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theorem proved term proof

cost_zero_iff_equilibrium

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formal statement (Lean)

 129theorem cost_zero_iff_equilibrium {x : ℝ} (hx : 0 < x) :
 130    Cost.Jcost x = 0 ↔ x = 1 := by

proof body

Term-mode proof.

 131  refine ⟨?_, ?_⟩
 132  · intro h
 133    by_contra hne
 134    have hpos : 0 < Cost.Jcost x := Cost.Jcost_pos_of_ne_one x hx hne
 135    linarith
 136  · intro h
 137    rw [h]
 138    exact Cost.Jcost_unit0
 139
 140/-- Rewrite of `cost_zero_iff_equilibrium` in the equivalent contrapositive:
 141off equilibrium, the J-cost is strictly positive. -/

used by (3)

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depends on (18)

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