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Update InvariantSubset.lean
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pitmonticone committed Jun 20, 2024
1 parent 82a0c9d commit c04ff7e
Showing 1 changed file with 2 additions and 4 deletions.
6 changes: 2 additions & 4 deletions BET/TopologicalEntropy/InvariantSubset.lean
Original file line number Diff line number Diff line change
Expand Up @@ -39,12 +39,10 @@ theorem image_of_orbit_eq_orbit_of_image (x : X) (n : ℕ) :
. rw [← iterate_add_apply, add_comm, iterate_add_apply, Tnkx_eq_y]

/-- A subset F is T-invariant if, for any x ∈ F, T(x) ∈ F. Written with preimages. -/
def IsInvariant (T : X → X) (F : Set X) : Prop :=
F ⊆ T ⁻¹' F
def IsInvariant (T : X → X) (F : Set X) : Prop := F ⊆ T ⁻¹' F

theorem inv_def' {T : X → X} {F : Set X} (F_inv : IsInvariant T F) {x : X} (h : x ∈ F) :
T x ∈ F :=
F_inv h
T x ∈ F := F_inv h

theorem iter_of_inv_in_inv {T : X → X} {F : Set X} (F_inv : IsInvariant T F) (n : ℕ) :
F ⊆ T^[n] ⁻¹' F := by
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