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added the second part of exercise 4.4.2 (b) #422

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teorth merged 1 commit into from
Dec 21, 2025
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added the second part of exercise 4.4.2 (b) #422

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8 changes: 7 additions & 1 deletion analysis/Analysis/Section_4_4.lean
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Expand Up @@ -44,14 +44,20 @@ theorem Rat.exists_between_rat {x y:ℚ} (h: x < y) : ∃ z:ℚ, x < z ∧ z < y
. convert add_lt_add_right h' (x/2) using 1 <;> ring
convert add_lt_add_right h' (y/2) using 1 <;> ring

/-- Exercise 4.4.2 -/
/-- Exercise 4.4.2 (a) -/
theorem Nat.no_infinite_descent : ¬ ∃ a:ℕ → ℕ, ∀ n, a (n+1) < a n := by
sorry

/-- Exercise 4.4.2 (b) -/
def Int.infinite_descent : Decidable (∃ a:ℕ → ℤ, ∀ n, a (n+1) < a n) := by
-- the first line of this construction should be either `apply isTrue` or `apply isFalse`.
sorry

/-- Exercise 4.4.2 (b) -/
def Rat.pos_infinite_descent : Decidable (∃ a:ℕ → {x: ℚ // 0 < x}, ∀ n, a (n+1) < a n) := by
-- the first line of this construction should be either `apply isTrue` or `apply isFalse`.
sorry

#check even_iff_exists_two_mul
#check odd_iff_exists_bit1

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