dynamics.flow | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

717c0732

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ef7acf40

bump to nightly-2023-10-07-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

d191b687

Diff

@@ -76,7 +76,7 @@ theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α
 #print IsFwInvariant.isInvariant /-
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
-theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
+theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddCommMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
 #align is_fw_invariant.is_invariant IsFwInvariant.isInvariant
 -/
@@ -84,8 +84,8 @@ theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ →
 #print isFwInvariant_iff_isInvariant /-
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
-theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α} :
-    IsFwInvariant ϕ s ↔ IsInvariant ϕ s :=
+theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddCommMonoid τ] {ϕ : τ → α → α}
+    {s : Set α} : IsFwInvariant ϕ s ↔ IsInvariant ϕ s :=
   ⟨IsFwInvariant.isInvariant, IsInvariant.isFwInvariant⟩
 #align is_fw_invariant_iff_is_invariant isFwInvariant_iff_isInvariant
 -/

ef7acf40

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo
 -/
-import Mathbin.Topology.Algebra.Group.Basic
-import Mathbin.Logic.Function.Iterate
+import Topology.Algebra.Group.Basic
+import Logic.Function.Iterate
 
 #align_import dynamics.flow from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"

ef7acf40

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -138,7 +138,7 @@ protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ}
 #align flow.continuous Flow.continuous
 -/
 
-alias Flow.continuous ← _root_.continuous.flow
+alias _root_.continuous.flow := Flow.continuous
 #align continuous.flow Continuous.flow
 
 #print Flow.map_add /-

ef7acf40

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo
-
-! This file was ported from Lean 3 source module dynamics.flow
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Group.Basic
 import Mathbin.Logic.Function.Iterate
 
+#align_import dynamics.flow from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
+
 /-!
 # Flows and invariant sets

ef7acf40

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -56,9 +56,11 @@ def IsInvariant (ϕ : τ → α → α) (s : Set α) : Prop :=
 
 variable (ϕ : τ → α → α) (s : Set α)
 
+#print isInvariant_iff_image /-
 theorem isInvariant_iff_image : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s ⊆ s := by
   simp_rw [IsInvariant, maps_to']
 #align is_invariant_iff_image isInvariant_iff_image
+-/
 
 #print IsFwInvariant /-
 /-- A set `s ⊆ α` is forward-invariant under `ϕ : τ → α → α` if
@@ -68,22 +70,28 @@ def IsFwInvariant [Preorder τ] [Zero τ] (ϕ : τ → α → α) (s : Set α) :
 #align is_fw_invariant IsFwInvariant
 -/
 
+#print IsInvariant.isFwInvariant /-
 theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsInvariant ϕ s) : IsFwInvariant ϕ s := fun t ht => h t
 #align is_invariant.is_fw_invariant IsInvariant.isFwInvariant
+-/
 
+#print IsFwInvariant.isInvariant /-
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
 #align is_fw_invariant.is_invariant IsFwInvariant.isInvariant
+-/
 
+#print isFwInvariant_iff_isInvariant /-
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α} :
     IsFwInvariant ϕ s ↔ IsInvariant ϕ s :=
   ⟨IsFwInvariant.isInvariant, IsInvariant.isFwInvariant⟩
 #align is_fw_invariant_iff_is_invariant isFwInvariant_iff_isInvariant
+-/
 
 end Invariant
 
@@ -92,6 +100,7 @@ end Invariant
 -/
 
 
+#print Flow /-
 /-- A flow on a topological space `α` by an a additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
 structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
@@ -101,6 +110,7 @@ structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd
   map_add' : ∀ t₁ t₂ x, to_fun (t₁ + t₂) x = to_fun t₁ (to_fun t₂ x)
   map_zero' : ∀ x, to_fun 0 x = x
 #align flow Flow
+-/
 
 namespace Flow
 
@@ -116,33 +126,44 @@ instance : Inhabited (Flow τ α) :=
 instance : CoeFun (Flow τ α) fun _ => τ → α → α :=
   ⟨Flow.toFun⟩
 
+#print Flow.ext /-
 @[ext]
 theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) → ϕ₁ = ϕ₂
   | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by congr; funext; exact h _ _
 #align flow.ext Flow.ext
+-/
 
+#print Flow.continuous /-
 @[continuity]
 protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ} (ht : Continuous t)
     {f : β → α} (hf : Continuous f) : Continuous fun x => ϕ (t x) (f x) :=
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
+-/
 
 alias Flow.continuous ← _root_.continuous.flow
 #align continuous.flow Continuous.flow
 
+#print Flow.map_add /-
 theorem map_add (t₁ t₂ : τ) (x : α) : ϕ (t₁ + t₂) x = ϕ t₁ (ϕ t₂ x) :=
   ϕ.map_add' _ _ _
 #align flow.map_add Flow.map_add
+-/
 
+#print Flow.map_zero /-
 @[simp]
 theorem map_zero : ϕ 0 = id :=
   funext ϕ.map_zero'
 #align flow.map_zero Flow.map_zero
+-/
 
+#print Flow.map_zero_apply /-
 theorem map_zero_apply (x : α) : ϕ 0 x = x :=
   ϕ.map_zero' x
 #align flow.map_zero_apply Flow.map_zero_apply
+-/
 
+#print Flow.fromIter /-
 /-- Iterations of a continuous function from a topological space `α`
     to itself defines a semiflow by `ℕ` on `α`. -/
 def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
@@ -152,7 +173,9 @@ def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
   map_add' := iterate_add_apply _
   map_zero' x := rfl
 #align flow.from_iter Flow.fromIter
+-/
 
