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formal statement (Lean)
40theorem doubledZeroDefect_recurrence (ρ : ℂ) :
41 doubledZeroDefect ρ = 2 * (zeroDefect ρ) ^ 2 + 4 * zeroDefect ρ := by
proof body
Term-mode proof.
42 rw [doubledZeroDefect_eq_cosh_sub_one, zeroDefect_eq_cosh_sub_one]
43 rw [Real.cosh_two_mul]
44 nlinarith [Real.cosh_sq (zeroDeviation ρ)]
45
46/-- The doubled zero defect is always nonnegative. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (10)
Lean names referenced from this declaration's body.
-
defect
in IndisputableMonolith.Foundation.LawOfExistence
decl_use
-
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
-
doubledZeroDefect
in IndisputableMonolith.NumberTheory.ZeroDoublingLaw
decl_use
-
doubledZeroDefect_eq_cosh_sub_one
in IndisputableMonolith.NumberTheory.ZeroDoublingLaw
decl_use
-
zeroDefect
in IndisputableMonolith.NumberTheory.ZeroLocationCost
decl_use
-
zeroDefect_eq_cosh_sub_one
in IndisputableMonolith.NumberTheory.ZeroLocationCost
decl_use
-
zeroDeviation
in IndisputableMonolith.NumberTheory.ZeroLocationCost
decl_use