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theorem proved tactic proof

lambda_rec_unique_root

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formal statement (Lean)

 100theorem lambda_rec_unique_root (lambda : ℝ) (hlambda : lambda > 0) :
 101    K lambda = 0 ↔ lambda = lambda_rec := by

proof body

Tactic-mode proof.

 102  unfold K lambda_rec ell0
 103  simp only [one_pow, div_one]
 104  constructor
 105  · intro h
 106    have hsq : lambda ^ 2 = 1 := by linarith
 107    have : (lambda - 1) * (lambda + 1) = 0 := by nlinarith
 108    rcases mul_eq_zero.mp this with h1 | h1
 109    · linarith
 110    · linarith
 111  · intro h
 112    rw [h]; ring
 113

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