`BookProof.ChapterF4.mgRun_undercount` (k : ℕ) (xs : List ι) (x : ι) : (mgRun k xs).1 x ≤ xs.count x
ProvedBookProof.ChapterF4.mgRun_undercounttheoremstimepiece
Prove the following Lean 4 theorem from ChapterF4.
BookProof.ChapterF4.mgRun_undercount (k : ℕ) (xs : List ι) (x : ι) : (mgRun k xs).1 x ≤ xs.count x
Formalization note: Lean 4 identifier BookProof.ChapterF4.mgRun_undercount.
Preamble
-- Generated from ChapterF4.lean — theorem BookProof.ChapterF4.mgRun_undercount
import Mathlib
import Definitions.Def_ChapterF4
open BookProof.ChapterF4
open scoped BigOperators Matrix
variable {d k : ℕ}
variable {A : Type*} [NormedRing A] [NormedAlgebra ℂ A] [StarRing A] [ContinuousStar A]
[CompleteSpace A] [StarModule ℂ A]
variable {α κ Ω : Type*} [Fintype α] [DecidableEq α] [Fintype κ] [DecidableEq κ]
{mΩ : MeasurableSpace Ω}
variable {ι : Type*} [Fintype ι] [DecidableEq ι]Formal statement
theorem BookProof.ChapterF4.mgRun_undercount (k : ℕ) (xs : List ι) (x : ι) :
(mgRun k xs).1 x ≤ xs.count x := by sorry