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formal statement (Lean)
211theorem r_ref_exact_pos (r target : ℝ) (hr : 0 < r) (ht : 1 < target) :
212 0 < r_ref_exact r target := by
proof body
Term-mode proof.
213 unfold r_ref_exact
214 apply mul_pos hr
215 apply Real.rpow_pos_of_pos
216 exact div_pos (by linarith) abs_beta_running_pos
217
218/-- For target > 1 + |beta| (i.e., target above the G_ratio at self),
219 r_ref_exact > r. The reference scale is LARGER than the measurement scale. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (11)
Lean names referenced from this declaration's body.
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scale
in IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
decl_use
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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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abs_beta_running_pos
in IndisputableMonolith.Gravity.RunningG
decl_use
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G_ratio
in IndisputableMonolith.Gravity.RunningG
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r_ref_exact
in IndisputableMonolith.Gravity.RunningG
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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self
in IndisputableMonolith.RecogSpec.Core
decl_use
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beta
in IndisputableMonolith.Relativity.ILG.PPN
decl_use
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beta
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use