recognition /
Gravity /
Gravity.ILG /
explainer
lemma
proved
term proof
w_t_nonneg
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formal statement (Lean)
126 lemma w_t_nonneg (P : Params) (H : ParamProps P) (Tdyn τ0 : ℝ) :
127 0 ≤ w_t P Tdyn τ0 := by
proof body
Term-mode proof.
128 -- For defaultConfig, eps_t = 0.01 > 0.
129 -- Thus t = max(0.01, Tdyn/τ0) > 0.
130 -- rpow t alpha is non-negative for t > 0.
131 -- Result follows from Clag <= 1.
132 unfold w_t
133 exact w_t_nonneg_with defaultConfig defaultConfig_props P H Tdyn τ0
134
135 /-- Time-kernel is at least 1 when alpha >= 0, Clag >= 0 and Tdyn >= tau0. -/
depends on (29)
Lean names referenced from this declaration's body.
H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
tau0
in IndisputableMonolith.Compat.Constants
decl_use
tau0
in IndisputableMonolith.Constants
decl_use
alpha
in IndisputableMonolith.Constants.Alpha
decl_use
tau0
in IndisputableMonolith.Constants.Derivation
decl_use
Clag
in IndisputableMonolith.Constants.ILG
decl_use
Time
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
kernel
in IndisputableMonolith.Cosmology.BITKernelFamilies
decl_use
H
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
from
in IndisputableMonolith.Foundation.PrimitiveDistinction
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
defaultConfig
in IndisputableMonolith.Gravity.ILG
decl_use
defaultConfig_props
in IndisputableMonolith.Gravity.ILG
decl_use
ParamProps
in IndisputableMonolith.Gravity.ILG
decl_use
Params
in IndisputableMonolith.Gravity.ILG
decl_use
w_t
in IndisputableMonolith.Gravity.ILG
decl_use
w_t_nonneg_with
in IndisputableMonolith.Gravity.ILG
decl_use
Tdyn
in IndisputableMonolith.Gravity.ParameterizationBridge
decl_use
kernel
in IndisputableMonolith.ILG.Kernel
decl_use
ParamProps
in IndisputableMonolith.ILG.Params
decl_use
Params
in IndisputableMonolith.ILG.Params
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
ParamProps
in IndisputableMonolith.Relativity.ILG.Params
decl_use
Params
in IndisputableMonolith.Relativity.ILG.Params
decl_use
Params
in IndisputableMonolith.Spiral.SpiralField
decl_use