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theorem proved term proof

maintenanceBudget_pos

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formal statement (Lean)

 106theorem maintenanceBudget_pos {L : ℝ} (hL : 0 < L) : 0 < maintenanceBudget L := by

proof body

Term-mode proof.

 107  unfold maintenanceBudget
 108  apply div_pos (boundaryArea_pos hL)
 109  apply mul_pos
 110  apply mul_pos
 111  · linarith [planckArea_pos]
 112  · exact planckArea_pos
 113  · exact k_R_pos
 114
 115/-! ## §4. Maintenance Demand -/
 116
 117/-- The recognition cost of maintaining a boundary of extent L over the
 118    consciousness barrier period.
 119
 120    Uses the canonical J-cost: BoundaryCost = τ · J(L/λ_rec).
 121    In RS-native units with λ_rec = ℓ_P = 1:
 122        demand = 360 · J(L). -/

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