No prose has been written for this declaration yet. The Lean source and graph data below render
without it.
generate prose now
formal statement (Lean)
34theorem lambdaRS_band :
35 (1.88 : ℝ) < lambdaRS ∧ lambdaRS < 2.03 := by
proof body
Tactic-mode proof.
36 unfold lambdaRS
37 have h5 : phi ^ 5 = 5 * phi + 3 := phi5_eq
38 have h1 := phi_gt_onePointSixOne
39 have h2 := phi_lt_onePointSixTwo
40 constructor
41 · have : 8 * phi ^ 5 / 45 > 8 * (5 * 1.61 + 3) / 45 := by
42 apply div_lt_div_of_pos_right _ (by norm_num)
43 nlinarith
44 linarith
45 · have : 8 * phi ^ 5 / 45 < 8 * (5 * 1.62 + 3) / 45 := by
46 apply div_lt_div_of_pos_right _ (by norm_num)
47 nlinarith
48 linarith
49
50/-- Λ_RS > 0. -/
used by (3)
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.
-
phi_gt_onePointSixOne
in IndisputableMonolith.Constants
decl_use
-
phi_lt_onePointSixTwo
in IndisputableMonolith.Constants
decl_use
-
phi5_eq
in IndisputableMonolith.Cosmology.DarkEnergyEquationOfStateDepth
decl_use
-
phi5_eq
in IndisputableMonolith.Cosmology.HubbleTensionPipelineFromZAging
decl_use
-
phi5_eq
in IndisputableMonolith.Cosmology.InflatonPotentialStructural
decl_use
-
lambdaRS
in IndisputableMonolith.Cosmology.OmegaLambdaBITKernelBand
decl_use
-
phi5_eq
in IndisputableMonolith.Cosmology.OmegaLambdaBITKernelBand
decl_use
-
lambdaRS
in IndisputableMonolith.Physics.CosmologicalConstantFromRS
decl_use
-
lambdaRS_band
in IndisputableMonolith.Physics.CosmologicalConstantFromRS
decl_use
-
phi5_eq
in IndisputableMonolith.Physics.CosmologicalConstantFromRS
decl_use