topology.algebra.order.extend_from
⟷
Mathlib.Topology.Algebra.Order.ExtendFrom
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -87,7 +87,7 @@ theorem continuousOn_Ioc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
ContinuousOn (extendFrom (Ioo a b) f) (Ioc a b) :=
by
have := @continuousOn_Ico_extendFrom_Ioo αᵒᵈ _ _ _ _ _ _ _ f _ _ _ hab
- erw [dual_Ico, dual_Ioi, dual_Ioo] at this
+ erw [dual_Ico, dual_Ioi, dual_Ioo] at this
exact this hf hb
#align continuous_on_Ioc_extend_from_Ioo continuousOn_Ioc_extendFrom_Ioo
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
-import Mathbin.Topology.Order.Basic
-import Mathbin.Topology.ExtendFrom
+import Topology.Order.Basic
+import Topology.ExtendFrom
#align_import topology.algebra.order.extend_from from "leanprover-community/mathlib"@"3e32bc908f617039c74c06ea9a897e30c30803c2"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.extend_from
-! 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.Topology.Order.Basic
import Mathbin.Topology.ExtendFrom
+#align_import topology.algebra.order.extend_from from "leanprover-community/mathlib"@"3e32bc908f617039c74c06ea9a897e30c30803c2"
+
/-!
# Lemmas about `extend_from` in an order topology.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -27,6 +27,7 @@ universe u v
variable {α : Type u} {β : Type v}
+#print continuousOn_Icc_extendFrom_Ioo /-
theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {la lb : β}
(hab : a ≠ b) (hf : ContinuousOn f (Ioo a b)) (ha : Tendsto f (𝓝[>] a) (𝓝 la))
@@ -40,7 +41,9 @@ theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
· exact ⟨lb, hb.mono_left <| nhdsWithin_mono _ Ioo_subset_Iio_self⟩
· use f x, hf x h
#align continuous_on_Icc_extend_from_Ioo continuousOn_Icc_extendFrom_Ioo
+-/
+#print eq_lim_at_left_extendFrom_Ioo /-
theorem eq_lim_at_left_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [T2Space β] {f : α → β} {a b : α} {la : β} (hab : a < b)
(ha : Tendsto f (𝓝[>] a) (𝓝 la)) : extendFrom (Ioo a b) f a = la :=
@@ -50,7 +53,9 @@ theorem eq_lim_at_left_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [De
simp only [le_of_lt hab, left_mem_Icc, right_mem_Icc]
· simpa [hab]
#align eq_lim_at_left_extend_from_Ioo eq_lim_at_left_extendFrom_Ioo
+-/
+#print eq_lim_at_right_extendFrom_Ioo /-
theorem eq_lim_at_right_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [T2Space β] {f : α → β} {a b : α} {lb : β} (hab : a < b)
(hb : Tendsto f (𝓝[<] b) (𝓝 lb)) : extendFrom (Ioo a b) f b = lb :=
@@ -60,7 +65,9 @@ theorem eq_lim_at_right_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [D
simp only [le_of_lt hab, left_mem_Icc, right_mem_Icc]
· simpa [hab]
#align eq_lim_at_right_extend_from_Ioo eq_lim_at_right_extendFrom_Ioo
+-/
+#print continuousOn_Ico_extendFrom_Ioo /-
theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {la : β}
(hab : a < b) (hf : ContinuousOn f (Ioo a b)) (ha : Tendsto f (𝓝[>] a) (𝓝 la)) :
@@ -74,7 +81,9 @@ theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
simpa [hab]
· use f x, hf x h
#align continuous_on_Ico_extend_from_Ioo continuousOn_Ico_extendFrom_Ioo
+-/
+#print continuousOn_Ioc_extendFrom_Ioo /-
theorem continuousOn_Ioc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {lb : β}
(hab : a < b) (hf : ContinuousOn f (Ioo a b)) (hb : Tendsto f (𝓝[<] b) (𝓝 lb)) :
@@ -84,4 +93,5 @@ theorem continuousOn_Ioc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
erw [dual_Ico, dual_Ioi, dual_Ioo] at this
exact this hf hb
#align continuous_on_Ioc_extend_from_Ioo continuousOn_Ioc_extendFrom_Ioo
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -81,7 +81,7 @@ theorem continuousOn_Ioc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
ContinuousOn (extendFrom (Ioo a b) f) (Ioc a b) :=
by
have := @continuousOn_Ico_extendFrom_Ioo αᵒᵈ _ _ _ _ _ _ _ f _ _ _ hab
- erw [dual_Ico, dual_Ioi, dual_Ioo] at this
+ erw [dual_Ico, dual_Ioi, dual_Ioo] at this
exact this hf hb
#align continuous_on_Ioc_extend_from_Ioo continuousOn_Ioc_extendFrom_Ioo
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -21,7 +21,7 @@ import Mathbin.Topology.ExtendFrom
open Filter Set TopologicalSpace
-open Topology Classical
+open scoped Topology Classical
universe u v
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -27,12 +27,6 @@ universe u v
variable {α : Type u} {β : Type v}
-/- warning: continuous_on_Icc_extend_from_Ioo -> continuousOn_Icc_extendFrom_Ioo is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β} {lb : β}, (Ne.{succ u1} α a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β} {lb : β}, (Ne.{succ u2} α a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
-Case conversion may be inaccurate. Consider using '#align continuous_on_Icc_extend_from_Ioo continuousOn_Icc_extendFrom_Iooₓ'. -/
theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {la lb : β}
(hab : a ≠ b) (hf : ContinuousOn f (Ioo a b)) (ha : Tendsto f (𝓝[>] a) (𝓝 la))
