lemma
proved
term proof
kappa_einstein_eq
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formal statement (Lean)
451lemma kappa_einstein_eq : kappa_einstein = 8 * phi ^ (5 : ℝ) := by
proof body
Term-mode proof.
452 unfold kappa_einstein G hbar cLagLock lambda_rec ell0 c tau0 tick
453 simp only [one_pow, mul_one, div_one]
454 have hpi : Real.pi ≠ 0 := Real.pi_ne_zero
455 field_simp [hpi]
456 rw [Real.rpow_neg phi_pos.le]
457 field_simp [phi_ne_zero]
458
used by (11)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (24)
Lean names referenced from this declaration's body.
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lambda_rec
in IndisputableMonolith.Bridge.DataCore
decl_use
-
tau0
in IndisputableMonolith.Compat.Constants
decl_use
-
cLagLock
in IndisputableMonolith.Constants
decl_use
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ell0
in IndisputableMonolith.Constants
decl_use
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G
in IndisputableMonolith.Constants
decl_use
-
hbar
in IndisputableMonolith.Constants
decl_use
-
kappa_einstein
in IndisputableMonolith.Constants
decl_use
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lambda_rec
in IndisputableMonolith.Constants
decl_use
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phi_ne_zero
in IndisputableMonolith.Constants
decl_use
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tau0
in IndisputableMonolith.Constants
decl_use
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tick
in IndisputableMonolith.Constants
decl_use
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G
in IndisputableMonolith.Constants.Codata
decl_use
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hbar
in IndisputableMonolith.Constants.Codata
decl_use
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ell0
in IndisputableMonolith.Constants.Derivation
decl_use
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tau0
in IndisputableMonolith.Constants.Derivation
decl_use
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tick
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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G
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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le
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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mul_one
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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G
in IndisputableMonolith.Gravity.JCostInflaton
decl_use
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hbar
in IndisputableMonolith.Information.ComputationLimitsStructure
decl_use
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phi_ne_zero
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use
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phi_ne_zero
in IndisputableMonolith.PhiSupport.Lemmas
decl_use
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hbar
in IndisputableMonolith.Quantum.EntanglementEntropy
decl_use