Grouped exact word counts for the six global profiles

import Definitions.Def_mme_released_global_yz_certificate
import Definitions.Def_mme_released_global_frame_data
import Definitions.Def_mme_global_CW_joint_start_data
open BigOperators MME MME.TensorObj MME.ProfiledCW MME.ReleasedGlobal MME.ReleasedGlobalNumeric MME.ReleasedGlobalYZ MME.MoreAsymmetryExactSeed MME.RegionRate MME.RecursiveThinSplit MME.GlobalCW MME.RecursiveYZ
open scoped Classical
set_option autoImplicit false
set_option maxRecDepth 3000
universe u

theorem mme_released_global_yz_cached_counts (o : Fin 6) (i : Fin 2) (s : Fin 45) (t : Fin 81) :
    cachedCounts o i s t =
      ((jointRows o s).map (fun a ↦ if atom a.1 (RecursiveYZ.yzMode i) = codeWord t then a.2 else 0)).sum := by
  sorry