mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -51,7 +51,7 @@ theorem find_specified_factor {p : ℕ} (hp : Nat.Prime p) (hp' : IsCoprime (6 :
   have H : (6 : ℤ) * a (p - 2) ≡ 0 [ZMOD p]
   calc
     (6 : ℤ) * a (p - 2) = 3 * 2 ^ (p - 1) + 2 * 3 ^ (p - 1) + 6 ^ (p - 1) - 6 := by
-      simp only [a, mul_add, mul_sub, hp_sub_one, pow_succ]; ring
+      simp only [a, mul_add, mul_sub, hp_sub_one, pow_succ']; ring
     _ ≡ 3 * 1 + 2 * 1 + 1 - 6 [ZMOD p] :=-- At this step we use Fermat's little theorem
     by
       apply_rules [Int.ModEq.sub_right, Int.ModEq.add, Int.ModEq.mul_left,

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -99,7 +99,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
   -- So `3 ≤ p`
   have hp₃ : 3 ≤ p :=
     by
-    have : 2 ≠ p := by rwa [Nat.coprime_primes Nat.prime_two hp] at hp₂ 
+    have : 2 ≠ p := by rwa [Nat.coprime_primes Nat.prime_two hp] at hp₂
     apply Nat.lt_of_le_of_ne hp.two_le this
   -- Testing the special property of `k` for the `p - 2`th term of the sequence, we see that `p` is
   -- coprime to `a (p - 2)`.
@@ -107,7 +107,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
     by
     refine' ((h (p - 2) _).of_isCoprime_of_dvd_right (int.coe_nat_dvd.mpr k.min_fac_dvd)).symm
     exact le_tsub_of_add_le_right hp₃
-  rw [(nat.prime_iff_prime_int.mp hp).coprime_iff_not_dvd] at this 
+  rw [(nat.prime_iff_prime_int.mp hp).coprime_iff_not_dvd] at this
   -- But also, by our previous lemma, `p` divides `a (p - 2)`.
   have : ↑p ∣ a (p - 2) := find_specified_factor hp hp₆
   -- Contradiction!

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -100,7 +100,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
   have hp₃ : 3 ≤ p :=
     by
     have : 2 ≠ p := by rwa [Nat.coprime_primes Nat.prime_two hp] at hp₂ 
-    apply Nat.lt_of_le_and_ne hp.two_le this
+    apply Nat.lt_of_le_of_ne hp.two_le this
   -- Testing the special property of `k` for the `p - 2`th term of the sequence, we see that `p` is
   -- coprime to `a (p - 2)`.
   have : IsCoprime (↑p) (a (p - 2)) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,7 +3,7 @@ Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 -/
-import Mathbin.FieldTheory.Finite.Basic
+import FieldTheory.Finite.Basic
 
 #align_import imo.imo2005_q4 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -89,7 +89,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
     exact (id (h 2 one_le_two) : IsCoprime (8 * 6 : ℤ) k).of_mul_left_right
   -- In particular `p` is coprime to `2` (we record the `nat.coprime` version since that's what's
   -- needed later).
-  have hp₂ : Nat.coprime 2 p := by
+  have hp₂ : Nat.Coprime 2 p := by
     rw [← Nat.isCoprime_iff_coprime]
     exact (id hp₆ : IsCoprime (3 * 2 : ℤ) p).of_mul_left_right
   -- Suppose for the sake of contradiction that `k ≠ 1`.  Then `p` is genuinely a prime factor of

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module imo.imo2005_q4
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.FieldTheory.Finite.Basic
 
+#align_import imo.imo2005_q4 from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # IMO 2005 Q4
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module imo.imo2005_q4
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.FieldTheory.Finite.Basic
 /-!
 # IMO 2005 Q4
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Problem: Determine all positive integers relatively prime to all the terms of the infinite sequence
 `a n = 2 ^ n + 3 ^ n + 6 ^ n - 1`, for `n ≥ 1`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -57,7 +57,6 @@ theorem find_specified_factor {p : ℕ} (hp : Nat.Prime p) (hp' : IsCoprime (6 :
       apply_rules [Int.ModEq.sub_right, Int.ModEq.add, Int.ModEq.mul_left,
         Int.ModEq.pow_card_sub_one_eq_one hp]
     _ = 0 := by norm_num
-    
   -- Since `6` has an inverse mod `p`, `a (p - 2)` itself is a multiple of `p`
   calc
     (a (p - 2) : ℤ) = 1 * a (p - 2) := by ring
@@ -65,7 +64,6 @@ theorem find_specified_factor {p : ℕ} (hp : Nat.Prime p) (hp' : IsCoprime (6 :
     _ = b * (6 * a (p - 2)) := by ring
     _ ≡ b * 0 [ZMOD p] := (Int.ModEq.mul_left _ H)
     _ = 0 := by ring
-    
 #align imo2005_q4.find_specified_factor Imo2005Q4.find_specified_factor
 
 end imo2005_q4

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

Reduce the diff of #11499

Renames

All in the Int namespace:

