Fix broken lines in Sum.lean for v4.23.0

Changes

4 changed files (+20/-20)

• Sum.lean
  • @@ -13,7 +13,9 @@ lemma geom_sum (N : ℕ) (b : ℝ) (hN : 2 ≤ N) (hb : 2 ≤ b) : ∑ a ∈ Ico
    _ = 1 / (b - 1) - 1 / b - b / (b ^ N * (b - 1)) := by have : b - 1 ≠ 0 := by linarith field_simp - ring + ring_nf + rw [mul_assoc, ← mul_pow, mul_inv_cancel₀ (by linarith)] + simp _ = 1 / (b - 1) - 1 / b - 1 / (b ^ (N - 1) * (b - 1)) := by have h₁ : b ≠ 0 := by linarith have h₂ : b ^ N * (b - 1) = b * (b ^ (N - 1) * (b - 1)) := by
  • @@ -33,11 +35,11 @@ lemma telescope_sum (N : ℕ) (h : 2 ≤ N): ∑ a ∈ Ico 2 N, ∑ b ∈ Ico 2
    suffices ∑ b ∈ Ico 2 N, ((1 : ℝ) / (b - 1) - (1 : ℝ) / b) = 1 - (1 : ℝ) / (N - 1) by rw [this] induction h with | refl => - field_simp + simp norm_num | step h ih => rw [sum_Ico_succ_top, ih] - field_simp + simp exact h -- Exponentials grow quickly
  • @@ -89,8 +91,8 @@ theorem double_sum : Tendsto (fun N : ℕ => ∑ a ∈ Ico 2 N, ∑ b ∈ Ico 2
    rw [mul_div_assoc] exact mul_le_mul h₄ h₅ (by norm_num) (by norm_num) have := sum_le_sum h₂ - field_simp - field_simp at this + simp + simp [Nat.cast_sub h₁] at this exact this ring_nf at this have : 1 < 1 + ε - 1 / (n - 1) - (n - 2) / 2 ^ (n - 1) := by
  • @@ -128,11 +130,9 @@ theorem double_sum : Tendsto (fun N : ℕ => ∑ a ∈ Ico 2 N, ∑ b ∈ Ico 2
    linarith · -- Less than 1 have h₂ b (bico : b ∈ Ico 2 n) : 0 < (1 : ℝ) / (b ^ (n - 1) * (b - 1)) := by - field_simp + rw [one_div_pos] have : 1 < (b : ℝ) := Nat.one_lt_cast.mpr (List.left_le_of_mem_range' bico) exact mul_pos (pow_pos (by linarith) (n - 1)) (by linarith) - have := sum_nonneg (fun b a => le_of_lt (h₂ b a)) - have : 0 < (1 : ℝ) / (n - 1) := by - field_simp - omega + have := sum_nonneg <| fun b a => le_of_lt (h₂ b a) + have : 0 < (1 : ℝ) / (n - 1) := by simp [Nat.one_lt_cast.mpr h₁] grind
• lake-manifest.json
  • @@ -5,17 +5,17 @@
    "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "90c0e186fd333cbdddbe0e5148aa3cd2d24dcf9a", + "rev": "37df177aaa770670452312393d4e84aaad56e7b6", "name": "mathlib", "manifestFile": "lake-manifest.json", - "inputRev": "v4.23.0-rc2", + "inputRev": "v4.23.0", "inherited": false, "configFile": "lakefile.lean"}, {"url": "https://github.com/leanprover-community/plausible", "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "240eddc1bb31420fbbc57fe5cc579435c2522493", + "rev": "a22e7c1fa7707fb7ea75f2f9fd6b14de2b7b87a9", "name": "plausible", "manifestFile": "lake-manifest.json", "inputRev": "main",
  • @@ -35,7 +35,7 @@
    "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "dba7fbc707774d1ba830fd44d7f92a717e9bf57f", + "rev": "7fca1d4a190761bac0028848f73dc9a59fcb4957", "name": "importGraph", "manifestFile": "lake-manifest.json", "inputRev": "main",
  • @@ -55,7 +55,7 @@
    "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "523c8ee53f7057447fc62ec14e506fda4cf63dfa", + "rev": "247ff80701c76760523b5d7c180b27b7708faf38", "name": "aesop", "manifestFile": "lake-manifest.json", "inputRev": "master",
  • @@ -65,7 +65,7 @@
    "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "f85ad59c9b60647ef736719c23edd4578f723806", + "rev": "9b703a545097978aef0e7e243ab8b71c32a9ff65", "name": "Qq", "manifestFile": "lake-manifest.json", "inputRev": "master",
  • @@ -75,7 +75,7 @@
    "type": "git", "subDir": null, "scope": "leanprover-community", - "rev": "6e89c7370ca3a91b7d1f29ef7d727a9d027d7b0d", + "rev": "d117e2c28cba42e974bc22568ac999492a34e812", "name": "batteries", "manifestFile": "lake-manifest.json", "inputRev": "main",
  • @@ -85,7 +85,7 @@
    "type": "git", "subDir": null, "scope": "leanprover", - "rev": "cacb481a1eaa4d7d4530a27b606c60923da21caf", + "rev": "41c5d0b8814dec559e2e1441171db434fe2281cc", "name": "Cli", "manifestFile": "lake-manifest.json", "inputRev": "main",
• lakefile.toml
  • @@ -13,4 +13,4 @@ root = "Gcd"
    [[require]] name = "mathlib" scope = "leanprover-community" - rev = "v4.23.0-rc2" + rev = "v4.23.0"
• lean-toolchain
  • @@ -1,1 +1,1 @@
    - leanprover/lean4:v4.23.0-rc2 + leanprover/lean4:v4.23.0