@@ -47,12 +41,6 @@ theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
· use f x, hf x h
#align continuous_on_Icc_extend_from_Ioo continuousOn_Icc_extendFrom_Ioo
-/- warning: eq_lim_at_left_extend_from_Ioo -> eq_lim_at_left_extendFrom_Ioo is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f a) la)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : T2Space.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (Eq.{succ u1} β (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f a) la)
-Case conversion may be inaccurate. Consider using '#align eq_lim_at_left_extend_from_Ioo eq_lim_at_left_extendFrom_Iooₓ'. -/
theorem eq_lim_at_left_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [T2Space β] {f : α → β} {a b : α} {la : β} (hab : a < b)
(ha : Tendsto f (𝓝[>] a) (𝓝 la)) : extendFrom (Ioo a b) f a = la :=
@@ -63,12 +51,6 @@ theorem eq_lim_at_left_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [De
· simpa [hab]
#align eq_lim_at_left_extend_from_Ioo eq_lim_at_left_extendFrom_Ioo
-/- warning: eq_lim_at_right_extend_from_Ioo -> eq_lim_at_right_extendFrom_Ioo is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f b) lb)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : T2Space.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (Eq.{succ u1} β (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f b) lb)
-Case conversion may be inaccurate. Consider using '#align eq_lim_at_right_extend_from_Ioo eq_lim_at_right_extendFrom_Iooₓ'. -/
theorem eq_lim_at_right_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [T2Space β] {f : α → β} {a b : α} {lb : β} (hab : a < b)
(hb : Tendsto f (𝓝[<] b) (𝓝 lb)) : extendFrom (Ioo a b) f b = lb :=
@@ -79,12 +61,6 @@ theorem eq_lim_at_right_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [D
· simpa [hab]
#align eq_lim_at_right_extend_from_Ioo eq_lim_at_right_extendFrom_Ioo
-/- warning: continuous_on_Ico_extend_from_Ioo -> continuousOn_Ico_extendFrom_Ioo is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
-Case conversion may be inaccurate. Consider using '#align continuous_on_Ico_extend_from_Ioo continuousOn_Ico_extendFrom_Iooₓ'. -/
theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {la : β}
(hab : a < b) (hf : ContinuousOn f (Ioo a b)) (ha : Tendsto f (𝓝[>] a) (𝓝 la)) :
@@ -99,12 +75,6 @@ theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
· use f x, hf x h
#align continuous_on_Ico_extend_from_Ioo continuousOn_Ico_extendFrom_Ioo
-/- warning: continuous_on_Ioc_extend_from_Ioo -> continuousOn_Ioc_extendFrom_Ioo is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
-Case conversion may be inaccurate. Consider using '#align continuous_on_Ioc_extend_from_Ioo continuousOn_Ioc_extendFrom_Iooₓ'. -/
theorem continuousOn_Ioc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {lb : β}
(hab : a < b) (hf : ContinuousOn f (Ioo a b)) (hb : Tendsto f (𝓝[<] b) (𝓝 lb)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -91,8 +91,7 @@ theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
ContinuousOn (extendFrom (Ioo a b) f) (Ico a b) :=
by
apply continuousOn_extendFrom
- · rw [closure_Ioo hab.ne]
- exact Ico_subset_Icc_self
+ · rw [closure_Ioo hab.ne]; exact Ico_subset_Icc_self
· intro x x_in
rcases eq_left_or_mem_Ioo_of_mem_Ico x_in with (rfl | h)
· use la
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -29,7 +29,7 @@ variable {α : Type u} {β : Type v}
/- warning: continuous_on_Icc_extend_from_Ioo -> continuousOn_Icc_extendFrom_Ioo is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β} {lb : β}, (Ne.{succ u1} α a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β} {lb : β}, (Ne.{succ u1} α a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β} {lb : β}, (Ne.{succ u2} α a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
Case conversion may be inaccurate. Consider using '#align continuous_on_Icc_extend_from_Ioo continuousOn_Icc_extendFrom_Iooₓ'. -/
@@ -49,7 +49,7 @@ theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
/- warning: eq_lim_at_left_extend_from_Ioo -> eq_lim_at_left_extendFrom_Ioo is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f a) la)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f a) la)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : T2Space.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (Eq.{succ u1} β (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f a) la)
Case conversion may be inaccurate. Consider using '#align eq_lim_at_left_extend_from_Ioo eq_lim_at_left_extendFrom_Iooₓ'. -/
@@ -65,7 +65,7 @@ theorem eq_lim_at_left_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [De
