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formal statement (Lean)
25theorem self_recognition_zero_cost (e : LedgerForcing.RecognitionEvent) :
26 e.ratio = 1 → recognition_cost e = 0 := by
proof body
Term-mode proof.
27 intro h
28 simp only [recognition_cost, h, LedgerForcing.J]
29 norm_num
30
31/-- Non-trivial recognition has positive cost.
32 Uses the fact that J(x) = (x + 1/x)/2 - 1 ≥ 0, with = 0 iff x = 1. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (8)
Lean names referenced from this declaration's body.
-
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
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RecognitionEvent
in IndisputableMonolith.Foundation.LedgerForcing
decl_use
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
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cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
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RecognitionEvent
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
-
recognition_cost
in IndisputableMonolith.Foundation.RecognitionForcing
decl_use
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RecognitionEvent
in IndisputableMonolith.Information.InformationIsLedger
decl_use
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that
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use