data.nat.prime | Mathlib porting status

(last sync)

refactor(data/nat/parity): reduce imports, add/delete lemmas (#18221)

Sync mathlib3 with API changes introduced while porting data.nat.parity to Mathlib 4 in leanprover-community/mathlib4#1661.

Add even.two_dvd, even.trans_dvd, has_dvd.dvd.even, odd.of_dvd_nat, and odd.ne_two_of_dvd_nat.
Rename nat.even_sub_one_of_prime_ne_two to nat.prime.even_sub_one, move to data.nat.prime.
Delete odd.factors_ne_two.
Replace is_primitive_root.pow_sub_one_norm_prime_pow_of_one_le with is_primitive_root.pow_sub_one_norm_prime_pow_of_ne_zero, assume ≠ 0 instead of 1 ≤.

Diff

@@ -447,6 +447,9 @@ by rw [even_iff_two_dvd, prime_dvd_prime_iff_eq prime_two hp, eq_comm]
 lemma prime.odd_of_ne_two {p : ℕ} (hp : p.prime) (h_two : p ≠ 2) : odd p :=
 hp.eq_two_or_odd'.resolve_left h_two
 
+lemma prime.even_sub_one {p : ℕ} (hp : p.prime) (h2 : p ≠ 2) : even (p - 1) :=
+let ⟨n, hn⟩ := hp.odd_of_ne_two h2 in ⟨n, by rw [hn, nat.add_sub_cancel, two_mul]⟩
+
 /-- A prime `p` satisfies `p % 2 = 1` if and only if `p ≠ 2`. -/
 lemma prime.mod_two_eq_one_iff_ne_two {p : ℕ} [fact p.prime] : p % 2 = 1 ↔ p ≠ 2 :=
 begin

(no changes)

412b1515

feat(group_theory/order_of_element): a condition on o(x) and o(y) that implies o(xy)=o(y) (#17997)

The main theorem is order_of_mul_eq_right_of_forall_prime_mul_dvd, which depends on order_of_dvd_lcm_mul, a variant of order_of_mul_dvd_lcm, and dvd_of_forall_prime_mul_dvd.
Also add lemmas factorization_prime_le_iff_dvd and factorization_lcm that were used in another approach towards the same theorem.

Co-authored-by: Oliver Nash <github@olivernash.org>

Diff

@@ -402,6 +402,14 @@ theorem exists_dvd_of_not_prime2 {n : ℕ} (n2 : 2 ≤ n) (np : ¬ prime n) :
 theorem exists_prime_and_dvd {n : ℕ} (hn : n ≠ 1) : ∃ p, prime p ∧ p ∣ n :=
 ⟨min_fac n, min_fac_prime hn, min_fac_dvd _⟩
 
+theorem dvd_of_forall_prime_mul_dvd {a b : ℕ}
+  (hdvd : ∀ p : ℕ, p.prime → p ∣ a → p * a ∣ b) : a ∣ b :=
+begin
+  obtain rfl | ha := eq_or_ne a 1, { apply one_dvd },
+  obtain ⟨p, hp⟩ := exists_prime_and_dvd ha,
+  exact trans (dvd_mul_left a p) (hdvd p hp.1 hp.2),
+end
+
 /-- Euclid's theorem on the **infinitude of primes**.
 Here given in the form: for every `n`, there exists a prime number `p ≥ n`. -/
 theorem exists_infinite_primes (n : ℕ) : ∃ p, n ≤ p ∧ prime p :=

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -799,7 +799,7 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     have pdvdxy : p ∣ x * y := by rw [h] <;> simp [sq]
     -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
     suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
-      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip; rw [and_comm']] <;> [skip;
+      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip; rw [and_comm]] <;> [skip;
             rw [mul_comm] at h pdvdxy] <;>
           apply this <;>
         assumption

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -9,7 +9,7 @@ import Data.Int.Dvd.Basic
 import Data.Int.Units
 import Data.Nat.Factorial.Basic
 import Data.Nat.GCD.Basic
-import Data.Nat.Sqrt
+import Data.Nat.Defs
 import Order.Bounds.Basic
 import Tactic.ByContra

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -8,7 +8,7 @@ import Algebra.Parity
 import Data.Int.Dvd.Basic
 import Data.Int.Units
 import Data.Nat.Factorial.Basic
-import Data.Nat.Gcd.Basic
+import Data.Nat.GCD.Basic
 import Data.Nat.Sqrt
 import Order.Bounds.Basic
 import Tactic.ByContra
@@ -120,7 +120,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (m «expr ∣ » p) -/
 #print Nat.prime_def_lt'' /-
 theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p :=
   by
@@ -734,7 +734,7 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
   by
   induction' n with n IH
   · exact pp.not_dvd_one.elim h
-  · rw [pow_succ] at h; exact (pp.dvd_mul.1 h).elim id IH
+  · rw [pow_succ'] at h; exact (pp.dvd_mul.1 h).elim id IH
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 -/
 
