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formal statement (Lean)
181theorem strict_transmutation_progress
182 (cfg : NuclearConfig) (h_unstable : cfg.ratio ≠ 1) :
183 ∃ step : TransmutationStep,
184 step.initial = cfg ∧
185 nuclearCost step.final < nuclearCost step.initial := by
proof body
Term-mode proof.
186 have hcost_pos := transmutation_cost_pos cfg h_unstable
187 have hscz : nuclearCost stable_config = 0 := stable_config_zero_cost
188 refine ⟨⟨cfg, stable_config, ?_⟩, rfl, ?_⟩
189 · linarith [hscz.le, hcost_pos]
190 · linarith [hscz.le, hcost_pos]
191
192/-! ## §VI. RS Transmutation Efficiency -/
193
194/-- The transmutation efficiency: ratio of cost reduction to initial cost. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
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en006_certificate
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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depends on (16)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
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step
in IndisputableMonolith.Complexity.CellularAutomata
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NuclearConfig
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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nuclearCost
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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stable_config
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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stable_config_zero_cost
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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transmutation_cost_pos
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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TransmutationStep
in IndisputableMonolith.Engineering.FissionTransmutationStructure
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le
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
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cost
in IndisputableMonolith.Foundation.ObserverForcing
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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Efficiency
in IndisputableMonolith.Safety.DampeningField
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