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

@@ -51,7 +51,8 @@ theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k +
 theorem perfect_two_pow_hMul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
     Nat.Perfect (2 ^ k * mersenne (k + 1)) :=
   by
-  rw [Nat.perfect_iff_sum_divisors_eq_two_mul, ← mul_assoc, ← pow_succ, ← sigma_one_apply, mul_comm,
+  rw [Nat.perfect_iff_sum_divisors_eq_two_mul, ← mul_assoc, ← pow_succ', ← sigma_one_apply,
+    mul_comm,
     is_multiplicative_sigma.map_mul_of_coprime
       (nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)),
     sigma_two_pow_eq_mersenne_succ]
@@ -81,7 +82,7 @@ theorem eq_two_pow_hMul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k
   contrapose! hg
   rcases hg with ⟨k, rfl⟩
   apply Dvd.intro k
-  rw [pow_succ', mul_assoc, ← hm]
+  rw [pow_succ, mul_assoc, ← hm]
 #align theorems_100.nat.eq_two_pow_mul_odd Theorems100.Nat.eq_two_pow_hMul_odd
 
 /-- **Perfect Number Theorem**: Euler's theorem that even perfect numbers can be factored as a
@@ -95,7 +96,7 @@ theorem eq_two_pow_hMul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n)
   rw [even_iff_two_dvd] at hm
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     is_multiplicative_sigma.map_mul_of_coprime (nat.prime_two.coprime_pow_of_not_dvd hm).symm,
-    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
+    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ'] at perf
   rcases Nat.Coprime.dvd_of_dvd_mul_left
       (nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩

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

@@ -92,29 +92,29 @@ theorem eq_two_pow_hMul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n)
   have hpos := perf.2
   rcases eq_two_pow_mul_odd hpos with ⟨k, m, rfl, hm⟩
   use k
-  rw [even_iff_two_dvd] at hm 
+  rw [even_iff_two_dvd] at hm
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     is_multiplicative_sigma.map_mul_of_coprime (nat.prime_two.coprime_pow_of_not_dvd hm).symm,
-    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf 
+    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
   rcases Nat.Coprime.dvd_of_dvd_mul_left
       (nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩
-  rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf 
+  rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf
   have h := mul_left_cancel₀ (ne_of_gt (mersenne_pos (Nat.succ_pos _))) perf
   rw [sigma_one_apply, Nat.sum_divisors_eq_sum_properDivisors_add_self, ← succ_mersenne, add_mul,
-    one_mul, add_comm] at h 
+    one_mul, add_comm] at h
   have hj := add_left_cancel h
   cases Nat.sum_properDivisors_dvd (by rw [hj]; apply Dvd.intro_left (mersenne (k + 1)) rfl)
   · have j1 : j = 1 := Eq.trans hj.symm h_1
-    rw [j1, mul_one, Nat.sum_properDivisors_eq_one_iff_prime] at h_1 
+    rw [j1, mul_one, Nat.sum_properDivisors_eq_one_iff_prime] at h_1
     simp [h_1, j1]
   · have jcon := Eq.trans hj.symm h_1
-    rw [← one_mul j, ← mul_assoc, mul_one] at jcon 
+    rw [← one_mul j, ← mul_assoc, mul_one] at jcon
     have jcon2 := mul_right_cancel₀ _ jcon
     · exfalso
       cases k
       · apply hm
-        rw [← jcon2, pow_zero, one_mul, one_mul] at ev 
+        rw [← jcon2, pow_zero, one_mul, one_mul] at ev
         rw [← jcon2, one_mul]
         exact even_iff_two_dvd.mp ev
       apply ne_of_lt _ jcon2

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

@@ -39,7 +39,7 @@ theorem odd_mersenne_succ (k : ℕ) : ¬2 ∣ mersenne (k + 1) := by
 
 namespace Nat
 
-open Nat.ArithmeticFunction Finset
+open ArithmeticFunction Finset
 
 open scoped ArithmeticFunction
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathbin.NumberTheory.ArithmeticFunction
-import Mathbin.NumberTheory.LucasLehmer
-import Mathbin.Algebra.GeomSum
-import Mathbin.RingTheory.Multiplicity
+import NumberTheory.ArithmeticFunction
+import NumberTheory.LucasLehmer
+import Algebra.GeomSum
+import RingTheory.Multiplicity
 
 #align_import wiedijk_100_theorems.perfect_numbers from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