@@ -745,7 +745,7 @@ theorem Prime.not_prime_pow {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
     lt_irrefl x <|
       calc
         x = x ^ 1 := (pow_one _).symm
-        _ < x ^ n := (pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
+        _ < x ^ n := (Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
         _ = x := hxn.symm
 #align nat.prime.pow_not_prime Nat.Prime.not_prime_pow
 -/
@@ -917,12 +917,12 @@ theorem eq_one_iff_not_exists_prime_dvd {n : ℕ} : n = 1 ↔ ∀ p : ℕ, p.Pri
 theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {m n k l : ℕ}
     (hpm : p ^ k ∣ m) (hpn : p ^ l ∣ n) (hpmn : p ^ (k + l + 1) ∣ m * n) :
     p ^ (k + 1) ∣ m ∨ p ^ (l + 1) ∣ n :=
-  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ'] at hpmn
+  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ] at hpmn
   have hpd2 : p ∣ m * n / p ^ (k + l) := dvd_div_of_mul_dvd hpd
   have hpd3 : p ∣ m * n / (p ^ k * p ^ l) := by simpa [pow_add] using hpd2
   have hpd4 : p ∣ m / p ^ k * (n / p ^ l) := by simpa [Nat.div_mul_div_comm hpm hpn] using hpd3
   have hpd5 : p ∣ m / p ^ k ∨ p ∣ n / p ^ l := (Prime.dvd_mul p_prime).1 hpd4
-  suffices p ^ k * p ∣ m ∨ p ^ l * p ∣ n by rwa [pow_succ', pow_succ']
+  suffices p ^ k * p ∣ m ∨ p ^ l * p ∣ n by rwa [pow_succ, pow_succ]
   hpd5.elim (fun this : p ∣ m / p ^ k => Or.inl <| mul_dvd_of_dvd_div hpm this)
     fun this : p ∣ n / p ^ l => Or.inr <| mul_dvd_of_dvd_div hpn this
 #align nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
@@ -931,14 +931,14 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 #print Nat.prime_iff_prime_int /-
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>
-    ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
-      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h <;>
-        rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
+    ⟨Int.natCast_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
+      rw [← Int.dvd_natAbs, Int.natCast_dvd_natCast, Int.natAbs_mul, hp.dvd_mul] at h <;>
+        rwa [← Int.dvd_natAbs, Int.natCast_dvd_natCast, ← Int.dvd_natAbs, Int.natCast_dvd_natCast]⟩,
     fun hp =>
     Nat.prime_iff.2
-      ⟨Int.coe_nat_ne_zero.1 hp.1,
+      ⟨Int.natCast_ne_zero.1 hp.1,
         mt Nat.isUnit_iff.1 fun h => by simpa [h, not_prime_one] using hp, fun a b => by
-        simpa only [Int.coe_nat_dvd, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
+        simpa only [Int.natCast_dvd_natCast, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
 #align nat.prime_iff_prime_int Nat.prime_iff_prime_int
 -/

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -113,7 +113,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
   by
   obtain ⟨n, hn⟩ := hm
   have := pp.is_unit_or_is_unit hn
-  rw [Nat.isUnit_iff, Nat.isUnit_iff] at this 
+  rw [Nat.isUnit_iff, Nat.isUnit_iff] at this
   apply Or.imp_right _ this
   rintro rfl
   rw [hn, mul_one]
@@ -154,7 +154,7 @@ theorem prime_def_lt' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m → m <
         ⟨fun h m2 l d => not_lt_of_ge m2 ((h l d).symm ▸ by decide), fun h l d =>
           by
           rcases m with (_ | _ | m)
-          · rw [eq_zero_of_zero_dvd d] at p2 ; revert p2; exact by decide
+          · rw [eq_zero_of_zero_dvd d] at p2; revert p2; exact by decide
           · rfl
           · exact (h (by decide) l).elim d⟩
 #align nat.prime_def_lt' Nat.prime_def_lt'
@@ -170,7 +170,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
         fun m m2 l ⟨k, e⟩ => by
         cases' le_total m k with mk km
         · exact this mk m2 e
-        · rw [mul_comm] at e 
+        · rw [mul_comm] at e
           refine' this km (lt_of_mul_lt_mul_right _ (zero_le m)) e
           rwa [one_mul, ← e]⟩
 #align nat.prime_def_le_sqrt Nat.prime_def_le_sqrt
@@ -182,7 +182,7 @@ theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.Co
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
     rintro rfl
-    rw [zero_dvd_iff] at mdvd 
+    rw [zero_dvd_iff] at mdvd
     exact mlt.ne' mdvd
   exact (h m mlt hm).symm.eq_one_of_dvd mdvd
 #align nat.prime_of_coprime Nat.prime_of_coprime
@@ -375,9 +375,9 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
       cases' Nat.eq_or_lt_of_le (a m m2 d) with me ml
       · subst me; contradiction
       apply (Nat.eq_or_lt_of_le ml).resolve_left; intro me
-      rw [← me, e] at d ; change 2 * (i + 2) ∣ n at d 
+      rw [← me, e] at d; change 2 * (i + 2) ∣ n at d
       have := a _ le_rfl (dvd_of_mul_right_dvd d)
-      rw [e] at this ; exact absurd this (by decide)
+      rw [e] at this; exact absurd this (by decide)
 termination_by x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 -/
@@ -488,8 +488,8 @@ theorem minFac_le_div {n : ℕ} (pos : 0 < n) (np : ¬Prime n) : minFac n ≤ n
   match minFac_dvd n with
   | ⟨0, h0⟩ => absurd Pos <| by rw [h0, MulZeroClass.mul_zero] <;> exact by decide
   | ⟨1, h1⟩ => by
-    rw [mul_one] at h1 
-    rw [prime_def_min_fac, not_and_or, ← h1, eq_self_iff_true, not_true, or_false_iff, not_le] at np 
+    rw [mul_one] at h1
+    rw [prime_def_min_fac, not_and_or, ← h1, eq_self_iff_true, not_true, or_false_iff, not_le] at np
     rw [le_antisymm (le_of_lt_succ np) (succ_le_of_lt Pos), min_fac_one, Nat.div_one]
   | ⟨x + 2, hx⟩ =>
     by
@@ -521,7 +521,7 @@ theorem minFac_eq_one_iff {n : ℕ} : minFac n = 1 ↔ n = 1 :=
   · intro h
     by_contra hn
     have := min_fac_prime hn
-    rw [h] at this 
+    rw [h] at this
     exact not_prime_one this
   · rintro rfl; rfl
 #align nat.min_fac_eq_one_iff Nat.minFac_eq_one_iff
@@ -540,7 +540,7 @@ theorem minFac_eq_two_iff (n : ℕ) : minFac n = 2 ↔ 2 ∣ n :=
     have lb := min_fac_pos n
     apply ub.eq_or_lt.resolve_right fun h' => _
     have := le_antisymm (Nat.succ_le_of_lt lb) (lt_succ_iff.mp h')
-    rw [eq_comm, Nat.minFac_eq_one_iff] at this 
+    rw [eq_comm, Nat.minFac_eq_one_iff] at this
     subst this
     exact not_lt_of_le (le_of_dvd zero_lt_one h) one_lt_two
 #align nat.min_fac_eq_two_iff Nat.minFac_eq_two_iff
@@ -641,7 +641,7 @@ theorem Prime.even_sub_one {p : ℕ} (hp : p.Prime) (h2 : p ≠ 2) : Even (p - 1
 theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔ p ≠ 2 :=
   by
   refine' ⟨fun h hf => _, (Nat.Prime.eq_two_or_odd <| Fact.out p.prime).resolve_left⟩
-  rw [hf] at h 
+  rw [hf] at h
   simpa using h
 #align nat.prime.mod_two_eq_one_iff_ne_two Nat.Prime.mod_two_eq_one_iff_ne_two
 -/
@@ -734,7 +734,7 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
   by
   induction' n with n IH
   · exact pp.not_dvd_one.elim h
-  · rw [pow_succ] at h ; exact (pp.dvd_mul.1 h).elim id IH
+  · rw [pow_succ] at h; exact (pp.dvd_mul.1 h).elim id IH
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 -/
 
