OAI/NumberTheory/TwoPoint/Bounds/RunCoverage.lean
3 declarations, 0 contain sorry, 0 declared as axioms
Every observed regular class is present in an encoded regular segment.
- theorem
OAI.TwoPointCorrelations.columnRunHeads_coverline 14Source 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
- theorem
OAI.TwoPointCorrelations.mem_columnRunHeadsline 33 - theorem
OAI.TwoPointCorrelations.partitionColumnRuns_regular_coverline 40Source 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 …