ s), u b := by
+ blimsup u f p = ⨅ s ∈ f, ⨆ (b) (_ : p b ∧ b ∈ s), u b := by
refine' le_antisymm (sInf_le_sInf _) (iInf_le_iff.mpr fun a ha => le_sInf_iff.mpr fun a' ha' => _)
· rintro - ⟨s, rfl⟩
simp only [mem_setOf_eq, le_iInf_iff]
@@ -742,7 +742,7 @@ theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α}
#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
- blimsup u atTop p = ⨅ i, ⨆ (j) (_hj : p j ∧ i ≤ j), u j := by
+ blimsup u atTop p = ⨅ i, ⨆ (j) (_ : p j ∧ i ≤ j), u j := by
-- Porting note: Making this into a single simp only does not work?
simp only [blimsup_eq_limsup_subtype, Function.comp,
(atTop_basis.comap ((↑) : { x | p x } → ℕ)).limsup_eq_iInf_iSup, iSup_subtype, iSup_and]
@@ -764,17 +764,17 @@ theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n :
#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'
theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
- (h : f.HasBasis p s) : liminf u f = ⨆ (i) (_hi : p i), ⨅ a ∈ s i, u a :=
+ (h : f.HasBasis p s) : liminf u f = ⨆ (i) (_ : p i), ⨅ a ∈ s i, u a :=
@HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
- bliminf u f p = ⨆ s ∈ f, ⨅ (b) (_hb : p b ∧ b ∈ s), u b :=
+ bliminf u f p = ⨆ s ∈ f, ⨅ (b) (_ : p b ∧ b ∈ s), u b :=
@blimsup_eq_iInf_biSup αᵒᵈ β _ f p u
#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInf
theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
- bliminf u atTop p = ⨆ i, ⨅ (j) (_hj : p j ∧ i ≤ j), u j :=
+ bliminf u atTop p = ⨆ i, ⨅ (j) (_ : p j ∧ i ≤ j), u j :=
@blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
@@ -818,7 +818,7 @@ theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x := by
rw [liminf_eq]
refine' sSup_le fun b hb => _
- have hbx : ∃ᶠ _a in f, b ≤ x := by
+ have hbx : ∃ᶠ _ in f, b ≤ x := by
revert h
rw [← not_imp_not, not_frequently, not_frequently]
exact fun h => hb.mp (h.mono fun a hbx hba hax => hbx (hba.trans hax))
This fixes a bunch of spacing bugs in tactics. Mathlib counterpart of:
@@ -315,12 +315,12 @@ in complete and conditionally complete lattices but let automation fill automati
boundedness proofs in complete lattices, we use the tactic `isBounded_default` in the statements,
in the form `(hf : f.IsBounded (≥) . isBoundedDefault)`. -/
-macro "isBoundedDefault ": tactic =>
- `(tactic| (first
- | apply isCobounded_le_of_bot
- | apply isCobounded_ge_of_top
- | apply isBounded_le_of_top
- | apply isBounded_ge_of_bot))
+macro "isBoundedDefault" : tactic =>
+ `(tactic| first
+ | apply isCobounded_le_of_bot
+ | apply isCobounded_ge_of_top
+ | apply isBounded_le_of_top
+ | apply isBounded_ge_of_bot)
-- Porting note: The above is a lean 4 reconstruction of (note that applyc is not available (yet?)):
-- unsafe def is_bounded_default : tactic Unit :=
sSup
/iSup
(#3938)
As discussed on Zulip
supₛ
→ sSup
infₛ
→ sInf
supᵢ
→ iSup
infᵢ
→ iInf
bsupₛ
→ bsSup
binfₛ
→ bsInf
bsupᵢ
→ biSup
binfᵢ
→ biInf
csupₛ
→ csSup
cinfₛ
→ csInf
csupᵢ
→ ciSup
cinfᵢ
→ ciInf
unionₛ
→ sUnion
interₛ
→ sInter
unionᵢ
→ iUnion
interᵢ
→ iInter
bunionₛ
→ bsUnion
binterₛ
→ bsInter
bunionᵢ
→ biUnion
binterᵢ
→ biInter
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
@@ -17,9 +17,9 @@ import Mathlib.Order.Hom.CompleteLattice
Defines the liminf/limsup of a function taking values in a conditionally complete lattice, with
respect to an arbitrary filter.
-We define `limsupₛ f` (`liminfₛ f`) where `f` is a filter taking values in a conditionally complete
-lattice. `limsupₛ f` is the smallest element `a` such that, eventually, `u ≤ a` (and vice versa for
-`liminfₛ f`). To work with the Limsup along a function `u` use `limsupₛ (map u f)`.
+We define `limsSup f` (`limsInf f`) where `f` is a filter taking values in a conditionally complete
+lattice. `limsSup f` is the smallest element `a` such that, eventually, `u ≤ a` (and vice versa for
+`limsInf f`). To work with the Limsup along a function `u` use `limsSup (map u f)`.
Usually, one defines the Limsup as `inf (sup s)` where the Inf is taken over all sets in the filter.
For instance, in ℕ along a function `u`, this is `inf_n (sup_{k ≥ n} u k)` (and the latter quantity
@@ -334,63 +334,63 @@ section ConditionallyCompleteLattice
variable [ConditionallyCompleteLattice α]
--- Porting note: Renamed from Limsup and Liminf to limsupₛ and liminfₛ
-/-- The `limsupₛ` of a filter `f` is the infimum of the `a` such that, eventually for `f`,
+-- Porting note: Renamed from Limsup and Liminf to limsSup and limsInf
+/-- The `limsSup` of a filter `f` is the infimum of the `a` such that, eventually for `f`,
holds `x ≤ a`. -/
-def limsupₛ (f : Filter α) : α :=
- infₛ { a | ∀ᶠ n in f, n ≤ a }
+def limsSup (f : Filter α) : α :=
+ sInf { a | ∀ᶠ n in f, n ≤ a }
set_option linter.uppercaseLean3 false in
-#align filter.Limsup Filter.limsupₛ
+#align filter.Limsup Filter.limsSup
set_option linter.uppercaseLean3 false in
-/-- The `liminfₛ` of a filter `f` is the supremum of the `a` such that, eventually for `f`,
+/-- The `limsInf` of a filter `f` is the supremum of the `a` such that, eventually for `f`,
holds `x ≥ a`. -/
-def liminfₛ (f : Filter α) : α :=
- supₛ { a | ∀ᶠ n in f, a ≤ n }
+def limsInf (f : Filter α) : α :=
+ sSup { a | ∀ᶠ n in f, a ≤ n }
set_option linter.uppercaseLean3 false in
-#align filter.Liminf Filter.liminfₛ
+#align filter.Liminf Filter.limsInf
/-- The `limsup` of a function `u` along a filter `f` is the infimum of the `a` such that,
eventually for `f`, holds `u x ≤ a`. -/
def limsup (u : β → α) (f : Filter β) : α :=
- limsupₛ (map u f)
+ limsSup (map u f)
#align filter.limsup Filter.limsup
/-- The `liminf` of a function `u` along a filter `f` is the supremum of the `a` such that,
eventually for `f`, holds `u x ≥ a`. -/
def liminf (u : β → α) (f : Filter β) : α :=
- liminfₛ (map u f)
+ limsInf (map u f)
#align filter.liminf Filter.liminf
/-- The `blimsup` of a function `u` along a filter `f`, bounded by a predicate `p`, is the infimum
