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lemma proved term proof

J_stasis_nonneg

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formal statement (Lean)

 163lemma J_stasis_nonneg {x : ℝ} (hx : 0 < x) : 0 ≤ J_stasis x := by

proof body

Term-mode proof.

 164  unfold J_stasis
 165  apply mul_nonneg (by norm_num : (0:ℝ) ≤ 8) (J_nonneg hx)
 166
 167/-- **COST OF CHANGE**: The cost to evolve from x to y over one octave.
 168
 169    J_change(x,y) = J_transition(x,y) + J_stasis(y)
 170
 171    This includes:
 172    1. The transition cost to get from x to y
 173    2. The stasis cost to maintain y for one octave
 174
 175    The universe chooses change when J_change < J_stasis. -/

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