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theorem proved term proof

transmutation_cost_pos

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formal statement (Lean)

  83theorem transmutation_cost_pos (cfg : NuclearConfig) (h : cfg.ratio ≠ 1) :
  84    0 < nuclearCost cfg := by

proof body

Term-mode proof.

  85  have hge := nuclear_cost_nonneg cfg
  86  have hne : nuclearCost cfg ≠ 0 := fun hz =>
  87    h ((nuclear_cost_zero_iff_stable cfg).mp hz)
  88  exact lt_of_le_of_ne hge (Ne.symm hne)
  89
  90/-! ## §II. Transmutation Steps -/
  91
  92/-- A transmutation step: configuration changes from ratio x to ratio y.
  93    Valid iff it reduces J-cost (towards stability). -/

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