@@ -768,7 +768,7 @@ theorem Prime.eq_one_of_pow {x n : ℕ} (h : (x ^ n).Prime) : n = 1 :=
 theorem Prime.pow_eq_iff {p a k : ℕ} (hp : p.Prime) : a ^ k = p ↔ a = p ∧ k = 1 :=
   by
   refine' ⟨fun h => _, fun h => by rw [h.1, h.2, pow_one]⟩
-  rw [← h] at hp 
+  rw [← h] at hp
   rw [← h, hp.eq_one_of_pow, eq_self_iff_true, and_true_iff, pow_one]
 #align nat.prime.pow_eq_iff Nat.Prime.pow_eq_iff
 -/
@@ -800,12 +800,12 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
     suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
       obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip; rw [and_comm']] <;> [skip;
-            rw [mul_comm] at h pdvdxy ] <;>
+            rw [mul_comm] at h pdvdxy] <;>
           apply this <;>
         assumption
     clear! x y
     rintro x y hx hy h ⟨a, ha⟩
-    have hap : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h ⟩
+    have hap : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h⟩
     exact
       ((Nat.dvd_prime hp).1 hap).elim
         (fun _ => by
@@ -917,7 +917,7 @@ theorem eq_one_iff_not_exists_prime_dvd {n : ℕ} : n = 1 ↔ ∀ p : ℕ, p.Pri
 theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {m n k l : ℕ}
     (hpm : p ^ k ∣ m) (hpn : p ^ l ∣ n) (hpmn : p ^ (k + l + 1) ∣ m * n) :
     p ^ (k + 1) ∣ m ∨ p ^ (l + 1) ∣ n :=
-  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ'] at hpmn 
+  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ'] at hpmn
   have hpd2 : p ∣ m * n / p ^ (k + l) := dvd_div_of_mul_dvd hpd
   have hpd3 : p ∣ m * n / (p ^ k * p ^ l) := by simpa [pow_add] using hpd2
   have hpd4 : p ∣ m / p ^ k * (n / p ^ l) := by simpa [Nat.div_mul_div_comm hpm hpn] using hpd3
@@ -932,7 +932,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>
     ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
-      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h  <;>
+      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h <;>
         rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
     fun hp =>
     Nat.prime_iff.2

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -302,7 +302,7 @@ theorem minFac_lemma (n k : ℕ) (h : ¬n < k * k) : sqrt n - k < sqrt n + 2 - k
 #align nat.min_fac_lemma Nat.minFac_lemma
 -/
 
-/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
+/- ./././Mathport/Syntax/Translate/Command.lean:299:8: warning: using_well_founded used, estimated equivalent -/
 #print Nat.minFacAux /-
 /-- If `n < k * k`, then `min_fac_aux n k = n`, if `k | n`, then `min_fac_aux n k = k`.
   Otherwise, `min_fac_aux n k = min_fac_aux n (k+2)` using well-founded recursion.
@@ -315,8 +315,7 @@ def minFacAux (n : ℕ) : ℕ → ℕ
       else
         have := minFac_lemma n k h
         min_fac_aux (k + 2)
-termination_by
-  _ x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
+termination_by x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
 #align nat.min_fac_aux Nat.minFacAux
 -/
 
@@ -356,7 +355,7 @@ theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
 private def min_fac_prop (n k : ℕ) :=
   2 ≤ k ∧ k ∣ n ∧ ∀ m, 2 ≤ m → m ∣ n → k ≤ m
 
-/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
+/- ./././Mathport/Syntax/Translate/Command.lean:299:8: warning: using_well_founded used, estimated equivalent -/
 #print Nat.minFacAux_has_prop /-
 theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
     ∀ k i, k = 2 * i + 3 → (∀ m, 2 ≤ m → m ∣ n → k ≤ m) → MinFacProp n (minFacAux n k)
@@ -379,8 +378,7 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
       rw [← me, e] at d ; change 2 * (i + 2) ∣ n at d 
       have := a _ le_rfl (dvd_of_mul_right_dvd d)
       rw [e] at this ; exact absurd this (by decide)
-termination_by
-  _ x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
+termination_by x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 -/

bump to nightly-2023-12-23-06

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

b8c74971

Diff

@@ -302,6 +302,7 @@ theorem minFac_lemma (n k : ℕ) (h : ¬n < k * k) : sqrt n - k < sqrt n + 2 - k
 #align nat.min_fac_lemma Nat.minFac_lemma
 -/
 
+/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
 #print Nat.minFacAux /-
 /-- If `n < k * k`, then `min_fac_aux n k = n`, if `k | n`, then `min_fac_aux n k = k`.
   Otherwise, `min_fac_aux n k = min_fac_aux n (k+2)` using well-founded recursion.
@@ -314,7 +315,8 @@ def minFacAux (n : ℕ) : ℕ → ℕ
       else
         have := minFac_lemma n k h
         min_fac_aux (k + 2)
-termination_by' ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
+termination_by
+  _ x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
 #align nat.min_fac_aux Nat.minFacAux
 -/
 
@@ -354,6 +356,7 @@ theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
 private def min_fac_prop (n k : ℕ) :=
   2 ≤ k ∧ k ∣ n ∧ ∀ m, 2 ≤ m → m ∣ n → k ≤ m
 
