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theorem proved term proof

unity_is_equilibrium

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formal statement (Lean)

 527theorem unity_is_equilibrium {N : ℕ} (hN : 0 < N) :
 528    IsEquilibrium (unity_config N hN) := by

proof body

Term-mode proof.

 529  constructor
 530  · exact self_feasible _
 531  · intro c' hc'
 532    rw [unity_defect_zero hN]
 533    exact total_defect_nonneg c'
 534
 535/-- **Theorem (Equilibrium Is Attractive)**:
 536    Every variational trajectory converges to equilibrium in the sense
 537    that total defect is non-increasing and bounded below by zero.
 538
 539    The defect sequence {total_defect(traj(t))} is monotone decreasing
 540    and bounded below, hence convergent. -/

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