of the `a` such that, eventually for `f`, `u x ≤ a` whenever `p x` holds. -/
def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
- infₛ { a | ∀ᶠ x in f, p x → u x ≤ a }
+ sInf { a | ∀ᶠ x in f, p x → u x ≤ a }
#align filter.blimsup Filter.blimsup
/-- The `bliminf` of a function `u` along a filter `f`, bounded by a predicate `p`, is the supremum
of the `a` such that, eventually for `f`, `a ≤ u x` whenever `p x` holds. -/
def bliminf (u : β → α) (f : Filter β) (p : β → Prop) :=
- supₛ { a | ∀ᶠ x in f, p x → a ≤ u x }
+ sSup { a | ∀ᶠ x in f, p x → a ≤ u x }
#align filter.bliminf Filter.bliminf
section
variable {f : Filter β} {u : β → α} {p : β → Prop}
-theorem limsup_eq : limsup u f = infₛ { a | ∀ᶠ n in f, u n ≤ a } :=
+theorem limsup_eq : limsup u f = sInf { a | ∀ᶠ n in f, u n ≤ a } :=
rfl
#align filter.limsup_eq Filter.limsup_eq
-theorem liminf_eq : liminf u f = supₛ { a | ∀ᶠ n in f, a ≤ u n } :=
+theorem liminf_eq : liminf u f = sSup { a | ∀ᶠ n in f, a ≤ u n } :=
rfl
#align filter.liminf_eq Filter.liminf_eq
-theorem blimsup_eq : blimsup u f p = infₛ { a | ∀ᶠ x in f, p x → u x ≤ a } :=
+theorem blimsup_eq : blimsup u f p = sInf { a | ∀ᶠ x in f, p x → u x ≤ a } :=
rfl
#align filter.blimsup_eq Filter.blimsup_eq
-theorem bliminf_eq : bliminf u f p = supₛ { a | ∀ᶠ x in f, p x → a ≤ u x } :=
+theorem bliminf_eq : bliminf u f p = sSup { a | ∀ᶠ x in f, p x → a ≤ u x } :=
rfl
#align filter.bliminf_eq Filter.bliminf_eq
@@ -423,99 +423,99 @@ theorem bliminf_eq_liminf_subtype {f : Filter β} {u : β → α} {p : β → Pr
blimsup_eq_limsup_subtype (α := αᵒᵈ)
#align filter.bliminf_eq_liminf_subtype Filter.bliminf_eq_liminf_subtype
-theorem limsupₛ_le_of_le {f : Filter α} {a}
+theorem limsSup_le_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≤ ·) := by isBoundedDefault)
- (h : ∀ᶠ n in f, n ≤ a) : limsupₛ f ≤ a :=
- cinfₛ_le hf h
+ (h : ∀ᶠ n in f, n ≤ a) : limsSup f ≤ a :=
+ csInf_le hf h
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_le_of_le Filter.limsupₛ_le_of_le
+#align filter.Limsup_le_of_le Filter.limsSup_le_of_le
-theorem le_liminfₛ_of_le {f : Filter α} {a}
+theorem le_limsInf_of_le {f : Filter α} {a}
(hf : f.IsCobounded (· ≥ ·) := by isBoundedDefault)
- (h : ∀ᶠ n in f, a ≤ n) : a ≤ liminfₛ f :=
- le_csupₛ hf h
+ (h : ∀ᶠ n in f, a ≤ n) : a ≤ limsInf f :=
+ le_csSup hf h
set_option linter.uppercaseLean3 false in
-#align filter.le_Liminf_of_le Filter.le_liminfₛ_of_le
+#align filter.le_Liminf_of_le Filter.le_limsInf_of_le
theorem limsup_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by isBoundedDefault)
(h : ∀ᶠ n in f, u n ≤ a) : limsup u f ≤ a :=
- cinfₛ_le hf h
-#align filter.limsup_le_of_le Filter.limsupₛ_le_of_le
+ csInf_le hf h
+#align filter.limsup_le_of_le Filter.limsSup_le_of_le
theorem le_liminf_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsCoboundedUnder (· ≥ ·) u := by isBoundedDefault)
(h : ∀ᶠ n in f, a ≤ u n) : a ≤ liminf u f :=
- le_csupₛ hf h
+ le_csSup hf h
#align filter.le_liminf_of_le Filter.le_liminf_of_le
-theorem le_limsupₛ_of_le {f : Filter α} {a}
+theorem le_limsSup_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≤ ·) := by isBoundedDefault)
- (h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsupₛ f :=
- le_cinfₛ hf h
+ (h : ∀ b, (∀ᶠ n in f, n ≤ b) → a ≤ b) : a ≤ limsSup f :=
+ le_csInf hf h
set_option linter.uppercaseLean3 false in
-#align filter.le_Limsup_of_le Filter.le_limsupₛ_of_le
+#align filter.le_Limsup_of_le Filter.le_limsSup_of_le
-theorem liminfₛ_le_of_le {f : Filter α} {a}
+theorem limsInf_le_of_le {f : Filter α} {a}
(hf : f.IsBounded (· ≥ ·) := by isBoundedDefault)
- (h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : liminfₛ f ≤ a :=
- csupₛ_le hf h
+ (h : ∀ b, (∀ᶠ n in f, b ≤ n) → b ≤ a) : limsInf f ≤ a :=
+ csSup_le hf h
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_le_of_le Filter.liminfₛ_le_of_le
+#align filter.Liminf_le_of_le Filter.limsInf_le_of_le
theorem le_limsup_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≤ ·) u := by isBoundedDefault)
(h : ∀ b, (∀ᶠ n in f, u n ≤ b) → a ≤ b) : a ≤ limsup u f :=
- le_cinfₛ hf h
+ le_csInf hf h
#align filter.le_limsup_of_le Filter.le_limsup_of_le
theorem liminf_le_of_le {f : Filter β} {u : β → α} {a}
(hf : f.IsBoundedUnder (· ≥ ·) u := by isBoundedDefault)
(h : ∀ b, (∀ᶠ n in f, b ≤ u n) → b ≤ a) : liminf u f ≤ a :=
- csupₛ_le hf h
+ csSup_le hf h
#align filter.liminf_le_of_le Filter.liminf_le_of_le
-theorem liminfₛ_le_limsupₛ {f : Filter α} [NeBot f]
+theorem limsInf_le_limsSup {f : Filter α} [NeBot f]
(h₁ : f.IsBounded (· ≤ ·) := by isBoundedDefault)
(h₂ : f.IsBounded (· ≥ ·) := by isBoundedDefault):
- liminfₛ f ≤ limsupₛ f :=
+ limsInf f ≤ limsSup f :=
liminf_le_of_le h₂ fun a₀ ha₀ =>
le_limsup_of_le h₁ fun a₁ ha₁ =>
show a₀ ≤ a₁ from
let ⟨_, hb₀, hb₁⟩ := (ha₀.and ha₁).exists
le_trans hb₀ hb₁
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_le_Limsup Filter.liminfₛ_le_limsupₛ
+#align filter.Liminf_le_Limsup Filter.limsInf_le_limsSup
theorem liminf_le_limsup {f : Filter β} [NeBot f] {u : β → α}
(h : f.IsBoundedUnder (· ≤ ·) u := by isBoundedDefault)
(h' : f.IsBoundedUnder (· ≥ ·) u := by isBoundedDefault):
liminf u f ≤ limsup u f :=
- liminfₛ_le_limsupₛ h h'
+ limsInf_le_limsSup h h'
#align filter.liminf_le_limsup Filter.liminf_le_limsup
-theorem limsupₛ_le_limsupₛ {f g : Filter α}
+theorem limsSup_le_limsSup {f g : Filter α}
(hf : f.IsCobounded (· ≤ ·) := by isBoundedDefault)
(hg : g.IsBounded (· ≤ ·) := by isBoundedDefault)
- (h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsupₛ f ≤ limsupₛ g :=
- cinfₛ_le_cinfₛ hf hg h
+ (h : ∀ a, (∀ᶠ n in g, n ≤ a) → ∀ᶠ n in f, n ≤ a) : limsSup f ≤ limsSup g :=
+ csInf_le_csInf hf hg h
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_le_Limsup Filter.limsupₛ_le_limsupₛ
+#align filter.Limsup_le_Limsup Filter.limsSup_le_limsSup
-theorem liminfₛ_le_liminfₛ {f g : Filter α}
+theorem limsInf_le_limsInf {f g : Filter α}
(hf : f.IsBounded (· ≥ ·) := by isBoundedDefault)