+/- ./././Mathport/Syntax/Translate/Command.lean:298:8: warning: using_well_founded used, estimated equivalent -/
 #print Nat.minFacAux_has_prop /-
 theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
     ∀ k i, k = 2 * i + 3 → (∀ m, 2 ≤ m → m ∣ n → k ≤ m) → MinFacProp n (minFacAux n k)
@@ -376,7 +379,8 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
       rw [← me, e] at d ; change 2 * (i + 2) ∣ n at d 
       have := a _ le_rfl (dvd_of_mul_right_dvd d)
       rw [e] at this ; exact absurd this (by decide)
-termination_by' ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
+termination_by
+  _ x => WellFounded.wrap (measure_wf fun k => sqrt n + 2 - k) x
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 -/

bump to nightly-2023-12-20-06

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

058cd493

Diff

@@ -743,7 +743,7 @@ theorem Prime.not_prime_pow {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
     lt_irrefl x <|
       calc
         x = x ^ 1 := (pow_one _).symm
-        _ < x ^ n := (Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
+        _ < x ^ n := (pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
         _ = x := hxn.symm
 #align nat.prime.pow_not_prime Nat.Prime.not_prime_pow
 -/

bump to nightly-2023-12-06-06

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

d09917f6

Diff

@@ -217,7 +217,7 @@ theorem prime_three : Prime 3 := by decide
 #print Nat.Prime.five_le_of_ne_two_of_ne_three /-
 theorem Prime.five_le_of_ne_two_of_ne_three {p : ℕ} (hp : p.Prime) (h_two : p ≠ 2)
     (h_three : p ≠ 3) : 5 ≤ p := by
-  by_contra' h
+  by_contra! h
   revert h_two h_three hp
   decide!
 #align nat.prime.five_le_of_ne_two_of_ne_three Nat.Prime.five_le_of_ne_two_of_ne_three

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -736,8 +736,8 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 -/
 
-#print Nat.Prime.pow_not_prime /-
-theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun hp =>
+#print Nat.Prime.not_prime_pow /-
+theorem Prime.not_prime_pow {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun hp =>
   (hp.eq_one_or_self_of_dvd x <| dvd_trans ⟨x, sq _⟩ (pow_dvd_pow _ hn)).elim
     (fun hx1 => hp.ne_one <| hx1.symm ▸ one_pow _) fun hxn =>
     lt_irrefl x <|
@@ -745,20 +745,20 @@ theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
         x = x ^ 1 := (pow_one _).symm
         _ < x ^ n := (Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
         _ = x := hxn.symm
-#align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
+#align nat.prime.pow_not_prime Nat.Prime.not_prime_pow
 -/
 
-#print Nat.Prime.pow_not_prime' /-
-theorem Prime.pow_not_prime' {x : ℕ} : ∀ {n : ℕ}, n ≠ 1 → ¬(x ^ n).Prime
+#print Nat.Prime.not_prime_pow' /-
+theorem Prime.not_prime_pow' {x : ℕ} : ∀ {n : ℕ}, n ≠ 1 → ¬(x ^ n).Prime
   | 0 => fun _ => not_prime_one
   | 1 => fun h => (h rfl).elim
-  | n + 2 => fun _ => Prime.pow_not_prime le_add_self
-#align nat.prime.pow_not_prime' Nat.Prime.pow_not_prime'
+  | n + 2 => fun _ => Prime.not_prime_pow le_add_self
+#align nat.prime.pow_not_prime' Nat.Prime.not_prime_pow'
 -/
 
 #print Nat.Prime.eq_one_of_pow /-
 theorem Prime.eq_one_of_pow {x n : ℕ} (h : (x ^ n).Prime) : n = 1 :=
-  not_imp_not.mp Prime.pow_not_prime' h
+  not_imp_not.mp Prime.not_prime_pow' h
 #align nat.prime.eq_one_of_pow Nat.Prime.eq_one_of_pow
 -/

bump to nightly-2023-11-06-06

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

f9f7c90b

Diff

@@ -855,7 +855,7 @@ theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p
 
 #print Nat.coprime_of_lt_prime /-
 theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
-  (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
+  (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_asymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 -/

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -431,7 +431,7 @@ theorem le_minFac {m n : ℕ} : n = 1 ∨ m ≤ minFac n ↔ ∀ p, Prime p →
   ⟨fun h p pp d =>
     h.elim (by rintro rfl <;> cases pp.not_dvd_one d) fun h =>
       le_trans h <| minFac_le_of_dvd pp.two_le d,
-    fun H => or_iff_not_imp_left.2 fun n1 => H _ (minFac_prime n1) (minFac_dvd _)⟩
+    fun H => Classical.or_iff_not_imp_left.2 fun n1 => H _ (minFac_prime n1) (minFac_dvd _)⟩
 #align nat.le_min_fac Nat.le_minFac
 -/
 
@@ -697,7 +697,8 @@ theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬Coprime m n ↔ ∃ p, Prime p
 
 #print Nat.Prime.dvd_mul /-
 theorem Prime.dvd_mul {p m n : ℕ} (pp : Prime p) : p ∣ m * n ↔ p ∣ m ∨ p ∣ n :=
-  ⟨fun H => or_iff_not_imp_left.2 fun h => (pp.coprime_iff_not_dvd.2 h).dvd_of_dvd_mul_left H,
+  ⟨fun H =>
+    Classical.or_iff_not_imp_left.2 fun h => (pp.coprime_iff_not_dvd.2 h).dvd_of_dvd_mul_left H,
     Or.ndrec (fun h : p ∣ m => h.hMul_right _) fun h : p ∣ n => h.hMul_left _⟩
 #align nat.prime.dvd_mul Nat.Prime.dvd_mul
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,15 +3,15 @@ Copyright (c) 2015 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
-import Mathbin.Algebra.Associated
-import Mathbin.Algebra.Parity
-import Mathbin.Data.Int.Dvd.Basic
-import Mathbin.Data.Int.Units
-import Mathbin.Data.Nat.Factorial.Basic
-import Mathbin.Data.Nat.Gcd.Basic
-import Mathbin.Data.Nat.Sqrt
-import Mathbin.Order.Bounds.Basic
-import Mathbin.Tactic.ByContra
+import Algebra.Associated
+import Algebra.Parity
+import Data.Int.Dvd.Basic
+import Data.Int.Units
+import Data.Nat.Factorial.Basic
+import Data.Nat.Gcd.Basic
+import Data.Nat.Sqrt
+import Order.Bounds.Basic
+import Tactic.ByContra
 
 #align_import data.nat.prime from "leanprover-community/mathlib"@"8631e2d5ea77f6c13054d9151d82b83069680cb1"
 