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

@@ -96,7 +96,7 @@ theorem eq_two_pow_hMul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n)
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     is_multiplicative_sigma.map_mul_of_coprime (nat.prime_two.coprime_pow_of_not_dvd hm).symm,
     sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf 
-  rcases Nat.coprime.dvd_of_dvd_mul_left
+  rcases Nat.Coprime.dvd_of_dvd_mul_left
       (nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩
   rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -48,7 +48,7 @@ theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k +
 #align theorems_100.nat.sigma_two_pow_eq_mersenne_succ Theorems100.Nat.sigma_two_pow_eq_mersenne_succ
 
 /-- Euclid's theorem that Mersenne primes induce perfect numbers -/
-theorem perfect_two_pow_mul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
+theorem perfect_two_pow_hMul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
     Nat.Perfect (2 ^ k * mersenne (k + 1)) :=
   by
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul, ← mul_assoc, ← pow_succ, ← sigma_one_apply, mul_comm,
@@ -58,7 +58,7 @@ theorem perfect_two_pow_mul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1))
   · simp [pr, Nat.prime_two, sigma_one_apply]
   · apply mul_pos (pow_pos _ k) (mersenne_pos (Nat.succ_pos k))
     norm_num
-#align theorems_100.nat.perfect_two_pow_mul_mersenne_of_prime Theorems100.Nat.perfect_two_pow_mul_mersenne_of_prime
+#align theorems_100.nat.perfect_two_pow_mul_mersenne_of_prime Theorems100.Nat.perfect_two_pow_hMul_mersenne_of_prime
 
 theorem ne_zero_of_prime_mersenne (k : ℕ) (pr : (mersenne (k + 1)).Prime) : k ≠ 0 :=
   by
@@ -66,11 +66,11 @@ theorem ne_zero_of_prime_mersenne (k : ℕ) (pr : (mersenne (k + 1)).Prime) : k
   simpa [H, mersenne, Nat.not_prime_one] using pr
 #align theorems_100.nat.ne_zero_of_prime_mersenne Theorems100.Nat.ne_zero_of_prime_mersenne
 
-theorem even_two_pow_mul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
+theorem even_two_pow_hMul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
     Even (2 ^ k * mersenne (k + 1)) := by simp [ne_zero_of_prime_mersenne k pr, parity_simps]
-#align theorems_100.nat.even_two_pow_mul_mersenne_of_prime Theorems100.Nat.even_two_pow_mul_mersenne_of_prime
+#align theorems_100.nat.even_two_pow_mul_mersenne_of_prime Theorems100.Nat.even_two_pow_hMul_mersenne_of_prime
 
-theorem eq_two_pow_mul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k * m ∧ ¬Even m :=
+theorem eq_two_pow_hMul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k * m ∧ ¬Even m :=
   by
   have h := multiplicity.finite_nat_iff.2 ⟨nat.prime_two.ne_one, hpos⟩
   cases' multiplicity.pow_multiplicity_dvd h with m hm
@@ -82,12 +82,12 @@ theorem eq_two_pow_mul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k *
   rcases hg with ⟨k, rfl⟩
   apply Dvd.intro k
   rw [pow_succ', mul_assoc, ← hm]
-#align theorems_100.nat.eq_two_pow_mul_odd Theorems100.Nat.eq_two_pow_mul_odd
+#align theorems_100.nat.eq_two_pow_mul_odd Theorems100.Nat.eq_two_pow_hMul_odd
 
 /-- **Perfect Number Theorem**: Euler's theorem that even perfect numbers can be factored as a
   power of two times a Mersenne prime. -/
-theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (perf : Nat.Perfect n) :
-    ∃ k : ℕ, Nat.Prime (mersenne (k + 1)) ∧ n = 2 ^ k * mersenne (k + 1) :=
+theorem eq_two_pow_hMul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n)
+    (perf : Nat.Perfect n) : ∃ k : ℕ, Nat.Prime (mersenne (k + 1)) ∧ n = 2 ^ k * mersenne (k + 1) :=
   by
   have hpos := perf.2
   rcases eq_two_pow_mul_odd hpos with ⟨k, m, rfl, hm⟩
@@ -122,7 +122,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
       apply pow_lt_pow (Nat.lt_succ_self 1) (Nat.succ_lt_succ (Nat.succ_pos k))
     contrapose! hm
     simp [hm]
-#align theorems_100.nat.eq_two_pow_mul_prime_mersenne_of_even_perfect Theorems100.Nat.eq_two_pow_mul_prime_mersenne_of_even_perfect
+#align theorems_100.nat.eq_two_pow_mul_prime_mersenne_of_even_perfect Theorems100.Nat.eq_two_pow_hMul_prime_mersenne_of_even_perfect
 