(hg : g.IsCobounded (· ≥ ·) := by isBoundedDefault)
- (h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : liminfₛ f ≤ liminfₛ g :=
- csupₛ_le_csupₛ hg hf h
+ (h : ∀ a, (∀ᶠ n in f, a ≤ n) → ∀ᶠ n in g, a ≤ n) : limsInf f ≤ limsInf g :=
+ csSup_le_csSup hg hf h
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_le_Liminf Filter.liminfₛ_le_liminfₛ
+#align filter.Liminf_le_Liminf Filter.limsInf_le_limsInf
theorem limsup_le_limsup {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : u ≤ᶠ[f] v)
(hu : f.IsCoboundedUnder (· ≤ ·) u := by isBoundedDefault)
(hv : f.IsBoundedUnder (· ≤ ·) v := by isBoundedDefault) :
limsup u f ≤ limsup v f :=
- limsupₛ_le_limsupₛ hu hv fun _ => h.trans
+ limsSup_le_limsSup hu hv fun _ => h.trans
#align filter.limsup_le_limsup Filter.limsup_le_limsup
theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
@@ -526,28 +526,28 @@ theorem liminf_le_liminf {α : Type _} [ConditionallyCompleteLattice β] {f : Fi
limsup_le_limsup (β := βᵒᵈ) h hv hu
#align filter.liminf_le_liminf Filter.liminf_le_liminf
-theorem limsupₛ_le_limsupₛ_of_le {f g : Filter α} (h : f ≤ g)
+theorem limsSup_le_limsSup_of_le {f g : Filter α} (h : f ≤ g)
(hf : f.IsCobounded (· ≤ ·) := by isBoundedDefault)
(hg : g.IsBounded (· ≤ ·) := by isBoundedDefault) :
- limsupₛ f ≤ limsupₛ g :=
- limsupₛ_le_limsupₛ hf hg fun _ ha => h ha
+ limsSup f ≤ limsSup g :=
+ limsSup_le_limsSup hf hg fun _ ha => h ha
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_le_Limsup_of_le Filter.limsupₛ_le_limsupₛ_of_le
+#align filter.Limsup_le_Limsup_of_le Filter.limsSup_le_limsSup_of_le
-theorem liminfₛ_le_liminfₛ_of_le {f g : Filter α} (h : g ≤ f)
+theorem limsInf_le_limsInf_of_le {f g : Filter α} (h : g ≤ f)
(hf : f.IsBounded (· ≥ ·) := by isBoundedDefault)
(hg : g.IsCobounded (· ≥ ·) := by isBoundedDefault) :
- liminfₛ f ≤ liminfₛ g :=
- liminfₛ_le_liminfₛ hf hg fun _ ha => h ha
+ limsInf f ≤ limsInf g :=
+ limsInf_le_limsInf hf hg fun _ ha => h ha
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_le_Liminf_of_le Filter.liminfₛ_le_liminfₛ_of_le
+#align filter.Liminf_le_Liminf_of_le Filter.limsInf_le_limsInf_of_le
theorem limsup_le_limsup_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : f ≤ g)
{u : α → β}
(hf : f.IsCoboundedUnder (· ≤ ·) u := by isBoundedDefault)
(hg : g.IsBoundedUnder (· ≤ ·) u := by isBoundedDefault) :
limsup u f ≤ limsup u g :=
- limsupₛ_le_limsupₛ_of_le (map_mono h) hf hg
+ limsSup_le_limsSup_of_le (map_mono h) hf hg
#align filter.limsup_le_limsup_of_le Filter.limsup_le_limsup_of_le
theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g : Filter α} (h : g ≤ f)
@@ -555,18 +555,18 @@ theorem liminf_le_liminf_of_le {α β} [ConditionallyCompleteLattice β] {f g :
(hf : f.IsBoundedUnder (· ≥ ·) u := by isBoundedDefault)
(hg : g.IsCoboundedUnder (· ≥ ·) u := by isBoundedDefault) :
liminf u f ≤ liminf u g :=
- liminfₛ_le_liminfₛ_of_le (map_mono h) hf hg
+ limsInf_le_limsInf_of_le (map_mono h) hf hg
#align filter.liminf_le_liminf_of_le Filter.liminf_le_liminf_of_le
-theorem limsupₛ_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsupₛ (𝓟 s) = supₛ s :=
- by simp only [limsupₛ, eventually_principal]; exact cinfₛ_upper_bounds_eq_csupₛ h hs
+theorem limsSup_principal {s : Set α} (h : BddAbove s) (hs : s.Nonempty) : limsSup (𝓟 s) = sSup s :=
+ by simp only [limsSup, eventually_principal]; exact csInf_upper_bounds_eq_csSup h hs
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_principal Filter.limsupₛ_principal
+#align filter.Limsup_principal Filter.limsSup_principal
-theorem liminfₛ_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : liminfₛ (𝓟 s) = infₛ s :=
- limsupₛ_principal (α := αᵒᵈ) h hs
+theorem limsInf_principal {s : Set α} (h : BddBelow s) (hs : s.Nonempty) : limsInf (𝓟 s) = sInf s :=
+ limsSup_principal (α := αᵒᵈ) h hs
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_principal Filter.liminfₛ_principal
+#align filter.Liminf_principal Filter.limsInf_principal
theorem limsup_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} {u v : α → β}
(h : ∀ᶠ a in f, u a = v a) : limsup u f = limsup v f := by
@@ -598,7 +598,7 @@ theorem liminf_congr {α : Type _} [ConditionallyCompleteLattice β] {f : Filter
theorem limsup_const {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
(b : β) : limsup (fun _ => b) f = b := by
- simpa only [limsup_eq, eventually_const] using cinfₛ_Ici
+ simpa only [limsup_eq, eventually_const] using csInf_Ici
#align filter.limsup_const Filter.limsup_const
theorem liminf_const {α : Type _} [ConditionallyCompleteLattice β] {f : Filter α} [NeBot f]
@@ -613,28 +613,28 @@ section CompleteLattice
variable [CompleteLattice α]
@[simp]
-theorem limsupₛ_bot : limsupₛ (⊥ : Filter α) = ⊥ :=
- bot_unique <| infₛ_le <| by simp
+theorem limsSup_bot : limsSup (⊥ : Filter α) = ⊥ :=
+ bot_unique <| sInf_le <| by simp
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_bot Filter.limsupₛ_bot
+#align filter.Limsup_bot Filter.limsSup_bot
@[simp]
-theorem liminfₛ_bot : liminfₛ (⊥ : Filter α) = ⊤ :=
- top_unique <| le_supₛ <| by simp
+theorem limsInf_bot : limsInf (⊥ : Filter α) = ⊤ :=
+ top_unique <| le_sSup <| by simp
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_bot Filter.liminfₛ_bot
+#align filter.Liminf_bot Filter.limsInf_bot
@[simp]
-theorem limsupₛ_top : limsupₛ (⊤ : Filter α) = ⊤ :=
- top_unique <| le_infₛ <| by simp [eq_univ_iff_forall]; exact fun b hb => top_unique <| hb _
+theorem limsSup_top : limsSup (⊤ : Filter α) = ⊤ :=
+ top_unique <| le_sInf <| by simp [eq_univ_iff_forall]; exact fun b hb => top_unique <| hb _
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_top Filter.limsupₛ_top
+#align filter.Limsup_top Filter.limsSup_top
@[simp]
-theorem liminfₛ_top : liminfₛ (⊤ : Filter α) = ⊥ :=
- bot_unique <| supₛ_le <| by simp [eq_univ_iff_forall]; exact fun b hb => bot_unique <| hb _
+theorem limsInf_top : limsInf (⊤ : Filter α) = ⊥ :=