@@ -120,7 +120,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ∣ » p) -/
 #print Nat.prime_def_lt'' /-
 theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p :=
   by

bump to nightly-2023-09-20-06

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

e28e6964

Diff

@@ -177,7 +177,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
 -/
 
 #print Nat.prime_of_coprime /-
-theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.coprime m) : Prime n :=
+theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.Coprime m) : Prime n :=
   by
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
@@ -645,7 +645,7 @@ theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔
 -/
 
 #print Nat.coprime_of_dvd /-
-theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : coprime m n :=
+theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : Coprime m n :=
   by
   rw [coprime_iff_gcd_eq_one]
   by_contra g2
@@ -657,7 +657,7 @@ theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n
 -/
 
 #print Nat.coprime_of_dvd' /-
-theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : coprime m n :=
+theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : Coprime m n :=
   coprime_of_dvd fun k kp km kn => not_le_of_gt kp.one_lt <| le_of_dvd zero_lt_one <| H k kp km kn
 #align nat.coprime_of_dvd' Nat.coprime_of_dvd'
 -/
@@ -669,20 +669,20 @@ theorem factors_lemma {k} : (k + 2) / minFac (k + 2) < k + 2 :=
 -/
 
 #print Nat.Prime.coprime_iff_not_dvd /-
-theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : coprime p n ↔ ¬p ∣ n :=
+theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : Coprime p n ↔ ¬p ∣ n :=
   ⟨fun co d => pp.not_dvd_one <| co.dvd_of_dvd_mul_left (by simp [d]), fun nd =>
     coprime_of_dvd fun m m2 mp => ((prime_dvd_prime_iff_eq m2 pp).1 mp).symm ▸ nd⟩
 #align nat.prime.coprime_iff_not_dvd Nat.Prime.coprime_iff_not_dvd
 -/
 
 #print Nat.Prime.dvd_iff_not_coprime /-
-theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬coprime p n :=
+theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬Coprime p n :=
   iff_not_comm.2 pp.coprime_iff_not_dvd
 #align nat.prime.dvd_iff_not_coprime Nat.Prime.dvd_iff_not_coprime
 -/
 
 #print Nat.Prime.not_coprime_iff_dvd /-
-theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n :=
+theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬Coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n :=
   by
   apply Iff.intro
   · intro h
@@ -828,39 +828,39 @@ theorem Prime.dvd_factorial : ∀ {n p : ℕ} (hp : Prime p), p ∣ n ! ↔ p 
 -/
 
 #print Nat.Prime.coprime_pow_of_not_dvd /-
-theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : coprime a (p ^ m) :=
+theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : Coprime a (p ^ m) :=
   (pp.coprime_iff_not_dvd.2 h).symm.pow_right _
 #align nat.prime.coprime_pow_of_not_dvd Nat.Prime.coprime_pow_of_not_dvd
 -/
 
 #print Nat.coprime_primes /-
-theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : coprime p q ↔ p ≠ q :=
+theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : Coprime p q ↔ p ≠ q :=
   pp.coprime_iff_not_dvd.trans <| not_congr <| dvd_prime_two_le pq pp.two_le
 #align nat.coprime_primes Nat.coprime_primes
 -/
 
 #print Nat.coprime_pow_primes /-
 theorem coprime_pow_primes {p q : ℕ} (n m : ℕ) (pp : Prime p) (pq : Prime q) (h : p ≠ q) :
-    coprime (p ^ n) (q ^ m) :=
+    Coprime (p ^ n) (q ^ m) :=
   ((coprime_primes pp pq).2 h).pow _ _
 #align nat.coprime_pow_primes Nat.coprime_pow_primes
 -/
 
 #print Nat.coprime_or_dvd_of_prime /-
-theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : coprime p i ∨ p ∣ i := by
+theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p ∣ i := by
   rw [pp.dvd_iff_not_coprime] <;> apply em
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 -/
 
 #print Nat.coprime_of_lt_prime /-
-theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : coprime p n :=
+theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
   (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 -/
 
 #print Nat.eq_or_coprime_of_le_prime /-
 theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Prime p) :
-    p = n ∨ coprime p n :=
+    p = n ∨ Coprime p n :=
   hle.eq_or_lt.imp Eq.symm fun h => coprime_of_lt_prime n_pos h pp
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 -/
@@ -874,7 +874,7 @@ theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃
 #print Nat.Prime.dvd_mul_of_dvd_ne /-
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)
     (h1 : p1 ∣ n) (h2 : p2 ∣ n) : p1 * p2 ∣ n :=
-  coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
+  Coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
 #align nat.prime.dvd_mul_of_dvd_ne Nat.Prime.dvd_mul_of_dvd_ne
 -/

bump to nightly-2023-08-23-23

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

f612b9e0

Diff

@@ -714,7 +714,7 @@ theorem prime_iff {p : ℕ} : p.Prime ↔ Prime p :=
 #align nat.prime_iff Nat.prime_iff
 -/
 
-alias prime_iff ↔ prime.prime _root_.prime.nat_prime
+alias ⟨prime.prime, _root_.prime.nat_prime⟩ := prime_iff
 #align nat.prime.prime Nat.Prime.prime
 #align prime.nat_prime Prime.nat_prime

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -698,7 +698,7 @@ theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬coprime m n ↔ ∃ p, Prime p
 #print Nat.Prime.dvd_mul /-
 theorem Prime.dvd_mul {p m n : ℕ} (pp : Prime p) : p ∣ m * n ↔ p ∣ m ∨ p ∣ n :=
   ⟨fun H => or_iff_not_imp_left.2 fun h => (pp.coprime_iff_not_dvd.2 h).dvd_of_dvd_mul_left H,
-    Or.ndrec (fun h : p ∣ m => h.mul_right _) fun h : p ∣ n => h.mul_left _⟩
+    Or.ndrec (fun h : p ∣ m => h.hMul_right _) fun h : p ∣ n => h.hMul_left _⟩
 #align nat.prime.dvd_mul Nat.Prime.dvd_mul
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2015 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.nat.prime
-! leanprover-community/mathlib commit 8631e2d5ea77f6c13054d9151d82b83069680cb1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Associated
 import Mathbin.Algebra.Parity
@@ -18,6 +13,8 @@ import Mathbin.Data.Nat.Sqrt
 import Mathbin.Order.Bounds.Basic
 import Mathbin.Tactic.ByContra
 
+#align_import data.nat.prime from "leanprover-community/mathlib"@"8631e2d5ea77f6c13054d9151d82b83069680cb1"
+
 /-!
 # Prime numbers
 
