Entropy copies are bounded by the floored lower estimate
Provedmme_integer_step_entropyCopies_le_floormatrix-multiplicationmore-asymmetryregional-entropy
Every integer step's guaranteed copy count is bounded by its floored entropy lower estimate.
Since by division, this records the trivial but reusable upper bound used before any lower-bound analysis.
Formalization Note The proof unfolds the definition and applies division monotonicity.
Preamble
import Definitions.Def_mme_regional_entropy_copy_bound import Definitions.Def_mme_recursive_profiled_CW_data set_option autoImplicit false
Formal statement
theorem mme_integer_step_entropyCopies_le_floor : forall {ell M : Nat} {P : MME.ProfiledCW.Predicate M} (S : MME.RegionRealization.IntegerStep ell M P), S.entropyCopies ≤ ⌊S.entropyLower⌋₊ := by sorrySource
Definition of IntegerStep.entropyCopies; supporting lemma for regional copy bounds.