+ bot_unique <| sSup_le <| by simp [eq_univ_iff_forall]; exact fun b hb => bot_unique <| hb _
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_top Filter.liminfₛ_top
+#align filter.Liminf_top Filter.limsInf_top
@[simp]
theorem blimsup_false {f : Filter β} {u : β → α} : (blimsup u f fun _ => False) = ⊥ := by
@@ -649,7 +649,7 @@ theorem bliminf_false {f : Filter β} {u : β → α} : (bliminf u f fun _ => Fa
/-- Same as limsup_const applied to `⊥` but without the `NeBot f` assumption -/
theorem limsup_const_bot {f : Filter β} : limsup (fun _ : β => (⊥ : α)) f = (⊥ : α) := by
rw [limsup_eq, eq_bot_iff]
- exact infₛ_le (eventually_of_forall fun _ => le_rfl)
+ exact sInf_le (eventually_of_forall fun _ => le_rfl)
#align filter.limsup_const_bot Filter.limsup_const_bot
/-- Same as limsup_const applied to `⊤` but without the `NeBot f` assumption -/
@@ -657,57 +657,57 @@ theorem liminf_const_top {f : Filter β} : liminf (fun _ : β => (⊤ : α)) f =
limsup_const_bot (α := αᵒᵈ)
#align filter.liminf_const_top Filter.liminf_const_top
-theorem HasBasis.limsupₛ_eq_infᵢ_supₛ {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
- limsupₛ f = ⨅ (i) (_hi : p i), supₛ (s i) :=
- le_antisymm (le_infᵢ₂ fun i hi => infₛ_le <| h.eventually_iff.2 ⟨i, hi, fun _ => le_supₛ⟩)
- (le_infₛ fun _ ha =>
+theorem HasBasis.limsSup_eq_iInf_sSup {ι} {p : ι → Prop} {s} {f : Filter α} (h : f.HasBasis p s) :
+ limsSup f = ⨅ (i) (_hi : p i), sSup (s i) :=
+ le_antisymm (le_iInf₂ fun i hi => sInf_le <| h.eventually_iff.2 ⟨i, hi, fun _ => le_sSup⟩)
+ (le_sInf fun _ ha =>
let ⟨_, hi, ha⟩ := h.eventually_iff.1 ha
- infᵢ₂_le_of_le _ hi <| supₛ_le ha)
+ iInf₂_le_of_le _ hi <| sSup_le ha)
set_option linter.uppercaseLean3 false in
-#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsupₛ_eq_infᵢ_supₛ
+#align filter.has_basis.Limsup_eq_infi_Sup Filter.HasBasis.limsSup_eq_iInf_sSup
-theorem HasBasis.liminfₛ_eq_supᵢ_infₛ {p : ι → Prop} {s : ι → Set α} {f : Filter α}
- (h : f.HasBasis p s) : liminfₛ f = ⨆ (i) (_hi : p i), infₛ (s i) :=
- HasBasis.limsupₛ_eq_infᵢ_supₛ (α := αᵒᵈ) h
+theorem HasBasis.limsInf_eq_iSup_sInf {p : ι → Prop} {s : ι → Set α} {f : Filter α}
+ (h : f.HasBasis p s) : limsInf f = ⨆ (i) (_hi : p i), sInf (s i) :=
+ HasBasis.limsSup_eq_iInf_sSup (α := αᵒᵈ) h
set_option linter.uppercaseLean3 false in
-#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.liminfₛ_eq_supᵢ_infₛ
+#align filter.has_basis.Liminf_eq_supr_Inf Filter.HasBasis.limsInf_eq_iSup_sInf
-theorem limsupₛ_eq_infᵢ_supₛ {f : Filter α} : limsupₛ f = ⨅ s ∈ f, supₛ s :=
- f.basis_sets.limsupₛ_eq_infᵢ_supₛ
+theorem limsSup_eq_iInf_sSup {f : Filter α} : limsSup f = ⨅ s ∈ f, sSup s :=
+ f.basis_sets.limsSup_eq_iInf_sSup
set_option linter.uppercaseLean3 false in
-#align filter.Limsup_eq_infi_Sup Filter.limsupₛ_eq_infᵢ_supₛ
+#align filter.Limsup_eq_infi_Sup Filter.limsSup_eq_iInf_sSup
-theorem liminfₛ_eq_supᵢ_infₛ {f : Filter α} : liminfₛ f = ⨆ s ∈ f, infₛ s :=
- limsupₛ_eq_infᵢ_supₛ (α := αᵒᵈ)
+theorem limsInf_eq_iSup_sInf {f : Filter α} : limsInf f = ⨆ s ∈ f, sInf s :=
+ limsSup_eq_iInf_sSup (α := αᵒᵈ)
set_option linter.uppercaseLean3 false in
-#align filter.Liminf_eq_supr_Inf Filter.liminfₛ_eq_supᵢ_infₛ
+#align filter.Liminf_eq_supr_Inf Filter.limsInf_eq_iSup_sInf
-theorem limsup_le_supᵢ {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
- limsup_le_of_le (by isBoundedDefault) (eventually_of_forall (le_supᵢ u))
-#align filter.limsup_le_supr Filter.limsup_le_supᵢ
+theorem limsup_le_iSup {f : Filter β} {u : β → α} : limsup u f ≤ ⨆ n, u n :=
+ limsup_le_of_le (by isBoundedDefault) (eventually_of_forall (le_iSup u))
+#align filter.limsup_le_supr Filter.limsup_le_iSup
-theorem infᵢ_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
- le_liminf_of_le (by isBoundedDefault) (eventually_of_forall (infᵢ_le u))
-#align filter.infi_le_liminf Filter.infᵢ_le_liminf
+theorem iInf_le_liminf {f : Filter β} {u : β → α} : (⨅ n, u n) ≤ liminf u f :=
+ le_liminf_of_le (by isBoundedDefault) (eventually_of_forall (iInf_le u))
+#align filter.infi_le_liminf Filter.iInf_le_liminf
/-- In a complete lattice, the limsup of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
-theorem limsup_eq_infᵢ_supᵢ {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
- (f.basis_sets.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, id]
-#align filter.limsup_eq_infi_supr Filter.limsup_eq_infᵢ_supᵢ
+theorem limsup_eq_iInf_iSup {f : Filter β} {u : β → α} : limsup u f = ⨅ s ∈ f, ⨆ a ∈ s, u a :=
+ (f.basis_sets.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
+#align filter.limsup_eq_infi_supr Filter.limsup_eq_iInf_iSup
-theorem limsup_eq_infᵢ_supᵢ_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
- (atTop_basis.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, infᵢ_const]; rfl
-#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_infᵢ_supᵢ_of_nat
+theorem limsup_eq_iInf_iSup_of_nat {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i ≥ n, u i :=
+ (atTop_basis.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, iInf_const]; rfl
+#align filter.limsup_eq_infi_supr_of_nat Filter.limsup_eq_iInf_iSup_of_nat
-theorem limsup_eq_infᵢ_supᵢ_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
- simp only [limsup_eq_infᵢ_supᵢ_of_nat, supᵢ_ge_eq_supᵢ_nat_add]
-#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_infᵢ_supᵢ_of_nat'
+theorem limsup_eq_iInf_iSup_of_nat' {u : ℕ → α} : limsup u atTop = ⨅ n : ℕ, ⨆ i : ℕ, u (i + n) := by
+ simp only [limsup_eq_iInf_iSup_of_nat, iSup_ge_eq_iSup_nat_add]
+#align filter.limsup_eq_infi_supr_of_nat' Filter.limsup_eq_iInf_iSup_of_nat'
-theorem HasBasis.limsup_eq_infᵢ_supᵢ {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
+theorem HasBasis.limsup_eq_iInf_iSup {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : limsup u f = ⨅ (i) (_hi : p i), ⨆ a ∈ s i, u a :=
- (h.map u).limsupₛ_eq_infᵢ_supₛ.trans <| by simp only [supₛ_image, id]