+#print Flow.restrict /-
 /-- Restriction of a flow onto an invariant set. -/
 def restrict {s : Set α} (h : IsInvariant ϕ s) : Flow τ ↥s
     where
@@ -161,6 +184,7 @@ def restrict {s : Set α} (h : IsInvariant ϕ s) : Flow τ ↥s
   map_add' _ _ _ := Subtype.ext (map_add _ _ _ _)
   map_zero' _ := Subtype.ext (map_zero_apply _ _)
 #align flow.restrict Flow.restrict
+-/
 
 end Flow
 
@@ -169,13 +193,16 @@ namespace Flow
 variable {τ : Type _} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type _}
   [TopologicalSpace α] (ϕ : Flow τ α)
 
+#print Flow.isInvariant_iff_image_eq /-
 theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s = s :=
   (isInvariant_iff_image _ _).trans
     (Iff.intro
       (fun h t => Subset.antisymm (h t) fun _ hx => ⟨_, h (-t) ⟨_, hx, rfl⟩, by simp [← map_add]⟩)
       fun h t => by rw [h t])
 #align flow.is_invariant_iff_image_eq Flow.isInvariant_iff_image_eq
+-/
 
+#print Flow.reverse /-
 /-- The time-reversal of a flow `ϕ` by a (commutative, additive) group
     is defined `ϕ.reverse t x = ϕ (-t) x`. -/
 def reverse : Flow τ α where
@@ -184,7 +211,9 @@ def reverse : Flow τ α where
   map_add' _ _ _ := by rw [neg_add, map_add]
   map_zero' _ := by rw [neg_zero, map_zero_apply]
 #align flow.reverse Flow.reverse
+-/
 
+#print Flow.toHomeomorph /-
 /-- The map `ϕ t` as a homeomorphism. -/
 def toHomeomorph (t : τ) : α ≃ₜ α where
   toFun := ϕ t
@@ -192,10 +221,13 @@ def toHomeomorph (t : τ) : α ≃ₜ α where
   left_inv x := by rw [← map_add, neg_add_self, map_zero_apply]
   right_inv x := by rw [← map_add, add_neg_self, map_zero_apply]
 #align flow.to_homeomorph Flow.toHomeomorph
+-/
 
+#print Flow.image_eq_preimage /-
 theorem image_eq_preimage (t : τ) (s : Set α) : ϕ t '' s = ϕ (-t) ⁻¹' s :=
   (ϕ.toHomeomorph t).toEquiv.image_eq_preimage s
 #align flow.image_eq_preimage Flow.image_eq_preimage
+-/
 
 end Flow

ef7acf40

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -95,7 +95,7 @@ end Invariant
 /-- A flow on a topological space `α` by an a additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
 structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
-  [TopologicalSpace α] where
+    [TopologicalSpace α] where
   toFun : τ → α → α
   cont' : Continuous (uncurry to_fun)
   map_add' : ∀ t₁ t₂ x, to_fun (t₁ + t₂) x = to_fun t₁ (to_fun t₂ x)
@@ -118,7 +118,7 @@ instance : CoeFun (Flow τ α) fun _ => τ → α → α :=
 
 @[ext]
 theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) → ϕ₁ = ϕ₂
-  | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by congr ; funext; exact h _ _
+  | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by congr; funext; exact h _ _
 #align flow.ext Flow.ext
 
 @[continuity]

ef7acf40

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -56,12 +56,6 @@ def IsInvariant (ϕ : τ → α → α) (s : Set α) : Prop :=
 
 variable (ϕ : τ → α → α) (s : Set α)
 
-/- warning: is_invariant_iff_image -> isInvariant_iff_image is a dubious translation:
-lean 3 declaration is
-  forall {τ : Type.{u1}} {α : Type.{u2}} (ϕ : τ -> α -> α) (s : Set.{u2} α), Iff (IsInvariant.{u1, u2} τ α ϕ s) (forall (t : τ), HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.image.{u2, u2} α α (ϕ t) s) s)
-but is expected to have type
-  forall {τ : Type.{u2}} {α : Type.{u1}} (ϕ : τ -> α -> α) (s : Set.{u1} α), Iff (IsInvariant.{u2, u1} τ α ϕ s) (forall (t : τ), HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.image.{u1, u1} α α (ϕ t) s) s)
-Case conversion may be inaccurate. Consider using '#align is_invariant_iff_image isInvariant_iff_imageₓ'. -/
 theorem isInvariant_iff_image : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s ⊆ s := by
   simp_rw [IsInvariant, maps_to']
 #align is_invariant_iff_image isInvariant_iff_image
@@ -74,34 +68,16 @@ def IsFwInvariant [Preorder τ] [Zero τ] (ϕ : τ → α → α) (s : Set α) :
 #align is_fw_invariant IsFwInvariant
 -/
 
-/- warning: is_invariant.is_fw_invariant -> IsInvariant.isFwInvariant is a dubious translation:
-lean 3 declaration is
-  forall {τ : Type.{u1}} {α : Type.{u2}} [_inst_1 : Preorder.{u1} τ] [_inst_2 : Zero.{u1} τ] {ϕ : τ -> α -> α} {s : Set.{u2} α}, (IsInvariant.{u1, u2} τ α ϕ s) -> (IsFwInvariant.{u1, u2} τ α _inst_1 _inst_2 ϕ s)
-but is expected to have type
-  forall {τ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} τ] [_inst_2 : Zero.{u2} τ] {ϕ : τ -> α -> α} {s : Set.{u1} α}, (IsInvariant.{u2, u1} τ α ϕ s) -> (IsFwInvariant.{u2, u1} τ α _inst_1 _inst_2 ϕ s)
-Case conversion may be inaccurate. Consider using '#align is_invariant.is_fw_invariant IsInvariant.isFwInvariantₓ'. -/
 theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsInvariant ϕ s) : IsFwInvariant ϕ s := fun t ht => h t
 #align is_invariant.is_fw_invariant IsInvariant.isFwInvariant
 
