`higher_Z_more_demand`

proved

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module: IndisputableMonolith.Unification.ConsciousnessBandwidth
domain: Unification
line: 184 · github
papers citing: none yet

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IndisputableMonolith.Unification.ConsciousnessBandwidth on GitHub at line 184.

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formal source

 181        apply mul_le_mul_of_nonneg_left hfac hd
 182
 183/-- Higher Z-complexity strictly increases demand (when J > 0). -/
 184theorem higher_Z_more_demand {L : ℝ} (hL : 0 < L) (hL1 : L ≠ 1)
 185    {Z₁ Z₂ : ℤ} (hZ : |Z₁| < |Z₂|) :
 186    complexDemand L Z₁ < complexDemand L Z₂ := by
 187  unfold complexDemand
 188  have hd : 0 < maintenanceDemand L := by
 189    unfold maintenanceDemand
 190    apply mul_pos barrierPeriod_pos
 191    have : Cost.Jcost L ≠ 0 := by
 192      intro h
 193      exact hL1 ((Cost.Jcost_eq_zero_iff L hL).mp h)
 194    exact lt_of_le_of_ne (Cost.Jcost_nonneg hL) (Ne.symm this)
 195  apply mul_lt_mul_of_pos_left _ hd
 196  have : (↑|Z₁| : ℝ) < ↑|Z₂| := Int.cast_lt.mpr hZ
 197  linarith [mul_lt_mul_of_pos_right this k_R_pos]
 198
 199end ConsciousnessBandwidth
 200end Unification
 201end IndisputableMonolith

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