```
import Mathlib.Geometry.Euclidean.Triangle
import Mathlib.Tactic
/-!
# International Mathematical Olympiad 1983, Problem 6
Suppose that a,b,c are the side lengths of a triangle. Prove that
a²b(a - b) + b²c(b - c) + c²a(c - a) ≥ 0.
Determine when equality occurs.
-/
namespace Imo1983P6
/- determine -/ abbrev EqualityCondition (a b c : ℝ) : Prop := sorry
theorem imo1983_p6
(T : Affine.Triangle ℝ (EuclideanSpace ℝ (Fin 2)))
(a b c : ℝ)
(ha : a = dist (T.points 1) (T.points 2))
(hb : b = dist (T.points 2) (T.points 0))
(hc : c = dist (T.points 0) (T.points 1)) :
0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a)
∧ (0 = a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) ↔
EqualityCondition a b c) := sorry
end Imo1983P6
```

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