-/- warning: is_fw_invariant.is_invariant -> IsFwInvariant.isInvariant is a dubious translation:
-lean 3 declaration is
-  forall {τ : Type.{u1}} {α : Type.{u2}} [_inst_1 : CanonicallyOrderedAddMonoid.{u1} τ] {ϕ : τ -> α -> α} {s : Set.{u2} α}, (IsFwInvariant.{u1, u2} τ α (PartialOrder.toPreorder.{u1} τ (OrderedAddCommMonoid.toPartialOrder.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))) (AddZeroClass.toHasZero.{u1} τ (AddMonoid.toAddZeroClass.{u1} τ (AddCommMonoid.toAddMonoid.{u1} τ (OrderedAddCommMonoid.toAddCommMonoid.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))))) ϕ s) -> (IsInvariant.{u1, u2} τ α ϕ s)
-but is expected to have type
-  forall {τ : Type.{u2}} {α : Type.{u1}} [_inst_1 : CanonicallyOrderedAddMonoid.{u2} τ] {ϕ : τ -> α -> α} {s : Set.{u1} α}, (IsFwInvariant.{u2, u1} τ α (PartialOrder.toPreorder.{u2} τ (OrderedAddCommMonoid.toPartialOrder.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1))) (AddMonoid.toZero.{u2} τ (AddCommMonoid.toAddMonoid.{u2} τ (OrderedAddCommMonoid.toAddCommMonoid.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1)))) ϕ s) -> (IsInvariant.{u2, u1} τ α ϕ s)
-Case conversion may be inaccurate. Consider using '#align is_fw_invariant.is_invariant IsFwInvariant.isInvariantₓ'. -/
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
 #align is_fw_invariant.is_invariant IsFwInvariant.isInvariant
 
-/- warning: is_fw_invariant_iff_is_invariant -> isFwInvariant_iff_isInvariant is a dubious translation:
-lean 3 declaration is
-  forall {τ : Type.{u1}} {α : Type.{u2}} [_inst_1 : CanonicallyOrderedAddMonoid.{u1} τ] {ϕ : τ -> α -> α} {s : Set.{u2} α}, Iff (IsFwInvariant.{u1, u2} τ α (PartialOrder.toPreorder.{u1} τ (OrderedAddCommMonoid.toPartialOrder.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))) (AddZeroClass.toHasZero.{u1} τ (AddMonoid.toAddZeroClass.{u1} τ (AddCommMonoid.toAddMonoid.{u1} τ (OrderedAddCommMonoid.toAddCommMonoid.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))))) ϕ s) (IsInvariant.{u1, u2} τ α ϕ s)
-but is expected to have type
-  forall {τ : Type.{u2}} {α : Type.{u1}} [_inst_1 : CanonicallyOrderedAddMonoid.{u2} τ] {ϕ : τ -> α -> α} {s : Set.{u1} α}, Iff (IsFwInvariant.{u2, u1} τ α (PartialOrder.toPreorder.{u2} τ (OrderedAddCommMonoid.toPartialOrder.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1))) (AddMonoid.toZero.{u2} τ (AddCommMonoid.toAddMonoid.{u2} τ (OrderedAddCommMonoid.toAddCommMonoid.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1)))) ϕ s) (IsInvariant.{u2, u1} τ α ϕ s)
-Case conversion may be inaccurate. Consider using '#align is_fw_invariant_iff_is_invariant isFwInvariant_iff_isInvariantₓ'. -/
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α} :
@@ -116,12 +92,6 @@ end Invariant
 -/
 
 
-/- warning: flow -> Flow 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 flow Flowₓ'. -/
 /-- A flow on a topological space `α` by an a additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
 structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
@@ -146,75 +116,33 @@ instance : Inhabited (Flow τ α) :=
 instance : CoeFun (Flow τ α) fun _ => τ → α → α :=
   ⟨Flow.toFun⟩
 
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 @[ext]
 theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) → ϕ₁ = ϕ₂
   | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by congr ; funext; exact h _ _
 #align flow.ext Flow.ext
 
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 @[continuity]
 protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ} (ht : Continuous t)
     {f : β → α} (hf : Continuous f) : Continuous fun x => ϕ (t x) (f x) :=
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
 
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 alias Flow.continuous ← _root_.continuous.flow
 #align continuous.flow Continuous.flow
 
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 theorem map_add (t₁ t₂ : τ) (x : α) : ϕ (t₁ + t₂) x = ϕ t₁ (ϕ t₂ x) :=
   ϕ.map_add' _ _ _
 #align flow.map_add Flow.map_add
 
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 @[simp]
 theorem map_zero : ϕ 0 = id :=
   funext ϕ.map_zero'
 #align flow.map_zero Flow.map_zero
 
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 theorem map_zero_apply (x : α) : ϕ 0 x = x :=
   ϕ.map_zero' x
 #align flow.map_zero_apply Flow.map_zero_apply
 
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 /-- Iterations of a continuous function from a topological space `α`
     to itself defines a semiflow by `ℕ` on `α`. -/
 def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
@@ -225,12 +153,6 @@ def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
   map_zero' x := rfl
 #align flow.from_iter Flow.fromIter
 
