topology.instances.sign
⟷
Mathlib.Topology.Instances.Sign
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
-import Mathbin.Data.Sign
-import Mathbin.Topology.Order.Basic
+import Data.Sign
+import Topology.Order.Basic
#align_import topology.instances.sign from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module topology.instances.sign
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Sign
import Mathbin.Topology.Order.Basic
+#align_import topology.instances.sign from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
/-!
# Topology on `sign_type`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -35,19 +35,23 @@ section PartialOrder
variable [PartialOrder α] [DecidableRel ((· < ·) : α → α → Prop)] [OrderTopology α]
+#print continuousAt_sign_of_pos /-
theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.sign a :=
by
refine' (continuousAt_const : ContinuousAt (fun x => (1 : SignType)) a).congr _
rw [Filter.EventuallyEq, eventually_nhds_iff]
exact ⟨{x | 0 < x}, fun x hx => (sign_pos hx).symm, isOpen_lt' 0, h⟩
#align continuous_at_sign_of_pos continuousAt_sign_of_pos
+-/
+#print continuousAt_sign_of_neg /-
theorem continuousAt_sign_of_neg {a : α} (h : a < 0) : ContinuousAt SignType.sign a :=
by
refine' (continuousAt_const : ContinuousAt (fun x => (-1 : SignType)) a).congr _
rw [Filter.EventuallyEq, eventually_nhds_iff]
exact ⟨{x | x < 0}, fun x hx => (sign_neg hx).symm, isOpen_gt' 0, h⟩
#align continuous_at_sign_of_neg continuousAt_sign_of_neg
+-/
end PartialOrder
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -39,14 +39,14 @@ theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.si
by
refine' (continuousAt_const : ContinuousAt (fun x => (1 : SignType)) a).congr _
rw [Filter.EventuallyEq, eventually_nhds_iff]
- exact ⟨{ x | 0 < x }, fun x hx => (sign_pos hx).symm, isOpen_lt' 0, h⟩
+ exact ⟨{x | 0 < x}, fun x hx => (sign_pos hx).symm, isOpen_lt' 0, h⟩
#align continuous_at_sign_of_pos continuousAt_sign_of_pos
theorem continuousAt_sign_of_neg {a : α} (h : a < 0) : ContinuousAt SignType.sign a :=
by
refine' (continuousAt_const : ContinuousAt (fun x => (-1 : SignType)) a).congr _
rw [Filter.EventuallyEq, eventually_nhds_iff]
- exact ⟨{ x | x < 0 }, fun x hx => (sign_neg hx).symm, isOpen_gt' 0, h⟩
+ exact ⟨{x | x < 0}, fun x hx => (sign_neg hx).symm, isOpen_gt' 0, h⟩
#align continuous_at_sign_of_neg continuousAt_sign_of_neg
end PartialOrder
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -35,12 +35,6 @@ section PartialOrder
variable [PartialOrder α] [DecidableRel ((· < ·) : α → α → Prop)] [OrderTopology α]
-/- warning: continuous_at_sign_of_pos -> continuousAt_sign_of_pos is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1))) a) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.105 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.107 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.105 x._@.Mathlib.Topology.Instances.Sign._hyg.107)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1)) a) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
-Case conversion may be inaccurate. Consider using '#align continuous_at_sign_of_pos continuousAt_sign_of_posₓ'. -/
theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.sign a :=
by
refine' (continuousAt_const : ContinuousAt (fun x => (1 : SignType)) a).congr _
@@ -48,12 +42,6 @@ theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.si
exact ⟨{ x | 0 < x }, fun x hx => (sign_pos hx).symm, isOpen_lt' 0, h⟩
#align continuous_at_sign_of_pos continuousAt_sign_of_pos
-/- warning: continuous_at_sign_of_neg -> continuousAt_sign_of_neg is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1)))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.235 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.237 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.235 x._@.Mathlib.Topology.Instances.Sign._hyg.237)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
-Case conversion may be inaccurate. Consider using '#align continuous_at_sign_of_neg continuousAt_sign_of_negₓ'. -/
theorem continuousAt_sign_of_neg {a : α} (h : a < 0) : ContinuousAt SignType.sign a :=
by
refine' (continuousAt_const : ContinuousAt (fun x => (-1 : SignType)) a).congr _
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -37,7 +37,7 @@ variable [PartialOrder α] [DecidableRel ((· < ·) : α → α → Prop)] [Orde
/- warning: continuous_at_sign_of_pos -> continuousAt_sign_of_pos is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1))) a) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
+ forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1))) a) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.105 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.107 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.105 x._@.Mathlib.Topology.Instances.Sign._hyg.107)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1)) a) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
Case conversion may be inaccurate. Consider using '#align continuous_at_sign_of_pos continuousAt_sign_of_posₓ'. -/
@@ -50,7 +50,7 @@ theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.si
/- warning: continuous_at_sign_of_neg -> continuousAt_sign_of_neg is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1)))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
+ forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1)))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.235 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.237 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.235 x._@.Mathlib.Topology.Instances.Sign._hyg.237)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
Case conversion may be inaccurate. Consider using '#align continuous_at_sign_of_neg continuousAt_sign_of_negₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -52,7 +52,7 @@ theorem continuousAt_sign_of_pos {a : α} (h : 0 < a) : ContinuousAt SignType.si
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)))] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_1)))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 SignType.topologicalSpace (coeFn.{succ u1, succ u1} (OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (fun (_x : OrderHom.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) => α -> SignType) (OrderHom.hasCoeToFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (LinearOrder.toLattice.{0} SignType SignType.linearOrder))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.234 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.236 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.234 x._@.Mathlib.Topology.Instances.Sign._hyg.236)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
+ forall {α : Type.{u1}} [_inst_1 : Zero.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : PartialOrder.{u1} α] [_inst_4 : DecidableRel.{succ u1} α (fun (x._@.Mathlib.Topology.Instances.Sign._hyg.235 : α) (x._@.Mathlib.Topology.Instances.Sign._hyg.237 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) x._@.Mathlib.Topology.Instances.Sign._hyg.235 x._@.Mathlib.Topology.Instances.Sign._hyg.237)] [_inst_5 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α _inst_3)] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_3)) a (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_1))) -> (ContinuousAt.{u1, 0} α SignType _inst_2 instTopologicalSpaceSignType (OrderHom.toFun.{u1, 0} α SignType (PartialOrder.toPreorder.{u1} α _inst_3) (PartialOrder.toPreorder.{0} SignType (SemilatticeInf.toPartialOrder.{0} SignType (Lattice.toSemilatticeInf.{0} SignType (DistribLattice.toLattice.{0} SignType (instDistribLattice.{0} SignType SignType.instLinearOrderSignType))))) (SignType.sign.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α _inst_3) (fun (a : α) (b : α) => _inst_4 a b))) a)
Case conversion may be inaccurate. Consider using '#align continuous_at_sign_of_neg continuousAt_sign_of_negₓ'. -/
theorem continuousAt_sign_of_neg {a : α} (h : a < 0) : ContinuousAt SignType.sign a :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -23,7 +23,7 @@ instance : TopologicalSpace SignType :=
instance : DiscreteTopology SignType :=
⟨rfl⟩
-variable {α : Type _} [Zero α] [TopologicalSpace α]
+variable {α : Type*} [Zero α] [TopologicalSpace α]
section PartialOrder
@@ -2,15 +2,12 @@
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module topology.instances.sign
-! 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.Data.Sign
import Mathlib.Topology.Order.Basic
+#align_import topology.instances.sign from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
/-!
# Topology on `SignType`
The unported dependencies are