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theorem proved tactic proof

aggregate_eq_one_iff

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formal statement (Lean)

  12theorem aggregate_eq_one_iff {n : ℕ} (α x : Vec n) :
  13    aggregate α x = 1 ↔ dot α (logVec x) = 0 := by

proof body

Tactic-mode proof.

  14  unfold aggregate
  15  constructor
  16  · intro h
  17    have : Real.exp (dot α (logVec x)) = Real.exp 0 := by simpa using h
  18    exact Real.exp_injective this
  19  · intro h
  20    simp [h]
  21
  22/-- Zero-cost iff weighted log sum vanishes. -/

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