 /-- The Euclid-Euler theorem characterizing even perfect numbers -/
 theorem even_and_perfect_iff {n : ℕ} :

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -74,7 +74,7 @@ theorem eq_two_pow_mul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k *
   by
   have h := multiplicity.finite_nat_iff.2 ⟨nat.prime_two.ne_one, hpos⟩
   cases' multiplicity.pow_multiplicity_dvd h with m hm
-  use (multiplicity 2 n).get h, m
+  use(multiplicity 2 n).get h, m
   refine' ⟨hm, _⟩
   rw [even_iff_two_dvd]
   have hg := multiplicity.is_greatest' h (Nat.lt_succ_self _)

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.perfect_numbers
-! 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.NumberTheory.ArithmeticFunction
 import Mathbin.NumberTheory.LucasLehmer
 import Mathbin.Algebra.GeomSum
 import Mathbin.RingTheory.Multiplicity
 
+#align_import wiedijk_100_theorems.perfect_numbers from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # Perfect Numbers
 

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: Aaron Anderson
 
 ! This file was ported from Lean 3 source module wiedijk_100_theorems.perfect_numbers
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.Multiplicity
 /-!
 # Perfect Numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves Theorem 70 from the [100 Theorems List](https://www.cs.ru.nl/~freek/100/).
 
 The theorem characterizes even perfect numbers.

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

@@ -3,8 +3,8 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 
-! This file was ported from Lean 3 source module «100-theorems-list».«70_perfect_numbers»
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! This file was ported from Lean 3 source module wiedijk_100_theorems.perfect_numbers
+! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -47,7 +47,8 @@ theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k +
 /-- Euclid's theorem that Mersenne primes induce perfect numbers -/
 theorem perfect_two_pow_mul_mersenne_of_prime (k : ℕ) (pr : (mersenne (k + 1)).Prime) :
     Nat.Perfect (2 ^ k * mersenne (k + 1)) := by
-  rw [Nat.perfect_iff_sum_divisors_eq_two_mul, ← mul_assoc, ← pow_succ, ← sigma_one_apply, mul_comm,
+  rw [Nat.perfect_iff_sum_divisors_eq_two_mul, ← mul_assoc, ← pow_succ',
+    ← sigma_one_apply, mul_comm,
     isMultiplicative_sigma.map_mul_of_coprime
       (Nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)),
     sigma_two_pow_eq_mersenne_succ]
@@ -75,7 +76,7 @@ theorem eq_two_pow_mul_odd {n : ℕ} (hpos : 0 < n) : ∃ k m : ℕ, n = 2 ^ k *
   contrapose! hg
   rcases hg with ⟨k, rfl⟩
   apply Dvd.intro k
-  rw [pow_succ', mul_assoc, ← hm]
+  rw [pow_succ, mul_assoc, ← hm]
 #align theorems_100.nat.eq_two_pow_mul_odd Theorems100.Nat.eq_two_pow_mul_odd
 
 /-- **Perfect Number Theorem**: Euler's theorem that even perfect numbers can be factored as a
@@ -88,7 +89,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
   rw [even_iff_two_dvd] at hm
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     isMultiplicative_sigma.map_mul_of_coprime (Nat.prime_two.coprime_pow_of_not_dvd hm).symm,
-    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
+    sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ'] at perf
   rcases Nat.Coprime.dvd_of_dvd_mul_left
       (Nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -41,7 +41,7 @@ open ArithmeticFunction Finset
 
 theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k + 1) := by
   simp_rw [sigma_one_apply, mersenne, show 2 = 1 + 1 from rfl, ← geom_sum_mul_add 1 (k + 1)]
-  norm_num
+  set_option tactic.skipAssignedInstances false in norm_num
 #align theorems_100.nat.sigma_two_pow_eq_mersenne_succ Theorems100.Nat.sigma_two_pow_eq_mersenne_succ
 
 /-- Euclid's theorem that Mersenne primes induce perfect numbers -/

This changes Nat.ArithmeticFunction to ArithmeticFunction since the Nat part seems redundant.

See here on Zulip.