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 /-- Restriction of a flow onto an invariant set. -/
 def restrict {s : Set α} (h : IsInvariant ϕ s) : Flow τ ↥s
     where
@@ -247,12 +169,6 @@ namespace Flow
 variable {τ : Type _} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type _}
   [TopologicalSpace α] (ϕ : Flow τ α)
 
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-Case conversion may be inaccurate. Consider using '#align flow.is_invariant_iff_image_eq Flow.isInvariant_iff_image_eqₓ'. -/
 theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s = s :=
   (isInvariant_iff_image _ _).trans
     (Iff.intro
@@ -260,12 +176,6 @@ theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t
       fun h t => by rw [h t])
 #align flow.is_invariant_iff_image_eq Flow.isInvariant_iff_image_eq
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align flow.reverse Flow.reverseₓ'. -/
 /-- The time-reversal of a flow `ϕ` by a (commutative, additive) group
     is defined `ϕ.reverse t x = ϕ (-t) x`. -/
 def reverse : Flow τ α where
@@ -275,12 +185,6 @@ def reverse : Flow τ α where
   map_zero' _ := by rw [neg_zero, map_zero_apply]
 #align flow.reverse Flow.reverse
 
-/- warning: flow.to_homeomorph -> Flow.toHomeomorph 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 flow.to_homeomorph Flow.toHomeomorphₓ'. -/
 /-- The map `ϕ t` as a homeomorphism. -/
 def toHomeomorph (t : τ) : α ≃ₜ α where
   toFun := ϕ t
@@ -289,12 +193,6 @@ def toHomeomorph (t : τ) : α ≃ₜ α where
   right_inv x := by rw [← map_add, add_neg_self, map_zero_apply]
 #align flow.to_homeomorph Flow.toHomeomorph
 
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-Case conversion may be inaccurate. Consider using '#align flow.image_eq_preimage Flow.image_eq_preimageₓ'. -/
 theorem image_eq_preimage (t : τ) (s : Set α) : ϕ t '' s = ϕ (-t) ⁻¹' s :=
   (ϕ.toHomeomorph t).toEquiv.image_eq_preimage s
 #align flow.image_eq_preimage Flow.image_eq_preimage

ef7acf40

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -154,10 +154,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align flow.ext Flow.extₓ'. -/
 @[ext]
 theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) → ϕ₁ = ϕ₂
-  | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by
-    congr
-    funext
-    exact h _ _
+  | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by congr ; funext; exact h _ _
 #align flow.ext Flow.ext
 
 /- warning: flow.continuous -> Flow.continuous is a dubious translation:

ef7acf40

bump to nightly-2023-02-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo
 
 ! This file was ported from Lean 3 source module dynamics.flow
-! leanprover-community/mathlib commit 717c073262cd9d59b1a1dcda7e8ab570c5b63370
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Logic.Function.Iterate
 /-!
 # Flows and invariant sets
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines a flow on a topological space `α` by a topological
 monoid `τ` as a continuous monoid-act of `τ` on `α`. Anticipating the
 cases where `τ` is one of `ℕ`, `ℤ`, `ℝ⁺`, or `ℝ`, we use additive

717c0732

bump to nightly-2023-02-23-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

5ac40b03

Diff

@@ -169,14 +169,14 @@ protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ}
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
 
-/- warning: continuous.flow -> continuous.flow 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 continuous.flow continuous.flowₓ'. -/
+Case conversion may be inaccurate. Consider using '#align continuous.flow Continuous.flowₓ'. -/
 alias Flow.continuous ← _root_.continuous.flow
-#align continuous.flow continuous.flow
+#align continuous.flow Continuous.flow
 
 /- warning: flow.map_add -> Flow.map_add is a dubious translation:
 lean 3 declaration is

717c0732

bump to nightly-2023-02-23-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

c3065b01

Diff

@@ -43,34 +43,62 @@ section Invariant
 
 variable {τ : Type _} {α : Type _}
 
+#print IsInvariant /-
 /-- A set `s ⊆ α` is invariant under `ϕ : τ → α → α` if
     `ϕ t s ⊆ s` for all `t` in `τ`. -/
 def IsInvariant (ϕ : τ → α → α) (s : Set α) : Prop :=
   ∀ t, MapsTo (ϕ t) s s
 #align is_invariant IsInvariant
+-/
 
 variable (ϕ : τ → α → α) (s : Set α)
 
+/- warning: is_invariant_iff_image -> isInvariant_iff_image is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} {α : Type.{u2}} (ϕ : τ -> α -> α) (s : Set.{u2} α), Iff (IsInvariant.{u1, u2} τ α ϕ s) (forall (t : τ), HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.image.{u2, u2} α α (ϕ t) s) s)
+but is expected to have type
+  forall {τ : Type.{u2}} {α : Type.{u1}} (ϕ : τ -> α -> α) (s : Set.{u1} α), Iff (IsInvariant.{u2, u1} τ α ϕ s) (forall (t : τ), HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.image.{u1, u1} α α (ϕ t) s) s)
+Case conversion may be inaccurate. Consider using '#align is_invariant_iff_image isInvariant_iff_imageₓ'. -/
 theorem isInvariant_iff_image : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s ⊆ s := by
   simp_rw [IsInvariant, maps_to']
 #align is_invariant_iff_image isInvariant_iff_image
 
+#print IsFwInvariant /-
 /-- A set `s ⊆ α` is forward-invariant under `ϕ : τ → α → α` if
     `ϕ t s ⊆ s` for all `t ≥ 0`. -/
 def IsFwInvariant [Preorder τ] [Zero τ] (ϕ : τ → α → α) (s : Set α) : Prop :=
   ∀ ⦃t⦄, 0 ≤ t → MapsTo (ϕ t) s s
 #align is_fw_invariant IsFwInvariant
+-/
 
