`compensatory_nonneg_of_sqNorm_le_one`

proved

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module: IndisputableMonolith.Cost.Ndim.Bridge
domain: Cost
line: 55 · github
papers citing: none yet

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IndisputableMonolith.Cost.Ndim.Bridge on GitHub at line 55.

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formal source

  52  simpa [multiplicativeQuadratic, additiveQuadratic, one_mul] using hscaled
  53
  54/-- Under normalized weights (`‖α‖² ≤ 1`), the compensatory term is nonnegative. -/
  55theorem compensatory_nonneg_of_sqNorm_le_one {n : ℕ}
  56    (α ε : Vec n) (hα : dot α α ≤ 1) :
  57    0 ≤ compensatoryQuadratic α ε := by
  58  unfold compensatoryQuadratic
  59  have hle := multiplicative_le_additive_of_sqNorm_le_one α ε hα
  60  linarith
  61
  62end Ndim
  63end Cost
  64end IndisputableMonolith

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