/- warning: eq_lim_at_right_extend_from_Ioo -> eq_lim_at_right_extendFrom_Ioo is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f b) lb)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : T2Space.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (Eq.{succ u2} β (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f b) lb)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : T2Space.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (Eq.{succ u1} β (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f b) lb)
Case conversion may be inaccurate. Consider using '#align eq_lim_at_right_extend_from_Ioo eq_lim_at_right_extendFrom_Iooₓ'. -/
@@ -81,7 +81,7 @@ theorem eq_lim_at_right_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [D
/- warning: continuous_on_Ico_extend_from_Ioo -> continuousOn_Ico_extendFrom_Ioo is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (nhds.{u2} β _inst_5 la)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {la : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 a (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a)) (nhds.{u1} β _inst_5 la)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
Case conversion may be inaccurate. Consider using '#align continuous_on_Ico_extend_from_Ioo continuousOn_Ico_extendFrom_Iooₓ'. -/
@@ -102,7 +102,7 @@ theorem continuousOn_Ico_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [
/- warning: continuous_on_Ioc_extend_from_Ioo -> continuousOn_Ioc_extendFrom_Ioo is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : RegularSpace.{u2} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) -> (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (nhds.{u2} β _inst_5 lb)) -> (ContinuousOn.{u1, u2} α β _inst_1 _inst_5 (extendFrom.{u1, u2} α β _inst_1 _inst_5 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) f) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))] [_inst_4 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u1} β] [_inst_6 : RegularSpace.{u1} β _inst_5] {f : α -> β} {a : α} {b : α} {lb : β}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a b) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b)) -> (Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_1 b (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) b)) (nhds.{u1} β _inst_5 lb)) -> (ContinuousOn.{u2, u1} α β _inst_1 _inst_5 (extendFrom.{u2, u1} α β _inst_1 _inst_5 (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b) f) (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) a b))
Case conversion may be inaccurate. Consider using '#align continuous_on_Ioc_extend_from_Ioo continuousOn_Ioc_extendFrom_Iooₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
This splits up the file Mathlib/Topology/Order/Basic.lean
(currently > 2000 lines) into several smaller files.
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
import Mathlib.Topology.ExtendFrom
-import Mathlib.Topology.Order.Basic
+import Mathlib.Topology.Order.DenselyOrdered
#align_import topology.algebra.order.extend_from from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
Move files from Topology.Algebra.Order
to Topology.Order
when they do not contain any algebra. Also move Topology.LocalExtr
to Topology.Order.LocalExtr
.
According to git, the moves are:
Mathlib/Topology/{Algebra => }/Order/ExtendFrom.lean
Mathlib/Topology/{Algebra => }/Order/ExtrClosure.lean
Mathlib/Topology/{Algebra => }/Order/Filter.lean
Mathlib/Topology/{Algebra => }/Order/IntermediateValue.lean
Mathlib/Topology/{Algebra => }/Order/LeftRight.lean
Mathlib/Topology/{Algebra => }/Order/LeftRightLim.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneContinuity.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneConvergence.lean
Mathlib/Topology/{Algebra => }/Order/ProjIcc.lean
Mathlib/Topology/{Algebra => }/Order/T5.lean
Mathlib/Topology/{ => Order}/LocalExtr.lean
@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-/
-import Mathlib.Topology.Order.Basic
import Mathlib.Topology.ExtendFrom
+import Mathlib.Topology.Order.Basic
#align_import topology.algebra.order.extend_from from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
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.
@@ -17,7 +17,8 @@ set_option autoImplicit true
open Filter Set TopologicalSpace
-open Topology Classical
+open scoped Classical
+open Topology
theorem continuousOn_Icc_extendFrom_Ioo [TopologicalSpace α] [LinearOrder α] [DenselyOrdered α]
[OrderTopology α] [TopologicalSpace β] [RegularSpace β] {f : α → β} {a b : α} {la lb : β}
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.
@@ -12,6 +12,8 @@ import Mathlib.Topology.ExtendFrom
# Lemmas about `extendFrom` in an order topology.
-/
+set_option autoImplicit true
+
open Filter Set TopologicalSpace
@@ -2,15 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.extend_from
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Order.Basic
import Mathlib.Topology.ExtendFrom
+#align_import topology.algebra.order.extend_from from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
+
/-!
# Lemmas about `extendFrom` in an order topology.
-/
The unported dependencies are