@@ -123,7 +120,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ∣ » p) -/
 #print Nat.prime_def_lt'' /-
 theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p :=
   by

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -344,6 +344,7 @@ theorem minFac_one : minFac 1 = 1 :=
 #align nat.min_fac_one Nat.minFac_one
 -/
 
+#print Nat.minFac_eq /-
 theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
   | 0 => by simp
   | 1 => by simp [show 2 ≠ 1 by decide] <;> rw [min_fac_aux] <;> rfl
@@ -351,6 +352,7 @@ theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
     have : 2 ∣ n + 2 ↔ 2 ∣ n := (Nat.dvd_add_iff_left (by rfl)).symm
     simp [min_fac, this] <;> congr
 #align nat.min_fac_eq Nat.minFac_eq
+-/
 
 private def min_fac_prop (n k : ℕ) :=
   2 ≤ k ∧ k ∣ n ∧ ∀ m, 2 ≤ m → m ∣ n → k ≤ m
@@ -866,9 +868,11 @@ theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Pr
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 -/
 
+#print Nat.dvd_prime_pow /-
 theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃ k ≤ m, i = p ^ k := by
   simp_rw [dvd_prime_pow (prime_iff.mp pp) m, associated_eq_eq]
 #align nat.dvd_prime_pow Nat.dvd_prime_pow
+-/
 
 #print Nat.Prime.dvd_mul_of_dvd_ne /-
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)
@@ -924,6 +928,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 #align nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
 -/
 
+#print Nat.prime_iff_prime_int /-
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>
     ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
@@ -935,6 +940,7 @@ theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
         mt Nat.isUnit_iff.1 fun h => by simpa [h, not_prime_one] using hp, fun a b => by
         simpa only [Int.coe_nat_dvd, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
 #align nat.prime_iff_prime_int Nat.prime_iff_prime_int
+-/
 
 #print Nat.Primes /-
 /-- The type of prime numbers -/
@@ -1000,13 +1006,17 @@ end Nat
 
 namespace Int
 
+#print Int.prime_two /-
 theorem prime_two : Prime (2 : ℤ) :=
   Nat.prime_iff_prime_int.mp Nat.prime_two
 #align int.prime_two Int.prime_two
+-/
 
+#print Int.prime_three /-
 theorem prime_three : Prime (3 : ℤ) :=
   Nat.prime_iff_prime_int.mp Nat.prime_three
 #align int.prime_three Int.prime_three
+-/
 
 end Int

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -509,7 +509,6 @@ theorem minFac_sq_le_self {n : ℕ} (w : 0 < n) (h : ¬Prime n) : minFac n ^ 2 
     minFac n ^ 2 = minFac n * minFac n := sq (minFac n)
     _ ≤ n / minFac n * minFac n := (Nat.mul_le_mul_right (minFac n) t)
     _ ≤ n := div_mul_le_self n (minFac n)
-    
 #align nat.min_fac_sq_le_self Nat.minFac_sq_le_self
 -/
 
@@ -746,7 +745,6 @@ theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
         x = x ^ 1 := (pow_one _).symm
         _ < x ^ n := (Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
         _ = x := hxn.symm
-        
 #align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
 -/

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -123,7 +123,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m «expr ∣ » p) -/
 #print Nat.prime_def_lt'' /-
 theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p :=
   by

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -595,7 +595,7 @@ theorem exists_infinite_primes (n : ℕ) : ∃ p, n ≤ p ∧ Prime p :=
 
 #print Nat.not_bddAbove_setOf_prime /-
 /-- A version of `nat.exists_infinite_primes` using the `bdd_above` predicate. -/
-theorem not_bddAbove_setOf_prime : ¬BddAbove { p | Prime p } :=
+theorem not_bddAbove_setOf_prime : ¬BddAbove {p | Prime p} :=
   by
   rw [not_bddAbove_iff]
   intro n

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -116,7 +116,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
   by
   obtain ⟨n, hn⟩ := hm
   have := pp.is_unit_or_is_unit hn
-  rw [Nat.isUnit_iff, Nat.isUnit_iff] at this
+  rw [Nat.isUnit_iff, Nat.isUnit_iff] at this 
   apply Or.imp_right _ this
   rintro rfl
   rw [hn, mul_one]
@@ -157,7 +157,7 @@ theorem prime_def_lt' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m → m <
         ⟨fun h m2 l d => not_lt_of_ge m2 ((h l d).symm ▸ by decide), fun h l d =>
           by
           rcases m with (_ | _ | m)
-          · rw [eq_zero_of_zero_dvd d] at p2; revert p2; exact by decide
+          · rw [eq_zero_of_zero_dvd d] at p2 ; revert p2; exact by decide
           · rfl
           · exact (h (by decide) l).elim d⟩
 #align nat.prime_def_lt' Nat.prime_def_lt'
@@ -173,7 +173,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
         fun m m2 l ⟨k, e⟩ => by
         cases' le_total m k with mk km
         · exact this mk m2 e
-        · rw [mul_comm] at e
+        · rw [mul_comm] at e 
           refine' this km (lt_of_mul_lt_mul_right _ (zero_le m)) e
           rwa [one_mul, ← e]⟩
 #align nat.prime_def_le_sqrt Nat.prime_def_le_sqrt
@@ -185,7 +185,7 @@ theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.co
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
     rintro rfl
-    rw [zero_dvd_iff] at mdvd
+    rw [zero_dvd_iff] at mdvd 
     exact mlt.ne' mdvd
   exact (h m mlt hm).symm.eq_one_of_dvd mdvd
 #align nat.prime_of_coprime Nat.prime_of_coprime
@@ -290,7 +290,7 @@ theorem Prime.dvd_iff_eq {p a : ℕ} (hp : p.Prime) (a1 : a ≠ 1) : a ∣ p ↔
   refine' ⟨_, by rintro rfl; rfl⟩
   -- rintro ⟨j, rfl⟩ does not work, due to `nat.prime` depending on the class `irreducible`
   rintro ⟨j, hj⟩
-  rw [hj] at hp⊢
+  rw [hj] at hp ⊢
   rcases prime_mul_iff.mp hp with (⟨h, rfl⟩ | ⟨h, rfl⟩)
   · exact mul_one _
   · exact (a1 rfl).elim
@@ -316,8 +316,8 @@ def minFacAux (n : ℕ) : ℕ → ℕ
       if k ∣ n then k
       else
         have := minFac_lemma n k h
-        min_fac_aux (k + 2)termination_by'
-  ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
+        min_fac_aux (k + 2)
+termination_by' ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
 #align nat.min_fac_aux Nat.minFacAux
 -/
 
