recognition /
Cost /
Cost.Ndim.Calibration /
explainer
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formal statement (Lean)
27 theorem sqNorm_uniform {n : ℕ} {α : Vec n}
28 (hU : UniformWeights α) :
29 ∃ a : ℝ, sqNorm α = (n : ℝ) * a ^ 2 := by
proof body
Term-mode proof.
30 rcases hU with ⟨a, ha⟩
31 refine ⟨a, ?_⟩
32 unfold sqNorm dot
33 simp [ha, pow_two, Finset.card_univ]
34
35 /-- If weights are uniform and sum to one, each weight is `1/n` (for `n > 0`). -/
depends on (15)
Lean names referenced from this declaration's body.
sqNorm
in IndisputableMonolith.Cost.Ndim.Calibration
decl_use
UniformWeights
in IndisputableMonolith.Cost.Ndim.Calibration
decl_use
dot
in IndisputableMonolith.Cost.Ndim.Core
decl_use
Vec
in IndisputableMonolith.Cost.Ndim.Core
decl_use
one
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
one
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
uniform
in IndisputableMonolith.Information.ShannonEntropy
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
one
in IndisputableMonolith.RecogSpec.Core
decl_use