-#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_infᵢ_supᵢ
+ (h.map u).limsSup_eq_iInf_sSup.trans <| by simp only [sSup_image, id]
+#align filter.has_basis.limsup_eq_infi_supr Filter.HasBasis.limsup_eq_iInf_iSup
theorem blimsup_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
(h : ∀ᶠ x in f, u x ≠ ⊥ → (p x ↔ q x)) : blimsup u f p = blimsup u f q := by
@@ -724,88 +724,88 @@ theorem bliminf_congr' {f : Filter β} {p q : β → Prop} {u : β → α}
blimsup_congr' (α := αᵒᵈ) h
#align filter.bliminf_congr' Filter.bliminf_congr'
-theorem blimsup_eq_infᵢ_bsupᵢ {f : Filter β} {p : β → Prop} {u : β → α} :
+theorem blimsup_eq_iInf_biSup {f : Filter β} {p : β → Prop} {u : β → α} :
blimsup u f p = ⨅ s ∈ f, ⨆ (b) (_hb : p b ∧ b ∈ s), u b := by
- refine' le_antisymm (infₛ_le_infₛ _) (infᵢ_le_iff.mpr fun a ha => le_infₛ_iff.mpr fun a' ha' => _)
+ refine' le_antisymm (sInf_le_sInf _) (iInf_le_iff.mpr fun a ha => le_sInf_iff.mpr fun a' ha' => _)
· rintro - ⟨s, rfl⟩
- simp only [mem_setOf_eq, le_infᵢ_iff]
+ simp only [mem_setOf_eq, le_iInf_iff]
conv =>
congr
ext
rw [Imp.swap]
refine'
eventually_imp_distrib_left.mpr fun h => eventually_iff_exists_mem.2 ⟨s, h, fun x h₁ h₂ => _⟩
- exact @le_supᵢ₂ α β (fun b => p b ∧ b ∈ s) _ (fun b _ => u b) x ⟨h₂, h₁⟩
+ exact @le_iSup₂ α β (fun b => p b ∧ b ∈ s) _ (fun b _ => u b) x ⟨h₂, h₁⟩
· obtain ⟨s, hs, hs'⟩ := eventually_iff_exists_mem.mp ha'
have : ∀ (y : β), p y → y ∈ s → u y ≤ a' := fun y ↦ by rw [Imp.swap]; exact hs' y
- exact (le_infᵢ_iff.mp (ha s) hs).trans (by simpa only [supᵢ₂_le_iff, and_imp] )
-#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_infᵢ_bsupᵢ
+ exact (le_iInf_iff.mp (ha s) hs).trans (by simpa only [iSup₂_le_iff, and_imp] )
+#align filter.blimsup_eq_infi_bsupr Filter.blimsup_eq_iInf_biSup
-theorem blimsup_eq_infᵢ_bsupᵢ_of_nat {p : ℕ → Prop} {u : ℕ → α} :
+theorem blimsup_eq_iInf_biSup_of_nat {p : ℕ → Prop} {u : ℕ → α} :
blimsup u atTop p = ⨅ i, ⨆ (j) (_hj : p j ∧ i ≤ j), u j := by
-- Porting note: Making this into a single simp only does not work?
simp only [blimsup_eq_limsup_subtype, Function.comp,
- (atTop_basis.comap ((↑) : { x | p x } → ℕ)).limsup_eq_infᵢ_supᵢ, supᵢ_subtype, supᵢ_and]
- simp only [mem_setOf_eq, mem_preimage, mem_Ici, not_le, infᵢ_pos]
-#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_infᵢ_bsupᵢ_of_nat
+ (atTop_basis.comap ((↑) : { x | p x } → ℕ)).limsup_eq_iInf_iSup, iSup_subtype, iSup_and]
+ simp only [mem_setOf_eq, mem_preimage, mem_Ici, not_le, iInf_pos]
+#align filter.blimsup_eq_infi_bsupr_of_nat Filter.blimsup_eq_iInf_biSup_of_nat
/-- In a complete lattice, the liminf of a function is the infimum over sets `s` in the filter
of the supremum of the function over `s` -/
-theorem liminf_eq_supᵢ_infᵢ {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
- @limsup_eq_infᵢ_supᵢ αᵒᵈ β _ _ _
-#align filter.liminf_eq_supr_infi Filter.liminf_eq_supᵢ_infᵢ
+theorem liminf_eq_iSup_iInf {f : Filter β} {u : β → α} : liminf u f = ⨆ s ∈ f, ⨅ a ∈ s, u a :=
+ @limsup_eq_iInf_iSup αᵒᵈ β _ _ _
+#align filter.liminf_eq_supr_infi Filter.liminf_eq_iSup_iInf
-theorem liminf_eq_supᵢ_infᵢ_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
- @limsup_eq_infᵢ_supᵢ_of_nat αᵒᵈ _ u
-#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_supᵢ_infᵢ_of_nat
+theorem liminf_eq_iSup_iInf_of_nat {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i ≥ n, u i :=
+ @limsup_eq_iInf_iSup_of_nat αᵒᵈ _ u
+#align filter.liminf_eq_supr_infi_of_nat Filter.liminf_eq_iSup_iInf_of_nat
-theorem liminf_eq_supᵢ_infᵢ_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
- @limsup_eq_infᵢ_supᵢ_of_nat' αᵒᵈ _ _
-#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_supᵢ_infᵢ_of_nat'
+theorem liminf_eq_iSup_iInf_of_nat' {u : ℕ → α} : liminf u atTop = ⨆ n : ℕ, ⨅ i : ℕ, u (i + n) :=
+ @limsup_eq_iInf_iSup_of_nat' αᵒᵈ _ _
+#align filter.liminf_eq_supr_infi_of_nat' Filter.liminf_eq_iSup_iInf_of_nat'
-theorem HasBasis.liminf_eq_supᵢ_infᵢ {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
+theorem HasBasis.liminf_eq_iSup_iInf {p : ι → Prop} {s : ι → Set β} {f : Filter β} {u : β → α}
(h : f.HasBasis p s) : liminf u f = ⨆ (i) (_hi : p i), ⨅ a ∈ s i, u a :=
- @HasBasis.limsup_eq_infᵢ_supᵢ αᵒᵈ _ _ _ _ _ _ _ h
-#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_supᵢ_infᵢ
+ @HasBasis.limsup_eq_iInf_iSup αᵒᵈ _ _ _ _ _ _ _ h
+#align filter.has_basis.liminf_eq_supr_infi Filter.HasBasis.liminf_eq_iSup_iInf
-theorem bliminf_eq_supᵢ_binfᵢ {f : Filter β} {p : β → Prop} {u : β → α} :
+theorem bliminf_eq_iSup_biInf {f : Filter β} {p : β → Prop} {u : β → α} :
bliminf u f p = ⨆ s ∈ f, ⨅ (b) (_hb : p b ∧ b ∈ s), u b :=
- @blimsup_eq_infᵢ_bsupᵢ αᵒᵈ β _ f p u
-#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_supᵢ_binfᵢ
+ @blimsup_eq_iInf_biSup αᵒᵈ β _ f p u
+#align filter.bliminf_eq_supr_binfi Filter.bliminf_eq_iSup_biInf
-theorem bliminf_eq_supᵢ_binfᵢ_of_nat {p : ℕ → Prop} {u : ℕ → α} :
+theorem bliminf_eq_iSup_biInf_of_nat {p : ℕ → Prop} {u : ℕ → α} :
bliminf u atTop p = ⨆ i, ⨅ (j) (_hj : p j ∧ i ≤ j), u j :=
- @blimsup_eq_infᵢ_bsupᵢ_of_nat αᵒᵈ _ p u
-#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_supᵢ_binfᵢ_of_nat
+ @blimsup_eq_iInf_biSup_of_nat αᵒᵈ _ p u
+#align filter.bliminf_eq_supr_binfi_of_nat Filter.bliminf_eq_iSup_biInf_of_nat
-theorem limsup_eq_infₛ_supₛ {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
- limsup a F = infₛ ((fun I => supₛ (a '' I)) '' F.sets) := by
+theorem limsup_eq_sInf_sSup {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+ limsup a F = sInf ((fun I => sSup (a '' I)) '' F.sets) := by
refine' le_antisymm _ _
· rw [limsup_eq]
- refine' infₛ_le_infₛ fun x hx => _
+ refine' sInf_le_sInf fun x hx => _
rcases(mem_image _ F.sets x).mp hx with ⟨I, ⟨I_mem_F, hI⟩⟩
filter_upwards [I_mem_F]with i hi
- exact hI ▸ le_supₛ (mem_image_of_mem _ hi)
+ exact hI ▸ le_sSup (mem_image_of_mem _ hi)
· refine'
- le_infₛ_iff.mpr fun b hb =>