@@ -374,10 +374,10 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
       cases' Nat.eq_or_lt_of_le (a m m2 d) with me ml
       · subst me; contradiction
       apply (Nat.eq_or_lt_of_le ml).resolve_left; intro me
-      rw [← me, e] at d; change 2 * (i + 2) ∣ n at d
+      rw [← me, e] at d ; change 2 * (i + 2) ∣ n at d 
       have := a _ le_rfl (dvd_of_mul_right_dvd d)
-      rw [e] at this; exact absurd this (by decide)termination_by'
-  ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
+      rw [e] at this ; exact absurd this (by decide)
+termination_by' ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 -/
 
@@ -410,14 +410,14 @@ theorem minFac_prime {n : ℕ} (n1 : n ≠ 1) : Prime (minFac n) :=
 
 #print Nat.minFac_le_of_dvd /-
 theorem minFac_le_of_dvd {n : ℕ} : ∀ {m : ℕ}, 2 ≤ m → m ∣ n → minFac n ≤ m := by
-  by_cases n1 : n = 1 <;>
-    [exact fun m m2 d => n1.symm ▸ le_trans (by decide) m2;exact (min_fac_has_prop n1).2.2]
+  by_cases n1 : n = 1 <;> [exact fun m m2 d => n1.symm ▸ le_trans (by decide) m2;
+    exact (min_fac_has_prop n1).2.2]
 #align nat.min_fac_le_of_dvd Nat.minFac_le_of_dvd
 -/
 
 #print Nat.minFac_pos /-
 theorem minFac_pos (n : ℕ) : 0 < minFac n := by
-  by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide;exact (min_fac_prime n1).Pos]
+  by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide; exact (min_fac_prime n1).Pos]
 #align nat.min_fac_pos Nat.minFac_pos
 -/
 
@@ -487,8 +487,8 @@ theorem minFac_le_div {n : ℕ} (pos : 0 < n) (np : ¬Prime n) : minFac n ≤ n
   match minFac_dvd n with
   | ⟨0, h0⟩ => absurd Pos <| by rw [h0, MulZeroClass.mul_zero] <;> exact by decide
   | ⟨1, h1⟩ => by
-    rw [mul_one] at h1
-    rw [prime_def_min_fac, not_and_or, ← h1, eq_self_iff_true, not_true, or_false_iff, not_le] at np
+    rw [mul_one] at h1 
+    rw [prime_def_min_fac, not_and_or, ← h1, eq_self_iff_true, not_true, or_false_iff, not_le] at np 
     rw [le_antisymm (le_of_lt_succ np) (succ_le_of_lt Pos), min_fac_one, Nat.div_one]
   | ⟨x + 2, hx⟩ =>
     by
@@ -521,7 +521,7 @@ theorem minFac_eq_one_iff {n : ℕ} : minFac n = 1 ↔ n = 1 :=
   · intro h
     by_contra hn
     have := min_fac_prime hn
-    rw [h] at this
+    rw [h] at this 
     exact not_prime_one this
   · rintro rfl; rfl
 #align nat.min_fac_eq_one_iff Nat.minFac_eq_one_iff
@@ -540,7 +540,7 @@ theorem minFac_eq_two_iff (n : ℕ) : minFac n = 2 ↔ 2 ∣ n :=
     have lb := min_fac_pos n
     apply ub.eq_or_lt.resolve_right fun h' => _
     have := le_antisymm (Nat.succ_le_of_lt lb) (lt_succ_iff.mp h')
-    rw [eq_comm, Nat.minFac_eq_one_iff] at this
+    rw [eq_comm, Nat.minFac_eq_one_iff] at this 
     subst this
     exact not_lt_of_le (le_of_dvd zero_lt_one h) one_lt_two
 #align nat.min_fac_eq_two_iff Nat.minFac_eq_two_iff
@@ -641,7 +641,7 @@ theorem Prime.even_sub_one {p : ℕ} (hp : p.Prime) (h2 : p ≠ 2) : Even (p - 1
 theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔ p ≠ 2 :=
   by
   refine' ⟨fun h hf => _, (Nat.Prime.eq_two_or_odd <| Fact.out p.prime).resolve_left⟩
-  rw [hf] at h
+  rw [hf] at h 
   simpa using h
 #align nat.prime.mod_two_eq_one_iff_ne_two Nat.Prime.mod_two_eq_one_iff_ne_two
 -/
@@ -733,7 +733,7 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
   by
   induction' n with n IH
   · exact pp.not_dvd_one.elim h
-  · rw [pow_succ] at h; exact (pp.dvd_mul.1 h).elim id IH
+  · rw [pow_succ] at h ; exact (pp.dvd_mul.1 h).elim id IH
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 -/
 
@@ -768,7 +768,7 @@ theorem Prime.eq_one_of_pow {x n : ℕ} (h : (x ^ n).Prime) : n = 1 :=
 theorem Prime.pow_eq_iff {p a k : ℕ} (hp : p.Prime) : a ^ k = p ↔ a = p ∧ k = 1 :=
   by
   refine' ⟨fun h => _, fun h => by rw [h.1, h.2, pow_one]⟩
-  rw [← h] at hp
+  rw [← h] at hp 
   rw [← h, hp.eq_one_of_pow, eq_self_iff_true, and_true_iff, pow_one]
 #align nat.prime.pow_eq_iff Nat.Prime.pow_eq_iff
 -/
@@ -799,13 +799,13 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     have pdvdxy : p ∣ x * y := by rw [h] <;> simp [sq]
     -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
     suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
-      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip;rw [and_comm']] <;>
-            [skip;rw [mul_comm] at h pdvdxy] <;>
+      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip; rw [and_comm']] <;> [skip;
+            rw [mul_comm] at h pdvdxy ] <;>
           apply this <;>
         assumption
     clear! x y
     rintro x y hx hy h ⟨a, ha⟩
-    have hap : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h⟩
+    have hap : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h ⟩
     exact
       ((Nat.dvd_prime hp).1 hap).elim
         (fun _ => by
@@ -915,7 +915,7 @@ theorem eq_one_iff_not_exists_prime_dvd {n : ℕ} : n = 1 ↔ ∀ p : ℕ, p.Pri
 theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {m n k l : ℕ}
     (hpm : p ^ k ∣ m) (hpn : p ^ l ∣ n) (hpmn : p ^ (k + l + 1) ∣ m * n) :
     p ^ (k + 1) ∣ m ∨ p ^ (l + 1) ∣ n :=
-  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ'] at hpmn
+  have hpd : p ^ (k + l) * p ∣ m * n := by rwa [pow_succ'] at hpmn 
   have hpd2 : p ∣ m * n / p ^ (k + l) := dvd_div_of_mul_dvd hpd
   have hpd3 : p ∣ m * n / (p ^ k * p ^ l) := by simpa [pow_add] using hpd2
   have hpd4 : p ∣ m / p ^ k * (n / p ^ l) := by simpa [Nat.div_mul_div_comm hpm hpn] using hpd3
@@ -929,7 +929,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>
     ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
-      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h <;>
+      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h  <;>
         rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
     fun hp =>
     Nat.prime_iff.2

