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formal statement (Lean)
35lemma lambda_kin_from_tau_rec (U : RSUnits) : U.c * tau_rec_display U = lambda_kin_display U := by
proof body
Tactic-mode proof.
36 simp only [tau_rec_display, lambda_kin_display]
37 -- Goal: U.c * (2 * π * τ₀ / (8 * log φ)) = 2 * π * ℓ₀ / (8 * log φ)
38 have h : U.c * U.tau0 = U.ell0 := U.c_ell0_tau0
39 calc U.c * (2 * Real.pi * U.tau0 / (8 * Real.log phi))
40 = (2 * Real.pi * (U.c * U.tau0)) / (8 * Real.log phi) := by ring
41 _ = (2 * Real.pi * U.ell0) / (8 * Real.log phi) := by rw [h]
42
43/-- Canonical K-gate: both route ratios equal K_gate_ratio. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (15)
Lean names referenced from this declaration's body.
-
tau0
in IndisputableMonolith.Compat.Constants
decl_use
-
c_ell0_tau0
in IndisputableMonolith.Constants
decl_use
-
ell0
in IndisputableMonolith.Constants
decl_use
-
K
in IndisputableMonolith.Constants
decl_use
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RSUnits
in IndisputableMonolith.Constants
decl_use
-
tau0
in IndisputableMonolith.Constants
decl_use
-
ell0
in IndisputableMonolith.Constants.Derivation
decl_use
-
tau0
in IndisputableMonolith.Constants.Derivation
decl_use
-
K_gate_ratio
in IndisputableMonolith.Constants.KDisplayCore
decl_use
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lambda_kin_display
in IndisputableMonolith.Constants.KDisplayCore
decl_use
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tau_rec_display
in IndisputableMonolith.Constants.KDisplayCore
decl_use
-
K
in IndisputableMonolith.Constants.LambdaRecDerivation
decl_use
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U
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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U
in IndisputableMonolith.Recognition
decl_use
-
RSUnits
in IndisputableMonolith.TruthCore.Display
decl_use