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theorem proved tactic proof

defectIterate_exponential_lower

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formal statement (Lean)

 121theorem defectIterate_exponential_lower (t : ℝ) (n : ℕ) :
 122    (4 : ℝ) ^ n * defectIterate t 0 ≤ defectIterate t n := by

proof body

Tactic-mode proof.

 123  induction n with
 124  | zero => simp
 125  | succ n ih =>
 126    calc (4 : ℝ) ^ (n + 1) * defectIterate t 0
 127        = 4 * ((4 : ℝ) ^ n * defectIterate t 0) := by ring
 128      _ ≤ 4 * defectIterate t n := by nlinarith
 129      _ ≤ defectIterate t (n + 1) := defectIterate_four_mul_le t n
 130
 131/-- 1 ≤ 4^n for all n. -/

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