OAI/Analysis/LipschitzHilbert/Geometry/RectangleLastSelected.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

A finite subfamily of a selection run has a last member. All the other members were present in its actual previous set.

  1. theorem OAI.LipschitzHilbert.RectangleCoverRun.last_selected_witness line 14
  2. theorem OAI.LipschitzHilbert.RectangleCoverRun.selected_previous_witness line 48

    Source documentation

    Every strictly longer selected rectangle precedes the specified member and belongs to the previous set at its selection.

    theorem selected_previous_witness (h : RectangleCoverRun R blocked previous stock selected)
        (r : ι) (hr : r ∈ selected) :
        ∃ p : Finset ι, previous ⊆ p ∧
          (∀ j ∈ selected, (R r).long < (R j).long → j ∈ p) ∧ ¬blocked p r := by
    …

    Mentions: OAI.LipschitzHilbert.RectangleCoverRun