+/- warning: is_invariant.is_fw_invariant -> IsInvariant.isFwInvariant is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} {α : Type.{u2}} [_inst_1 : Preorder.{u1} τ] [_inst_2 : Zero.{u1} τ] {ϕ : τ -> α -> α} {s : Set.{u2} α}, (IsInvariant.{u1, u2} τ α ϕ s) -> (IsFwInvariant.{u1, u2} τ α _inst_1 _inst_2 ϕ s)
+but is expected to have type
+  forall {τ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} τ] [_inst_2 : Zero.{u2} τ] {ϕ : τ -> α -> α} {s : Set.{u1} α}, (IsInvariant.{u2, u1} τ α ϕ s) -> (IsFwInvariant.{u2, u1} τ α _inst_1 _inst_2 ϕ s)
+Case conversion may be inaccurate. Consider using '#align is_invariant.is_fw_invariant IsInvariant.isFwInvariantₓ'. -/
 theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsInvariant ϕ s) : IsFwInvariant ϕ s := fun t ht => h t
 #align is_invariant.is_fw_invariant IsInvariant.isFwInvariant
 
+/- warning: is_fw_invariant.is_invariant -> IsFwInvariant.isInvariant 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 is_fw_invariant.is_invariant IsFwInvariant.isInvariantₓ'. -/
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
 #align is_fw_invariant.is_invariant IsFwInvariant.isInvariant
 
+/- warning: is_fw_invariant_iff_is_invariant -> isFwInvariant_iff_isInvariant is a dubious translation:
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+  forall {τ : Type.{u1}} {α : Type.{u2}} [_inst_1 : CanonicallyOrderedAddMonoid.{u1} τ] {ϕ : τ -> α -> α} {s : Set.{u2} α}, Iff (IsFwInvariant.{u1, u2} τ α (PartialOrder.toPreorder.{u1} τ (OrderedAddCommMonoid.toPartialOrder.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))) (AddZeroClass.toHasZero.{u1} τ (AddMonoid.toAddZeroClass.{u1} τ (AddCommMonoid.toAddMonoid.{u1} τ (OrderedAddCommMonoid.toAddCommMonoid.{u1} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} τ _inst_1))))) ϕ s) (IsInvariant.{u1, u2} τ α ϕ s)
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+  forall {τ : Type.{u2}} {α : Type.{u1}} [_inst_1 : CanonicallyOrderedAddMonoid.{u2} τ] {ϕ : τ -> α -> α} {s : Set.{u1} α}, Iff (IsFwInvariant.{u2, u1} τ α (PartialOrder.toPreorder.{u2} τ (OrderedAddCommMonoid.toPartialOrder.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1))) (AddMonoid.toZero.{u2} τ (AddCommMonoid.toAddMonoid.{u2} τ (OrderedAddCommMonoid.toAddCommMonoid.{u2} τ (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u2} τ _inst_1)))) ϕ s) (IsInvariant.{u2, u1} τ α ϕ s)
+Case conversion may be inaccurate. Consider using '#align is_fw_invariant_iff_is_invariant isFwInvariant_iff_isInvariantₓ'. -/
 /-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `is_fw_invariant` and `is_invariant` are equivalent. -/
 theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α} :
@@ -85,6 +113,12 @@ end Invariant
 -/
 
 
+/- warning: flow -> Flow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align flow Flowₓ'. -/
 /-- A flow on a topological space `α` by an a additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
 structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
@@ -109,6 +143,12 @@ instance : Inhabited (Flow τ α) :=
 instance : CoeFun (Flow τ α) fun _ => τ → α → α :=
   ⟨Flow.toFun⟩
 
+/- warning: flow.ext -> Flow.ext is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align flow.ext Flow.extₓ'. -/
 @[ext]
 theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) → ϕ₁ = ϕ₂
   | ⟨f₁, _, _, _⟩, ⟨f₂, _, _, _⟩, h => by
@@ -117,28 +157,64 @@ theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) 
     exact h _ _
 #align flow.ext Flow.ext
 
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+Case conversion may be inaccurate. Consider using '#align flow.continuous Flow.continuousₓ'. -/
 @[continuity]
 protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ} (ht : Continuous t)
     {f : β → α} (hf : Continuous f) : Continuous fun x => ϕ (t x) (f x) :=
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
 
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+Case conversion may be inaccurate. Consider using '#align continuous.flow continuous.flowₓ'. -/
 alias Flow.continuous ← _root_.continuous.flow
-#align continuous.flow Continuous.flow
-
+#align continuous.flow continuous.flow
+
+/- warning: flow.map_add -> Flow.map_add is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align flow.map_add Flow.map_addₓ'. -/
 theorem map_add (t₁ t₂ : τ) (x : α) : ϕ (t₁ + t₂) x = ϕ t₁ (ϕ t₂ x) :=
   ϕ.map_add' _ _ _
 #align flow.map_add Flow.map_add
 
+/- warning: flow.map_zero -> Flow.map_zero is a dubious translation:
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 @[simp]
 theorem map_zero : ϕ 0 = id :=
   funext ϕ.map_zero'
 #align flow.map_zero Flow.map_zero
 
+/- warning: flow.map_zero_apply -> Flow.map_zero_apply is a dubious translation:
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 theorem map_zero_apply (x : α) : ϕ 0 x = x :=
   ϕ.map_zero' x
 #align flow.map_zero_apply Flow.map_zero_apply
 