- infₛ_le_of_le (mem_image_of_mem _ <| Filter.mem_sets.mpr hb) <| supₛ_le _
+ le_sInf_iff.mpr fun b hb =>
+ sInf_le_of_le (mem_image_of_mem _ <| Filter.mem_sets.mpr hb) <| sSup_le _
rintro _ ⟨_, h, rfl⟩
exact h
set_option linter.uppercaseLean3 false in
-#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_infₛ_supₛ
+#align filter.limsup_eq_Inf_Sup Filter.limsup_eq_sInf_sSup
-theorem liminf_eq_supₛ_infₛ {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
- liminf a F = supₛ ((fun I => infₛ (a '' I)) '' F.sets) :=
- @Filter.limsup_eq_infₛ_supₛ ι (OrderDual R) _ _ a
+theorem liminf_eq_sSup_sInf {ι R : Type _} (F : Filter ι) [CompleteLattice R] (a : ι → R) :
+ liminf a F = sSup ((fun I => sInf (a '' I)) '' F.sets) :=
+ @Filter.limsup_eq_sInf_sSup ι (OrderDual R) _ _ a
set_option linter.uppercaseLean3 false in
-#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_supₛ_infₛ
+#align filter.liminf_eq_Sup_Inf Filter.liminf_eq_sSup_sInf
-- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
@[simp, nolint simpNF]
theorem liminf_nat_add (f : ℕ → α) (k : ℕ) :
liminf (fun i => f (i + k)) atTop = liminf f atTop := by
- simp_rw [liminf_eq_supᵢ_infᵢ_of_nat]
- exact supᵢ_infᵢ_ge_nat_add f k
+ simp_rw [liminf_eq_iSup_iInf_of_nat]
+ exact iSup_iInf_ge_nat_add f k
#align filter.liminf_nat_add Filter.liminf_nat_add
-- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
@@ -817,7 +817,7 @@ theorem limsup_nat_add (f : ℕ → α) (k : ℕ) : limsup (fun i => f (i + k))
theorem liminf_le_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α} {u : α → β} {x : β}
(h : ∃ᶠ a in f, u a ≤ x) : liminf u f ≤ x := by
rw [liminf_eq]
- refine' supₛ_le fun b hb => _
+ refine' sSup_le fun b hb => _
have hbx : ∃ᶠ _a in f, b ≤ x := by
revert h
rw [← not_imp_not, not_frequently, not_frequently]
@@ -835,14 +835,14 @@ theorem le_limsup_of_frequently_le' {α β} [CompleteLattice β] {f : Filter α}
@[simp]
theorem CompleteLatticeHom.apply_limsup_iterate (f : CompleteLatticeHom α α) (a : α) :
f (limsup (fun n => (f^[n]) a) atTop) = limsup (fun n => (f^[n]) a) atTop := by
- rw [limsup_eq_infᵢ_supᵢ_of_nat', map_infᵢ]
- simp_rw [_root_.map_supᵢ, ← Function.comp_apply (f := f), ← Function.iterate_succ' f,
+ rw [limsup_eq_iInf_iSup_of_nat', map_iInf]
+ simp_rw [_root_.map_iSup, ← Function.comp_apply (f := f), ← Function.iterate_succ' f,
← Nat.add_succ]
- conv_rhs => rw [infᵢ_split _ ((· < ·) (0 : ℕ))]
- simp only [not_lt, le_zero_iff, infᵢ_infᵢ_eq_left, add_zero, infᵢ_nat_gt_zero_eq, left_eq_inf]
- refine' (infᵢ_le (fun i => ⨆ j, (f^[j + (i + 1)]) a) 0).trans _
- simp only [zero_add, Function.comp_apply, supᵢ_le_iff]
- exact fun i => le_supᵢ (fun i => (f^[i]) a) (i + 1)
+ conv_rhs => rw [iInf_split _ ((· < ·) (0 : ℕ))]
+ simp only [not_lt, le_zero_iff, iInf_iInf_eq_left, add_zero, iInf_nat_gt_zero_eq, left_eq_inf]
+ refine' (iInf_le (fun i => ⨆ j, (f^[j + (i + 1)]) a) 0).trans _
+ simp only [zero_add, Function.comp_apply, iSup_le_iff]
+ exact fun i => le_iSup (fun i => (f^[i]) a) (i + 1)
#align filter.complete_lattice_hom.apply_limsup_iterate Filter.CompleteLatticeHom.apply_limsup_iterate
/-- If `f : α → α` is a morphism of complete lattices, then the liminf of its iterates of any
@@ -855,15 +855,15 @@ theorem CompleteLatticeHom.apply_liminf_iterate (f : CompleteLatticeHom α α) (
variable {f g : Filter β} {p q : β → Prop} {u v : β → α}
theorem blimsup_mono (h : ∀ x, p x → q x) : blimsup u f p ≤ blimsup u f q :=
- infₛ_le_infₛ fun a ha => ha.mono <| by tauto
+ sInf_le_sInf fun a ha => ha.mono <| by tauto
#align filter.blimsup_mono Filter.blimsup_mono
theorem bliminf_antitone (h : ∀ x, p x → q x) : bliminf u f q ≤ bliminf u f p :=
- supₛ_le_supₛ fun a ha => ha.mono <| by tauto
+ sSup_le_sSup fun a ha => ha.mono <| by tauto
#align filter.bliminf_antitone Filter.bliminf_antitone
theorem mono_blimsup' (h : ∀ᶠ x in f, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
- infₛ_le_infₛ fun _ ha => (ha.and h).mono fun _ hx hx' => (hx.2 hx').trans (hx.1 hx')
+ sInf_le_sInf fun _ ha => (ha.and h).mono fun _ hx hx' => (hx.2 hx').trans (hx.1 hx')
#align filter.mono_blimsup' Filter.mono_blimsup'
theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsup v f p :=
@@ -871,7 +871,7 @@ theorem mono_blimsup (h : ∀ x, p x → u x ≤ v x) : blimsup u f p ≤ blimsu
#align filter.mono_blimsup Filter.mono_blimsup
theorem mono_bliminf' (h : ∀ᶠ x in f, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
- supₛ_le_supₛ fun _ ha => (ha.and h).mono fun _ hx hx' => (hx.1 hx').trans (hx.2 hx')
+ sSup_le_sSup fun _ ha => (ha.and h).mono fun _ hx hx' => (hx.1 hx').trans (hx.2 hx')
#align filter.mono_bliminf' Filter.mono_bliminf'
theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ bliminf v f p :=
@@ -879,11 +879,11 @@ theorem mono_bliminf (h : ∀ x, p x → u x ≤ v x) : bliminf u f p ≤ blimin
#align filter.mono_bliminf Filter.mono_bliminf
theorem bliminf_antitone_filter (h : f ≤ g) : bliminf u g p ≤ bliminf u f p :=
- supₛ_le_supₛ fun _ ha => ha.filter_mono h
+ sSup_le_sSup fun _ ha => ha.filter_mono h
#align filter.bliminf_antitone_filter Filter.bliminf_antitone_filter
theorem blimsup_monotone_filter (h : f ≤ g) : blimsup u f p ≤ blimsup u g p :=
- infₛ_le_infₛ fun _ ha => ha.filter_mono h
+ sInf_le_sInf fun _ ha => ha.filter_mono h
#align filter.blimsup_monotone_filter Filter.blimsup_monotone_filter
@@ -947,7 +947,7 @@ theorem bliminf_or_le_inf_aux_right : (bliminf u f fun x => p x ∨ q x) ≤ bli
coercion to `↑(RelIso.toRelEmbedding e).toEmbedding`.-/
theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
FunLike.coe e (blimsup u f p) = blimsup ((FunLike.coe e) ∘ u) f p := by
- simp only [blimsup_eq, map_infₛ, Function.comp_apply]
+ simp only [blimsup_eq, map_sInf, Function.comp_apply]
congr
ext c
obtain ⟨a, rfl⟩ := e.surjective c
@@ -959,16 +959,16 @@ theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
OrderIso.apply_blimsup (α := αᵒᵈ) (γ := γᵒᵈ) e.dual