@@ -37,7 +37,7 @@ theorem odd_mersenne_succ (k : ℕ) : ¬2 ∣ mersenne (k + 1) := by
 
 namespace Nat
 
-open Nat.ArithmeticFunction Finset
+open ArithmeticFunction Finset
 
 theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k + 1) := by
   simp_rw [sigma_one_apply, mersenne, show 2 = 1 + 1 from rfl, ← geom_sum_mul_add 1 (k + 1)]

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -7,6 +7,7 @@ import Mathlib.NumberTheory.ArithmeticFunction
 import Mathlib.NumberTheory.LucasLehmer
 import Mathlib.Algebra.GeomSum
 import Mathlib.RingTheory.Multiplicity
+import Mathlib.Tactic.NormNum.Prime
 
 #align_import wiedijk_100_theorems.perfect_numbers from "leanprover-community/mathlib"@"5563b1b49e86e135e8c7b556da5ad2f5ff881cad"
 

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -115,7 +115,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
       | .succ k =>
         apply ne_of_lt _ jcon2
         rw [mersenne, ← Nat.pred_eq_sub_one, Nat.lt_pred_iff, ← pow_one (Nat.succ 1)]
-        apply pow_lt_pow (Nat.lt_succ_self 1) (Nat.succ_lt_succ (Nat.succ_pos k))
+        apply pow_lt_pow_right (Nat.lt_succ_self 1) (Nat.succ_lt_succ (Nat.succ_pos k))
     contrapose! hm
     simp [hm]
 #align theorems_100.nat.eq_two_pow_mul_prime_mersenne_of_even_perfect Theorems100.Nat.eq_two_pow_mul_prime_mersenne_of_even_perfect

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>

@@ -39,8 +39,8 @@ namespace Nat
 open Nat.ArithmeticFunction Finset
 
 theorem sigma_two_pow_eq_mersenne_succ (k : ℕ) : σ 1 (2 ^ k) = mersenne (k + 1) := by
-  simp [sigma_one_apply, mersenne, Nat.prime_two, show 2 = 1 + 1 from rfl,
-    ← geom_sum_mul_add 1 (k + 1)]
+  simp_rw [sigma_one_apply, mersenne, show 2 = 1 + 1 from rfl, ← geom_sum_mul_add 1 (k + 1)]
+  norm_num
 #align theorems_100.nat.sigma_two_pow_eq_mersenne_succ Theorems100.Nat.sigma_two_pow_eq_mersenne_succ
 
 /-- Euclid's theorem that Mersenne primes induce perfect numbers -/

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

@@ -88,7 +88,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     isMultiplicative_sigma.map_mul_of_coprime (Nat.prime_two.coprime_pow_of_not_dvd hm).symm,
     sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
-  rcases Nat.coprime.dvd_of_dvd_mul_left
+  rcases Nat.Coprime.dvd_of_dvd_mul_left
       (Nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩
   rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf

This reverts commit 6f8e8104. Unfortunately this bump was not linted correctly, as CI did not run runLinter Mathlib.

We can unrevert once that's fixed.

@@ -88,7 +88,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     isMultiplicative_sigma.map_mul_of_coprime (Nat.prime_two.coprime_pow_of_not_dvd hm).symm,
     sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
-  rcases Nat.Coprime.dvd_of_dvd_mul_left
+  rcases Nat.coprime.dvd_of_dvd_mul_left
       (Nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩
   rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf

Some changes have already been review and delegated in #6910 and #7148.

The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac

The std bump PR was insta-merged already!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -88,7 +88,7 @@ theorem eq_two_pow_mul_prime_mersenne_of_even_perfect {n : ℕ} (ev : Even n) (p
   rw [Nat.perfect_iff_sum_divisors_eq_two_mul hpos, ← sigma_one_apply,
     isMultiplicative_sigma.map_mul_of_coprime (Nat.prime_two.coprime_pow_of_not_dvd hm).symm,
     sigma_two_pow_eq_mersenne_succ, ← mul_assoc, ← pow_succ] at perf
-  rcases Nat.coprime.dvd_of_dvd_mul_left
+  rcases Nat.Coprime.dvd_of_dvd_mul_left
       (Nat.prime_two.coprime_pow_of_not_dvd (odd_mersenne_succ _)) (Dvd.intro _ perf) with
     ⟨j, rfl⟩
   rw [← mul_assoc, mul_comm _ (mersenne _), mul_assoc] at perf

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.perfect_numbers
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.ArithmeticFunction
 import Mathlib.NumberTheory.LucasLehmer
 import Mathlib.Algebra.GeomSum
 import Mathlib.RingTheory.Multiplicity
 
+#align_import wiedijk_100_theorems.perfect_numbers from "leanprover-community/mathlib"@"5563b1b49e86e135e8c7b556da5ad2f5ff881cad"
+
 /-!
 # Perfect Numbers