+/- warning: flow.from_iter -> Flow.fromIter is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align flow.from_iter Flow.fromIterₓ'. -/
 /-- Iterations of a continuous function from a topological space `α`
     to itself defines a semiflow by `ℕ` on `α`. -/
 def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
@@ -149,6 +225,12 @@ def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α
   map_zero' x := rfl
 #align flow.from_iter Flow.fromIter
 
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+  forall {τ : Type.{u1}} [_inst_1 : AddMonoid.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : ContinuousAdd.{u1} τ _inst_2 (AddZeroClass.toAdd.{u1} τ (AddMonoid.toAddZeroClass.{u1} τ _inst_1))] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α] (ϕ : Flow.{u1, u2} τ _inst_2 _inst_1 _inst_3 α _inst_4) {s : Set.{u2} α}, (IsInvariant.{u1, u2} τ α (Flow.toFun.{u1, u2} τ _inst_2 _inst_1 _inst_3 α _inst_4 ϕ) s) -> (Flow.{u1, u2} τ _inst_2 _inst_1 _inst_3 (Set.Elem.{u2} α s) (instTopologicalSpaceSubtype.{u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) _inst_4))
+Case conversion may be inaccurate. Consider using '#align flow.restrict Flow.restrictₓ'. -/
 /-- Restriction of a flow onto an invariant set. -/
 def restrict {s : Set α} (h : IsInvariant ϕ s) : Flow τ ↥s
     where
@@ -165,6 +247,12 @@ namespace Flow
 variable {τ : Type _} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type _}
   [TopologicalSpace α] (ϕ : Flow τ α)
 
+/- warning: flow.is_invariant_iff_image_eq -> Flow.isInvariant_iff_image_eq is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α] (ϕ : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (s : Set.{u2} α), Iff (IsInvariant.{u1, u2} τ α (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (fun (_x : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) => τ -> α -> α) (Flow.hasCoeToFun.{u1, u2} τ (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) _inst_2 (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) ϕ) s) (forall (t : τ), Eq.{succ u2} (Set.{u2} α) (Set.image.{u2, u2} α α (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (fun (_x : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) => τ -> α -> α) (Flow.hasCoeToFun.{u1, u2} τ (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) _inst_2 (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) ϕ t) s) s)
+but is expected to have type
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α] (ϕ : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (s : Set.{u2} α), Iff (IsInvariant.{u1, u2} τ α (Flow.toFun.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4 ϕ) s) (forall (t : τ), Eq.{succ u2} (Set.{u2} α) (Set.image.{u2, u2} α α (Flow.toFun.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4 ϕ t) s) s)
+Case conversion may be inaccurate. Consider using '#align flow.is_invariant_iff_image_eq Flow.isInvariant_iff_image_eqₓ'. -/
 theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s = s :=
   (isInvariant_iff_image _ _).trans
     (Iff.intro
@@ -172,6 +260,12 @@ theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t
       fun h t => by rw [h t])
 #align flow.is_invariant_iff_image_eq Flow.isInvariant_iff_image_eq
 
+/- warning: flow.reverse -> Flow.reverse is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α], (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (Flow.reverse._proof_1.{u1} τ _inst_1 _inst_2 _inst_3) α _inst_4) -> (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (Flow.reverse._proof_2.{u1} τ _inst_1 _inst_2 _inst_3) α _inst_4)
+but is expected to have type
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α], (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) -> (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4)
+Case conversion may be inaccurate. Consider using '#align flow.reverse Flow.reverseₓ'. -/
 /-- The time-reversal of a flow `ϕ` by a (commutative, additive) group
     is defined `ϕ.reverse t x = ϕ (-t) x`. -/
 def reverse : Flow τ α where
@@ -181,6 +275,12 @@ def reverse : Flow τ α where
   map_zero' _ := by rw [neg_zero, map_zero_apply]
 #align flow.reverse Flow.reverse
 
+/- warning: flow.to_homeomorph -> Flow.toHomeomorph is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α], (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (Flow.toHomeomorph._proof_1.{u1} τ _inst_1 _inst_2 _inst_3) α _inst_4) -> τ -> (Homeomorph.{u2, u2} α α _inst_4 _inst_4)
+but is expected to have type
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α], (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.toContinuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) -> τ -> (Homeomorph.{u2, u2} α α _inst_4 _inst_4)
+Case conversion may be inaccurate. Consider using '#align flow.to_homeomorph Flow.toHomeomorphₓ'. -/
 /-- The map `ϕ t` as a homeomorphism. -/
 def toHomeomorph (t : τ) : α ≃ₜ α where
   toFun := ϕ t
@@ -189,6 +289,12 @@ def toHomeomorph (t : τ) : α ≃ₜ α where
   right_inv x := by rw [← map_add, add_neg_self, map_zero_apply]
 #align flow.to_homeomorph Flow.toHomeomorph
 
+/- warning: flow.image_eq_preimage -> Flow.image_eq_preimage is a dubious translation:
+lean 3 declaration is
+  forall {τ : Type.{u1}} [_inst_1 : AddCommGroup.{u1} τ] [_inst_2 : TopologicalSpace.{u1} τ] [_inst_3 : TopologicalAddGroup.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1)] {α : Type.{u2}} [_inst_4 : TopologicalSpace.{u2} α] (ϕ : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (t : τ) (s : Set.{u2} α), Eq.{succ u2} (Set.{u2} α) (Set.image.{u2, u2} α α (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (fun (_x : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) => τ -> α -> α) (Flow.hasCoeToFun.{u1, u2} τ (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) _inst_2 (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) ϕ t) s) (Set.preimage.{u2, u2} α α (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) (fun (_x : Flow.{u1, u2} τ _inst_2 (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) => τ -> α -> α) (Flow.hasCoeToFun.{u1, u2} τ (SubNegMonoid.toAddMonoid.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) _inst_2 (TopologicalAddGroup.to_continuousAdd.{u1} τ _inst_2 (AddCommGroup.toAddGroup.{u1} τ _inst_1) _inst_3) α _inst_4) ϕ (Neg.neg.{u1} τ (SubNegMonoid.toHasNeg.{u1} τ (AddGroup.toSubNegMonoid.{u1} τ (AddCommGroup.toAddGroup.{u1} τ _inst_1))) t)) s)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align flow.image_eq_preimage Flow.image_eq_preimageₓ'. -/
 theorem image_eq_preimage (t : τ) (s : Set α) : ϕ t '' s = ϕ (-t) ⁻¹' s :=
   (ϕ.toHomeomorph t).toEquiv.image_eq_preimage s
 #align flow.image_eq_preimage Flow.image_eq_preimage