#align filter.order_iso.apply_bliminf Filter.OrderIso.apply_bliminf
-theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : SupₛHom α γ) :
+theorem SupHom.apply_blimsup_le [CompleteLattice γ] (g : sSupHom α γ) :
g (blimsup u f p) ≤ blimsup (g ∘ u) f p := by
- simp only [blimsup_eq_infᵢ_bsupᵢ, Function.comp]
- refine' ((OrderHomClass.mono g).map_infᵢ₂_le _).trans _
- simp only [_root_.map_supᵢ, le_refl]
+ simp only [blimsup_eq_iInf_biSup, Function.comp]
+ refine' ((OrderHomClass.mono g).map_iInf₂_le _).trans _
+ simp only [_root_.map_iSup, le_refl]
#align filter.Sup_hom.apply_blimsup_le Filter.SupHom.apply_blimsup_le
-theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : InfₛHom α γ) :
+theorem InfHom.le_apply_bliminf [CompleteLattice γ] (g : sInfHom α γ) :
bliminf (g ∘ u) f p ≤ g (bliminf u f p) :=
- SupHom.apply_blimsup_le (α := αᵒᵈ) (γ := γᵒᵈ) (InfₛHom.dual g)
+ SupHom.apply_blimsup_le (α := αᵒᵈ) (γ := γᵒᵈ) (sInfHom.dual g)
#align filter.Inf_hom.le_apply_bliminf Filter.InfHom.le_apply_bliminf
end CompleteLattice
@@ -980,8 +980,8 @@ variable [CompleteDistribLattice α] {f : Filter β} {p q : β → Prop} {u : β
@[simp]
theorem blimsup_or_eq_sup : (blimsup u f fun x => p x ∨ q x) = blimsup u f p ⊔ blimsup u f q := by
refine' le_antisymm _ blimsup_sup_le_or
- simp only [blimsup_eq, infₛ_sup_eq, sup_infₛ_eq, le_infᵢ₂_iff, mem_setOf_eq]
- refine' fun a' ha' a ha => infₛ_le ((ha.and ha').mono fun b h hb => _)
+ simp only [blimsup_eq, sInf_sup_eq, sup_sInf_eq, le_iInf₂_iff, mem_setOf_eq]
+ refine' fun a' ha' a ha => sInf_le ((ha.and ha').mono fun b h hb => _)
exact Or.elim hb (fun hb => le_sup_of_le_left <| h.1 hb) fun hb => le_sup_of_le_right <| h.2 hb
#align filter.blimsup_or_eq_sup Filter.blimsup_or_eq_sup
@@ -991,9 +991,9 @@ theorem bliminf_or_eq_inf : (bliminf u f fun x => p x ∨ q x) = bliminf u f p
#align filter.bliminf_or_eq_inf Filter.bliminf_or_eq_inf
theorem sup_limsup [NeBot f] (a : α) : a ⊔ limsup u f = limsup (fun x => a ⊔ u x) f := by
- simp only [limsup_eq_infᵢ_supᵢ, supᵢ_sup_eq, sup_infᵢ₂_eq]
+ simp only [limsup_eq_iInf_iSup, iSup_sup_eq, sup_iInf₂_eq]
congr ; ext s; congr ; ext hs; congr
- exact (bsupᵢ_const (nonempty_of_mem hs)).symm
+ exact (biSup_const (nonempty_of_mem hs)).symm
#align filter.sup_limsup Filter.sup_limsup
theorem inf_liminf [NeBot f] (a : α) : a ⊓ liminf u f = liminf (fun x => a ⊓ u x) f :=
@@ -1001,9 +1001,9 @@ theorem inf_liminf [NeBot f] (a : α) : a ⊓ liminf u f = liminf (fun x => a
#align filter.inf_liminf Filter.inf_liminf
theorem sup_liminf (a : α) : a ⊔ liminf u f = liminf (fun x => a ⊔ u x) f := by
- simp only [liminf_eq_supᵢ_infᵢ]
- rw [sup_comm, bsupᵢ_sup (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
- simp_rw [infᵢ₂_sup_eq, sup_comm (a := a)]
+ simp only [liminf_eq_iSup_iInf]
+ rw [sup_comm, biSup_sup (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
+ simp_rw [iInf₂_sup_eq, sup_comm (a := a)]
#align filter.sup_liminf Filter.sup_liminf
theorem inf_limsup (a : α) : a ⊓ limsup u f = limsup (fun x => a ⊓ u x) f :=
@@ -1017,17 +1017,17 @@ section CompleteBooleanAlgebra
variable [CompleteBooleanAlgebra α] (f : Filter β) (u : β → α)
theorem limsup_compl : limsup u fᶜ = liminf (compl ∘ u) f := by
- simp only [limsup_eq_infᵢ_supᵢ, compl_infᵢ, compl_supᵢ, liminf_eq_supᵢ_infᵢ, Function.comp_apply]
+ simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Function.comp_apply]
#align filter.limsup_compl Filter.limsup_compl
theorem liminf_compl : liminf u fᶜ = limsup (compl ∘ u) f := by
- simp only [limsup_eq_infᵢ_supᵢ, compl_infᵢ, compl_supᵢ, liminf_eq_supᵢ_infᵢ, Function.comp_apply]
+ simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Function.comp_apply]
#align filter.liminf_compl Filter.liminf_compl
theorem limsup_sdiff (a : α) : limsup u f \ a = limsup (fun b => u b \ a) f := by
- simp only [limsup_eq_infᵢ_supᵢ, sdiff_eq]
- rw [binfᵢ_inf (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
- simp_rw [inf_comm, inf_supᵢ₂_eq, inf_comm]
+ simp only [limsup_eq_iInf_iSup, sdiff_eq]
+ rw [biInf_inf (⟨univ, univ_mem⟩ : ∃ i : Set β, i ∈ f)]
+ simp_rw [inf_comm, inf_iSup₂_eq, inf_comm]
#align filter.limsup_sdiff Filter.limsup_sdiff
theorem liminf_sdiff [NeBot f] (a : α) : liminf u f \ a = liminf (fun b => u b \ a) f := by
@@ -1052,17 +1052,17 @@ variable {p : ι → Prop} {s : ι → Set α}
theorem cofinite.blimsup_set_eq :
blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } := by
- simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, infₛ_eq_interₛ, exists_prop]
+ simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, sInf_eq_sInter, exists_prop]
ext x
refine' ⟨fun h => _, fun hx t h => _⟩ <;> contrapose! h
- · simp only [mem_interₛ, mem_setOf_eq, not_forall, exists_prop]
+ · simp only [mem_sInter, mem_setOf_eq, not_forall, exists_prop]
exact ⟨{x}ᶜ, by simpa using h, by simp⟩
· exact hx.mono fun i hi => ⟨hi.1, fun hit => h (hit hi.2)⟩
#align filter.cofinite.blimsup_set_eq Filter.cofinite.blimsup_set_eq
theorem cofinite.bliminf_set_eq : bliminf s cofinite p = { x | { n | p n ∧ x ∉ s n }.Finite } := by
rw [← compl_inj_iff]
- simp only [bliminf_eq_supᵢ_binfᵢ, compl_infᵢ, compl_supᵢ, ← blimsup_eq_infᵢ_bsupᵢ,
+ simp only [bliminf_eq_iSup_biInf, compl_iInf, compl_iSup, ← blimsup_eq_iInf_biSup,
cofinite.blimsup_set_eq]
rfl
#align filter.cofinite.bliminf_set_eq Filter.cofinite.bliminf_set_eq
@@ -1082,8 +1082,8 @@ theorem cofinite.liminf_set_eq : liminf s cofinite = { x | { n | x ∉ s n }.Fin
theorem exists_forall_mem_of_hasBasis_mem_blimsup {l : Filter β} {b : ι → Set β} {q : ι → Prop}
(hl : l.HasBasis q b) {u : β → Set α} {p : β → Prop} {x : α} (hx : x ∈ blimsup u l p) :
∃ f : { i | q i } → β, ∀ i, x ∈ u (f i) ∧ p (f i) ∧ f i ∈ b i := by
- rw [blimsup_eq_infᵢ_bsupᵢ] at hx
- simp only [supᵢ_eq_unionᵢ, infᵢ_eq_interᵢ, mem_interᵢ, mem_unionᵢ, exists_prop] at hx
+ rw [blimsup_eq_iInf_biSup] at hx
+ simp only [iSup_eq_iUnion, iInf_eq_iInter, mem_iInter, mem_iUnion, exists_prop] at hx
