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doc(Dynamics/Flow): document missing entry (#12953)
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This is the only nolint entry in the Dynamics/ directory. While at this, slightly clean up the formatting of the file.
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grunweg authored and callesonne committed Jun 4, 2024
1 parent c4da512 commit ed73116
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14 changes: 6 additions & 8 deletions Mathlib/Dynamics/Flow.lean
Original file line number Diff line number Diff line change
Expand Up @@ -12,7 +12,7 @@ import Mathlib.Logic.Function.Iterate
# Flows and invariant sets
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
monoid `τ` as a continuous monoid-action of `τ` on `α`. Anticipating the
cases where `τ` is one of `ℕ`, `ℤ`, `ℝ⁺`, or `ℝ`, we use additive
notation for the monoids, though the definition does not require
commutativity.
Expand All @@ -34,8 +34,6 @@ open Set Function Filter
/-!
### Invariant sets
-/


section Invariant

variable {τ : Type*} {α : Type*}
Expand Down Expand Up @@ -82,11 +80,11 @@ end Invariant
### Flows
-/


/-- 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
/-- The map `τ → α → α` underlying a flow of `τ` on `α`. -/
toFun : τ → α → α
cont' : Continuous (uncurry toFun)
map_add' : ∀ t₁ t₂ x, toFun (t₁ + t₂) x = toFun t₁ (toFun t₂ x)
Expand All @@ -95,8 +93,8 @@ structure Flow (τ : Type*) [TopologicalSpace τ] [AddMonoid τ] [ContinuousAdd

namespace Flow

variable {τ : Type*} [AddMonoid τ] [TopologicalSpace τ] [ContinuousAdd τ] {α : Type*}
[TopologicalSpace α] (ϕ : Flow τ α)
variable {τ : Type*} [AddMonoid τ] [TopologicalSpace τ] [ContinuousAdd τ]
{α : Type*} [TopologicalSpace α] (ϕ : Flow τ α)

instance : Inhabited (Flow τ α) :=
⟨{ toFun := fun _ x => x
Expand Down Expand Up @@ -154,8 +152,8 @@ end Flow

namespace Flow

variable {τ : Type*} [AddCommGroup τ] [TopologicalSpace τ] [TopologicalAddGroup τ] {α : Type*}
[TopologicalSpace α] (ϕ : Flow τ α)
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 :=
(isInvariant_iff_image _ _).trans
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1 change: 0 additions & 1 deletion scripts/nolints.json
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Expand Up @@ -184,7 +184,6 @@
["docBlame", "FirstOrder.«term∀'_»"],
["docBlame", "FirstOrder.«term∃'_»"],
["docBlame", "FirstOrder.«term∼_»"],
["docBlame", "Flow.toFun"],
["docBlame", "Function.app"],
["docBlame", "Function.compLeft"],
["docBlame", "Function.compRight"],
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