717c0732

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

717c0732

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -84,7 +84,7 @@ end Invariant
 
 
 /-- A flow on a topological space `α` by an additive topological
-    monoid `τ` is a continuous monoid action of `τ` on `α`.-/
+    monoid `τ` is a continuous monoid action of `τ` on `α`. -/
 structure Flow (τ : Type*) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type*)
   [TopologicalSpace α] where
   toFun : τ → α → α

717c0732

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -178,7 +178,7 @@ def reverse : Flow τ α where
 -- Porting note: Homeomorphism.continuous_invFun : Continuous invFun := by continuity
 @[continuity]
 theorem continuous_toFun (t : τ) : Continuous (ϕ.toFun t) := by
-  rw [←curry_uncurry ϕ.toFun]
+  rw [← curry_uncurry ϕ.toFun]
   apply continuous_curry
   exact ϕ.cont'

717c0732

feat(Topology): continuity from a product with a discrete space (#7511)

Add four pairs of lemmas continuous((Within)At/On)_prod_of_discrete_left/right in ContinuousOn.lean: to check continuity of a function from X × Y to Z with X discrete, it suffices to check continuity of every slice of it with x : X fixed.
Remove duplicate lemmas continuous_uncurry_of_discreteTopology(_left) from Constructions.lean in favor of the more general (iff) version.
Move the lemma continuous_iff_continuousOn_univ up.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

87eb696e

Diff

@@ -137,7 +137,7 @@ theorem map_zero_apply (x : α) : ϕ 0 x = x := ϕ.map_zero' x
     to itself defines a semiflow by `ℕ` on `α`. -/
 def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α where
   toFun n x := g^[n] x
-  cont' := continuous_uncurry_of_discreteTopology_left (Continuous.iterate h)
+  cont' := continuous_prod_of_discrete_left.mpr (Continuous.iterate h)
   map_add' := iterate_add_apply _
   map_zero' _x := rfl
 #align flow.from_iter Flow.fromIter

717c0732

chore: rename CanonicallyOrderedAddMonoid to ..AddCommMonoid (#7503)

Renames:

CanonicallyOrderedMonoid -> CanonicallyOrderedCommMonoid

CanonicallyOrderedAddMonoid -> CanonicallyOrderedAddCommMonoid

CanonicallyLinearOrderedMonoid -> CanonicallyLinearOrderedCommMonoid

CanonicallyLinearOrderedAddMonoid -> CanonicallyLinearOrderedAddCommMonoid

f3bc24c3

Diff

@@ -62,15 +62,16 @@ theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α
     (h : IsInvariant ϕ s) : IsFwInvariant ϕ s := fun t _ht => h t
 #align is_invariant.is_fw_invariant IsInvariant.isFwInvariant
 
-/-- If `τ` is a `CanonicallyOrderedAddMonoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
+/-- If `τ` is a `CanonicallyOrderedAddCommMonoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `IsFwInvariant` and `IsInvariant` are equivalent. -/
-theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
+theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddCommMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
 #align is_fw_invariant.is_invariant IsFwInvariant.isInvariant
 
-/-- If `τ` is a `CanonicallyOrderedAddMonoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
+/-- If `τ` is a `CanonicallyOrderedAddCommMonoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `IsFwInvariant` and `IsInvariant` are equivalent. -/
-theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α} :
+theorem isFwInvariant_iff_isInvariant [CanonicallyOrderedAddCommMonoid τ] {ϕ : τ → α → α}
+    {s : Set α} :
     IsFwInvariant ϕ s ↔ IsInvariant ϕ s :=
   ⟨IsFwInvariant.isInvariant, IsInvariant.isFwInvariant⟩
 #align is_fw_invariant_iff_is_invariant isFwInvariant_iff_isInvariant

717c0732

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -119,7 +119,7 @@ protected theorem continuous {β : Type*} [TopologicalSpace β] {t : β → τ}
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
 
-alias Flow.continuous ← _root_.Continuous.flow
+alias _root_.Continuous.flow := Flow.continuous
 #align continuous.flow Continuous.flow
 
 theorem map_add (t₁ t₂ : τ) (x : α) : ϕ (t₁ + t₂) x = ϕ t₁ (ϕ t₂ x) := ϕ.map_add' _ _ _

717c0732

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -38,7 +38,7 @@ open Set Function Filter
 
 section Invariant
 
-variable {τ : Type _} {α : Type _}
+variable {τ : Type*} {α : Type*}
 
 /-- A set `s ⊆ α` is invariant under `ϕ : τ → α → α` if
     `ϕ t s ⊆ s` for all `t` in `τ`. -/
@@ -84,7 +84,7 @@ end Invariant
 