choose g hg hg' using hx
refine' ⟨fun i : { i | q i } => g (b i) (hl.mem_of_mem i.2), fun i => ⟨_, _⟩⟩
· exact hg' (b i) (hl.mem_of_mem i.2)
@@ -1101,21 +1101,21 @@ end SetLattice
section ConditionallyCompleteLinearOrder
-theorem frequently_lt_of_lt_limsupₛ {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
+theorem frequently_lt_of_lt_limsSup {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≤ ·) := by isBoundedDefault)
- (h : a < limsupₛ f) : ∃ᶠ n in f, a < n := by
+ (h : a < limsSup f) : ∃ᶠ n in f, a < n := by
contrapose! h
simp only [not_frequently, not_lt] at h
- exact limsupₛ_le_of_le hf h
+ exact limsSup_le_of_le hf h
set_option linter.uppercaseLean3 false in
-#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsupₛ
+#align filter.frequently_lt_of_lt_Limsup Filter.frequently_lt_of_lt_limsSup
-theorem frequently_lt_of_liminfₛ_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
+theorem frequently_lt_of_limsInf_lt {f : Filter α} [ConditionallyCompleteLinearOrder α] {a : α}
(hf : f.IsCobounded (· ≥ ·) := by isBoundedDefault)
- (h : liminfₛ f < a) : ∃ᶠ n in f, n < a :=
- frequently_lt_of_lt_limsupₛ (α := OrderDual α) hf h
+ (h : limsInf f < a) : ∃ᶠ n in f, n < a :=
+ frequently_lt_of_lt_limsSup (α := OrderDual α) hf h
set_option linter.uppercaseLean3 false in
-#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_liminfₛ_lt
+#align filter.frequently_lt_of_Liminf_lt Filter.frequently_lt_of_limsInf_lt
theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearOrder β] {u : α → β}
{b : β} (h : b < liminf u f)
@@ -1123,7 +1123,7 @@ theorem eventually_lt_of_lt_liminf {f : Filter α} [ConditionallyCompleteLinearO
∀ᶠ a in f, b < u a := by
obtain ⟨c, hc, hbc⟩ : ∃ (c : β) (_ : c ∈ { c : β | ∀ᶠ n : α in f, c ≤ u n }), b < c := by
simp_rw [exists_prop]
- exact exists_lt_of_lt_csupₛ hu h
+ exact exists_lt_of_lt_csSup hu h
exact hc.mono fun x hx => lt_of_lt_of_le hbc hx
#align filter.eventually_lt_of_lt_liminf Filter.eventually_lt_of_lt_liminf
@@ -1156,7 +1156,7 @@ theorem frequently_lt_of_lt_limsup {α β} [ConditionallyCompleteLinearOrder β]
(hu : f.IsCoboundedUnder (· ≤ ·) u := by isBoundedDefault)
(h : b < limsup u f) : ∃ᶠ x in f, b < u x := by
contrapose! h
- apply limsupₛ_le_of_le hu
+ apply limsSup_le_of_le hu
simpa using h
#align filter.frequently_lt_of_lt_limsup Filter.frequently_lt_of_lt_limsup
@@ -1208,10 +1208,10 @@ theorem GaloisConnection.l_limsup_le [ConditionallyCompleteLattice β]
(hlv : f.IsBoundedUnder (· ≤ ·) fun x => l (v x) := by isBoundedDefault)
(hv_co : f.IsCoboundedUnder (· ≤ ·) v := by isBoundedDefault) :
l (limsup v f) ≤ limsup (fun x => l (v x)) f := by
- refine' le_limsupₛ_of_le hlv fun c hc => _
+ refine' le_limsSup_of_le hlv fun c hc => _
rw [Filter.eventually_map] at hc
simp_rw [gc _ _] at hc⊢
- exact limsupₛ_le_of_le hv_co hc
+ exact limsSup_le_of_le hv_co hc
#align galois_connection.l_limsup_le GaloisConnection.l_limsup_le
theorem OrderIso.limsup_apply {γ} [ConditionallyCompleteLattice β] [ConditionallyCompleteLattice γ]
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -802,8 +802,8 @@ set_option linter.uppercaseLean3 false in
-- Porting note: simp_nf linter incorrectly says: lhs does not simplify when using simp on itself.
@[simp, nolint simpNF]
-theorem liminf_nat_add (f : ℕ → α) (k : ℕ) : liminf (fun i => f (i + k)) atTop = liminf f atTop :=
- by
+theorem liminf_nat_add (f : ℕ → α) (k : ℕ) :
+ liminf (fun i => f (i + k)) atTop = liminf f atTop := by
simp_rw [liminf_eq_supᵢ_infᵢ_of_nat]
exact supᵢ_infᵢ_ge_nat_add f k
#align filter.liminf_nat_add Filter.liminf_nat_add
@@ -1050,8 +1050,8 @@ section SetLattice
variable {p : ι → Prop} {s : ι → Set α}
-theorem cofinite.blimsup_set_eq : blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } :=
- by
+theorem cofinite.blimsup_set_eq :
+ blimsup s cofinite p = { x | { n | p n ∧ x ∈ s n }.Infinite } := by
simp only [blimsup_eq, le_eq_subset, eventually_cofinite, not_forall, infₛ_eq_interₛ, exists_prop]
ext x
refine' ⟨fun h => _, fun hx t h => _⟩ <;> contrapose! h
This PR fixes two things:
align
statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align
). This is often seen in the mathport output after ending calc
blocks.#align
statements. (This was needed for a script I wrote for #3630.)@@ -252,7 +252,6 @@ theorem _root_.OrderIso.isBoundedUnder_le_comp [Preorder α] [Preorder β] (e :
{u : γ → α} : (IsBoundedUnder (· ≤ ·) l fun x => e (u x)) ↔ IsBoundedUnder (· ≤ ·) l u :=
(Function.Surjective.exists e.surjective).trans <|
exists_congr fun a => by simp only [eventually_map, e.le_iff_le]
-
#align order_iso.is_bounded_under_le_comp OrderIso.isBoundedUnder_le_comp
@[simp]
The changes I made were.
Use FunLike.coe
instead of the previous definition for the coercion from RelEmbedding
To functions and OrderIso
to functions. The previous definition was
instance : CoeFun (r ↪r s) fun _ => α → β :=
-- ⟨fun o => o.toEmbedding⟩
This does not display nicely.
I also restored the simp
attributes on a few lemmas that had their simp
attributes removed during the port. Eventually
we might want a RelEmbeddingLike
class, but this PR does not implement that.
I also added a few lemmas that proved that coercions to function commute with RelEmbedding.toRelHom
or similar.
The other changes are just fixing the build. One strange issue is that the lemma Finset.mapEmbedding_apply
seems to be harder to use, it has to be used with rw
instead of simp
Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com>
@@ -952,9 +952,7 @@ theorem OrderIso.apply_blimsup [CompleteLattice γ] (e : α ≃o γ) :
congr
ext c
obtain ⟨a, rfl⟩ := e.surjective c
- -- Porting note: Also needed to add this next line
- have : ↑(RelIso.toRelEmbedding e).toEmbedding = FunLike.coe e := rfl
- simp [this]
+ simp
#align filter.order_iso.apply_blimsup Filter.OrderIso.apply_blimsup
theorem OrderIso.apply_bliminf [CompleteLattice γ] (e : α ≃o γ) :
The unported dependencies are