theorem
proved
term proof
Jcost_pos_of_ne_one
show as:
view Lean formalization →
formal statement (Lean)
231theorem Jcost_pos_of_ne_one (r : ℝ) (hr : 0 < r) (hr_ne : r ≠ 1) :
232 0 < Jcost r := by
proof body
Term-mode proof.
233 have h := Jcost_eq_sq (ne_of_gt hr)
234 rw [h]
235 apply div_pos
236 · have : r - 1 ≠ 0 := sub_ne_zero.mpr hr_ne
237 positivity
238 · positivity
239
240/-! ## §5 Working Memory Capacity -/
241
242/-- Working memory capacity prediction: φ³ ≈ 4.236.
243 The cache hierarchy at ratio φ gives Level 1 (working memory)
244 capacity = φ³ relative to Level 0 (focal attention, capacity 1). -/
used by (40)
-
srCost_pos_off_threshold -
aestheticCost_pos_off_optimum -
resonance_increases_stability -
above_threshold_positive -
oxidative_stress -
forecastCost_pos_off_unit -
chainCost_pos_off_unit -
Jcost_phi_pos -
asymmetry_positive_cost -
crossSectionRatio_pos -
dmCrossSection_pos -
hubble_tension_pos -
jcost_phi_pos -
potential_positive -
V_pos_off_vacuum -
jcost_ground_state -
Jcost_eq_zero_iff -
Jcost_pos_of_ne_one -
Jcost_pos_of_ne_one -
shared_sensitivity -
biased_reasoning_cost -
disease_cost -
market_arbitrage_gap -
minimum_at_one -
off_equilibrium_game_cost -
off_target_cost -
recognition_deficit -
turbulent_cost -
deviation_increases_cost -
nash_stability_at_homeostasis