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formal statement (Lean)
41theorem lambdaRS_band : (1.88 : ℝ) < lambdaRS ∧ lambdaRS < 2.03 := by
proof body
Tactic-mode proof.
42 unfold lambdaRS
43 have h5 : phi ^ 5 = 5 * phi + 3 := phi5_eq
44 have h1 := phi_gt_onePointSixOne
45 have h2 := phi_lt_onePointSixTwo
46 rw [h5]
47 constructor
48 · have : 8 * (5 * phi + 3) / 45 > 8 * (5 * 1.61 + 3) / 45 := by
49 apply div_lt_div_of_pos_right _ (by norm_num)
50 nlinarith
51 linarith
52 · have : 8 * (5 * phi + 3) / 45 < 8 * (5 * 1.62 + 3) / 45 := by
53 apply div_lt_div_of_pos_right _ (by norm_num)
54 nlinarith
55 linarith
56
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
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phi_lt_onePointSixTwo
in IndisputableMonolith.Constants
decl_use
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phi5_eq
in IndisputableMonolith.Cosmology.DarkEnergyEquationOfStateDepth
decl_use
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phi5_eq
in IndisputableMonolith.Cosmology.HubbleTensionPipelineFromZAging
decl_use
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phi5_eq
in IndisputableMonolith.Cosmology.InflatonPotentialStructural
decl_use
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lambdaRS
in IndisputableMonolith.Cosmology.OmegaLambdaBITKernelBand
decl_use
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lambdaRS_band
in IndisputableMonolith.Cosmology.OmegaLambdaBITKernelBand
decl_use
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phi5_eq
in IndisputableMonolith.Cosmology.OmegaLambdaBITKernelBand
decl_use
-
lambdaRS
in IndisputableMonolith.Physics.CosmologicalConstantFromRS
decl_use
-
phi5_eq
in IndisputableMonolith.Physics.CosmologicalConstantFromRS
decl_use