 /-- A flow on a topological space `α` by an additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
-structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
+structure Flow (τ : Type*) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type*)
   [TopologicalSpace α] where
   toFun : τ → α → α
   cont' : Continuous (uncurry toFun)
@@ -94,7 +94,7 @@ structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd
 
 namespace Flow
 
-variable {τ : Type _} [AddMonoid τ] [TopologicalSpace τ] [ContinuousAdd τ] {α : Type _}
+variable {τ : Type*} [AddMonoid τ] [TopologicalSpace τ] [ContinuousAdd τ] {α : Type*}
   [TopologicalSpace α] (ϕ : Flow τ α)
 
 instance : Inhabited (Flow τ α) :=
@@ -114,7 +114,7 @@ theorem ext : ∀ {ϕ₁ ϕ₂ : Flow τ α}, (∀ t x, ϕ₁ t x = ϕ₂ t x) 
 #align flow.ext Flow.ext
 
 @[continuity]
-protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ} (ht : Continuous t)
+protected theorem continuous {β : Type*} [TopologicalSpace β] {t : β → τ} (ht : Continuous t)
     {f : β → α} (hf : Continuous f) : Continuous fun x => ϕ (t x) (f x) :=
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
@@ -153,7 +153,7 @@ end Flow
 
 namespace Flow
 
-variable {τ : Type _} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type _}
+variable {τ : Type*} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type*}
   [TopologicalSpace α] (ϕ : Flow τ α)
 
 theorem isInvariant_iff_image_eq (s : Set α) : IsInvariant ϕ s ↔ ∀ t, ϕ t '' s = s :=

717c0732

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo
-
-! This file was ported from Lean 3 source module dynamics.flow
-! leanprover-community/mathlib commit 717c073262cd9d59b1a1dcda7e8ab570c5b63370
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Algebra.Group.Basic
 import Mathlib.Logic.Function.Iterate
 
+#align_import dynamics.flow from "leanprover-community/mathlib"@"717c073262cd9d59b1a1dcda7e8ab570c5b63370"
+
 /-!
 # Flows and invariant sets

717c0732

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -138,7 +138,7 @@ theorem map_zero_apply (x : α) : ϕ 0 x = x := ϕ.map_zero' x
 /-- Iterations of a continuous function from a topological space `α`
     to itself defines a semiflow by `ℕ` on `α`. -/
 def fromIter {g : α → α} (h : Continuous g) : Flow ℕ α where
-  toFun n x := (g^[n]) x
+  toFun n x := g^[n] x
   cont' := continuous_uncurry_of_discreteTopology_left (Continuous.iterate h)
   map_add' := iterate_add_apply _
   map_zero' _x := rfl

717c0732

chore: fix grammar 2/3 (#5002)

Part 2 of #5001

9e80ae3b

Diff

@@ -85,7 +85,7 @@ end Invariant
 -/
 
 
-/-- A flow on a topological space `α` by an a additive topological
+/-- A flow on a topological space `α` by an additive topological
     monoid `τ` is a continuous monoid action of `τ` on `α`.-/
 structure Flow (τ : Type _) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd τ] (α : Type _)
   [TopologicalSpace α] where

717c0732

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -27,7 +27,7 @@ commutative) monoid, we additionally define forward invariance, where
 `t` ranges over those elements which are nonnegative.
 
 Additionally, we define such constructions as the restriction of a
-flow onto an invariant subset, and the time-reveral of a flow by a
+flow onto an invariant subset, and the time-reversal of a flow by a
 group.
 -/

717c0732

chore: tidy various files (#2462)

c2182a74

Diff

@@ -65,7 +65,7 @@ theorem IsInvariant.isFwInvariant [Preorder τ] [Zero τ] {ϕ : τ → α → α
     (h : IsInvariant ϕ s) : IsFwInvariant ϕ s := fun t _ht => h t
 #align is_invariant.is_fw_invariant IsInvariant.isFwInvariant
 
-/-- If `τ` is a `canonically_ordered_add_monoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
+/-- If `τ` is a `CanonicallyOrderedAddMonoid` (e.g., `ℕ` or `ℝ≥0`), then the notions
 `IsFwInvariant` and `IsInvariant` are equivalent. -/
 theorem IsFwInvariant.isInvariant [CanonicallyOrderedAddMonoid τ] {ϕ : τ → α → α} {s : Set α}
     (h : IsFwInvariant ϕ s) : IsInvariant ϕ s := fun t => h (zero_le t)
@@ -122,8 +122,8 @@ protected theorem continuous {β : Type _} [TopologicalSpace β] {t : β → τ}
   ϕ.cont'.comp (ht.prod_mk hf)
 #align flow.continuous Flow.continuous
 
-alias Flow.continuous ← _root_.continuous.flow
-#align continuous.flow continuous.flow
+alias Flow.continuous ← _root_.Continuous.flow
+#align continuous.flow Continuous.flow
 
 theorem map_add (t₁ t₂ : τ) (x : α) : ϕ (t₁ + t₂) x = ϕ t₁ (ϕ t₂ x) := ϕ.map_add' _ _ _
 #align flow.map_add Flow.map_add
@@ -197,4 +197,3 @@ theorem image_eq_preimage (t : τ) (s : Set α) : ϕ t '' s = ϕ (-t) ⁻¹' s :
 #align flow.image_eq_preimage Flow.image_eq_preimage
 
 end Flow
-

717c0732

feat: Port Dynamics.Flow (#2451)

4375498b

`dynamics.flow` ⟷ `Mathlib.Dynamics.Flow`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 9 + 388

dynamics.flow ⟷ Mathlib.Dynamics.Flow

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 9 + 388

`dynamics.flow` ⟷ `Mathlib.Dynamics.Flow`