• ofNat_eq_cast → ofNat_eq_natCast
• cast_eq_cast_iff_Nat → natCast_inj
• natCast_eq_ofNat → ofNat_eq_natCast
• coe_nat_sub → natCast_sub
• coe_nat_nonneg → natCast_nonneg
• sign_coe_add_one → sign_natCast_add_one
• nat_succ_eq_int_succ → natCast_succ
• succ_neg_nat_succ → succ_neg_natCast_succ
• coe_pred_of_pos → natCast_pred_of_pos
• coe_nat_div → natCast_div
• coe_nat_ediv → natCast_ediv
• sign_coe_nat_of_nonzero → sign_natCast_of_ne_zero
• toNat_coe_nat → toNat_natCast
• toNat_coe_nat_add_one → toNat_natCast_add_one
• coe_nat_dvd → natCast_dvd_natCast
• coe_nat_dvd_left → natCast_dvd
• coe_nat_dvd_right → dvd_natCast
• le_coe_nat_sub → le_natCast_sub
• succ_coe_nat_pos → succ_natCast_pos
• coe_nat_modEq_iff → natCast_modEq_iff
• coe_natAbs → natCast_natAbs
• coe_nat_eq_zero → natCast_eq_zero
• coe_nat_ne_zero → natCast_ne_zero
• coe_nat_ne_zero_iff_pos → natCast_ne_zero_iff_pos
• abs_coe_nat → abs_natCast
• coe_nat_nonpos_iff → natCast_nonpos_iff

Also rename Nat.coe_nat_dvd to Nat.cast_dvd_cast

@@ -66,7 +66,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
   have hp : Nat.Prime p := Nat.minFac_prime hk'
   replace h : ∀ n, 1 ≤ n → ¬(p : ℤ) ∣ a n := fun n hn ↦ by
     have : IsCoprime (a n) p :=
-      .of_isCoprime_of_dvd_right (h n hn) (Int.coe_nat_dvd.mpr k.minFac_dvd)
+      .of_isCoprime_of_dvd_right (h n hn) (Int.natCast_dvd_natCast.mpr k.minFac_dvd)
     rwa [isCoprime_comm,(Nat.prime_iff_prime_int.mp hp).coprime_iff_not_dvd] at this
   -- For `p = 2` and `p = 3`, take `n = 1` and `n = 2`, respectively
   by_cases hp2 : p = 2

@@ -29,7 +29,7 @@ def a (n : ℕ) : ℤ :=
 theorem find_specified_factor {p : ℕ} (hp : Nat.Prime p) (hp2 : p ≠ 2) (hp3 : p ≠ 3) :
     ↑p ∣ a (p - 2) := by
   -- Since `p` is neither `2` nor `3`, it is coprime with `2`, `3`, and `6`
-  rw [Ne.def, ← Nat.prime_dvd_prime_iff_eq hp (by decide), ← Nat.Prime.coprime_iff_not_dvd hp]
+  rw [Ne, ← Nat.prime_dvd_prime_iff_eq hp (by decide), ← Nat.Prime.coprime_iff_not_dvd hp]
     at hp2 hp3
   have : Int.gcd p 6 = 1 := Nat.coprime_mul_iff_right.2 ⟨hp2, hp3⟩
   -- Nat arithmetic needed to deal with powers

See Zulip thread for the discussion.

@@ -79,5 +79,5 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
   refine h (p - 2) ?_ (find_specified_factor hp hp2 hp3)
   calc
     1 = 3 - 2 := by norm_num
-    _ ≤ p - 2 := tsub_le_tsub_right (Nat.succ_le_of_lt $ hp.two_le.lt_of_ne' hp2) _
+    _ ≤ p - 2 := tsub_le_tsub_right (Nat.succ_le_of_lt <| hp.two_le.lt_of_ne' hp2) _
 #align imo2005_q4 imo2005_q4

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -29,7 +29,7 @@ def a (n : ℕ) : ℤ :=
 theorem find_specified_factor {p : ℕ} (hp : Nat.Prime p) (hp2 : p ≠ 2) (hp3 : p ≠ 3) :
     ↑p ∣ a (p - 2) := by
   -- Since `p` is neither `2` nor `3`, it is coprime with `2`, `3`, and `6`
-  rw [Ne.def, ← Nat.prime_dvd_prime_iff_eq hp (by norm_num), ← Nat.Prime.coprime_iff_not_dvd hp]
+  rw [Ne.def, ← Nat.prime_dvd_prime_iff_eq hp (by decide), ← Nat.Prime.coprime_iff_not_dvd hp]
     at hp2 hp3
   have : Int.gcd p 6 = 1 := Nat.coprime_mul_iff_right.2 ⟨hp2, hp3⟩
   -- Nat arithmetic needed to deal with powers
@@ -71,10 +71,10 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
   -- For `p = 2` and `p = 3`, take `n = 1` and `n = 2`, respectively
   by_cases hp2 : p = 2
   · rw [hp2] at h
-    apply h 1 <;> norm_num
+    apply h 1 <;> decide
   by_cases hp3 : p = 3
   · rw [hp3] at h
-    apply h 2 <;> norm_num
+    apply h 2 <;> decide
   -- Otherwise, take `n = p - 2`
   refine h (p - 2) ?_ (find_specified_factor hp hp2 hp3)
   calc

@@ -57,7 +57,7 @@ theorem imo2005_q4 {k : ℕ} (hk : 0 < k) : (∀ n : ℕ, 1 ≤ n → IsCoprime
     rintro rfl n -
     exact isCoprime_one_right
   intro h
-  -- Conversely, suppose `k` is a number with the property, and let `p` be `k.min_fac` (by
+  -- Conversely, suppose `k` is a number with the property, and let `p` be `k.minFac` (by
   -- definition this is the minimal prime factor of `k` if `k ≠ 1`, and otherwise `1`.
   let p := k.minFac
   -- Suppose for the sake of contradiction that `k ≠ 1`.  Then `p` is genuinely a prime factor of

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module imo.imo2005_q4
-! leanprover-community/mathlib commit 308826471968962c6b59c7ff82a22757386603e3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.FieldTheory.Finite.Basic
 
+#align_import imo.imo2005_q4 from "leanprover-community/mathlib"@"308826471968962c6b59c7ff82a22757386603e3"
+
 /-!
 # IMO 2005 Q4
 

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Johan Commelin <johan@commelin.net>