OAI/NumberTheory/TwoPoint/Bounds/RunCoverage.lean

GitHub source file

3 declarations, 0 contain sorry, 0 declared as axioms

Every observed regular class is present in an encoded regular segment.

  1. theorem OAI.TwoPointCorrelations.columnRunHeads_cover line 14

    Source documentation

    Greedy compression can suppress only the preceding label; no observed class disappears from the previous-label/run-head pair.

    theorem columnRunHeads_cover (l : List α) (previous : Option α) (a : α) (ha : a ∈ l) :
        previous = some a ∨ a ∈ columnRunHeads (l.map some) previous := by
    …

    Mentions: OAI.TwoPointCorrelations.columnRunHeads

  2. theorem OAI.TwoPointCorrelations.mem_columnRunHeads line 33
  3. theorem OAI.TwoPointCorrelations.partitionColumnRuns_regular_cover line 40

    Source documentation

    A regular observed run occurs in one of the actual regular pieces, so the shared forest numbering applies to it.

    theorem partitionColumnRuns_regular_cover (omitted : α → Bool) (runs : List α)
        (a : α) (ha : a ∈ runs) (hregular : omitted a = false) :
        ∃ segment, Sum.inl segment ∈ partitionColumnRuns omitted runs ∧ a ∈ segment := by
    …

    Mentions: OAI.TwoPointCorrelations.partitionColumnRuns