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -42,7 +42,7 @@ This file deals with prime numbers: natural numbers `p ≥ 2` whose only divisor
 
 open Bool Subtype
 
-open Nat
+open scoped Nat
 
 namespace Nat

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -344,12 +344,6 @@ theorem minFac_one : minFac 1 = 1 :=
 #align nat.min_fac_one Nat.minFac_one
 -/
 
-/- warning: nat.min_fac_eq -> Nat.minFac_eq is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{1} Nat (Nat.minFac n) (ite.{1} Nat (Dvd.Dvd.{0} Nat Nat.hasDvd (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (Nat.decidableDvd (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Nat.minFacAux n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
-but is expected to have type
-  forall (n : Nat), Eq.{1} Nat (Nat.minFac n) (ite.{1} Nat (Dvd.dvd.{0} Nat Nat.instDvdNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (Nat.decidable_dvd (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.minFacAux n (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))))
-Case conversion may be inaccurate. Consider using '#align nat.min_fac_eq Nat.minFac_eqₓ'. -/
 theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
   | 0 => by simp
   | 1 => by simp [show 2 ≠ 1 by decide] <;> rw [min_fac_aux] <;> rfl
@@ -874,12 +868,6 @@ theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Pr
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 -/
 
-/- warning: nat.dvd_prime_pow -> Nat.dvd_prime_pow is a dubious translation:
-lean 3 declaration is
-  forall {p : Nat}, (Nat.Prime p) -> (forall {m : Nat} {i : Nat}, Iff (Dvd.Dvd.{0} Nat Nat.hasDvd i (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p m)) (Exists.{1} Nat (fun (k : Nat) => Exists.{0} (LE.le.{0} Nat Nat.hasLe k m) (fun (H : LE.le.{0} Nat Nat.hasLe k m) => Eq.{1} Nat i (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) p k)))))
-but is expected to have type
-  forall {p : Nat}, (Nat.Prime p) -> (forall {m : Nat} {i : Nat}, Iff (Dvd.dvd.{0} Nat Nat.instDvdNat i (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p m)) (Exists.{1} Nat (fun (k : Nat) => And (LE.le.{0} Nat instLENat k m) (Eq.{1} Nat i (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) p k)))))
-Case conversion may be inaccurate. Consider using '#align nat.dvd_prime_pow Nat.dvd_prime_powₓ'. -/
 theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃ k ≤ m, i = p ^ k := by
   simp_rw [dvd_prime_pow (prime_iff.mp pp) m, associated_eq_eq]
 #align nat.dvd_prime_pow Nat.dvd_prime_pow
@@ -938,12 +926,6 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 #align nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul
 -/
 
-/- warning: nat.prime_iff_prime_int -> Nat.prime_iff_prime_int is a dubious translation:
-lean 3 declaration is
-  forall {p : Nat}, Iff (Nat.Prime p) (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p))
-but is expected to have type
-  forall {p : Nat}, Iff (Nat.Prime p) (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.instCommSemiringInt) (Nat.cast.{0} Int instNatCastInt p))
-Case conversion may be inaccurate. Consider using '#align nat.prime_iff_prime_int Nat.prime_iff_prime_intₓ'. -/
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>
     ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.Pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
@@ -1020,22 +1002,10 @@ end Nat
 
 namespace Int
 
-/- warning: int.prime_two -> Int.prime_two is a dubious translation:
-lean 3 declaration is
-  Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) (OfNat.ofNat.{0} Int 2 (OfNat.mk.{0} Int 2 (bit0.{0} Int Int.hasAdd (One.one.{0} Int Int.hasOne))))
-but is expected to have type
-  Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.instCommSemiringInt) (OfNat.ofNat.{0} Int 2 (instOfNatInt 2))
-Case conversion may be inaccurate. Consider using '#align int.prime_two Int.prime_twoₓ'. -/
 theorem prime_two : Prime (2 : ℤ) :=
   Nat.prime_iff_prime_int.mp Nat.prime_two
 #align int.prime_two Int.prime_two
 
-/- warning: int.prime_three -> Int.prime_three is a dubious translation:
-lean 3 declaration is
-  Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) (OfNat.ofNat.{0} Int 3 (OfNat.mk.{0} Int 3 (bit1.{0} Int Int.hasOne Int.hasAdd (One.one.{0} Int Int.hasOne))))
-but is expected to have type
-  Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.instCommSemiringInt) (OfNat.ofNat.{0} Int 3 (instOfNatInt 3))
-Case conversion may be inaccurate. Consider using '#align int.prime_three Int.prime_threeₓ'. -/
 theorem prime_three : Prime (3 : ℤ) :=
   Nat.prime_iff_prime_int.mp Nat.prime_three
 #align int.prime_three Int.prime_three

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -157,9 +157,7 @@ theorem prime_def_lt' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m → m <
         ⟨fun h m2 l d => not_lt_of_ge m2 ((h l d).symm ▸ by decide), fun h l d =>
           by
           rcases m with (_ | _ | m)
-          · rw [eq_zero_of_zero_dvd d] at p2
-            revert p2
-            exact by decide
+          · rw [eq_zero_of_zero_dvd d] at p2; revert p2; exact by decide
           · rfl
           · exact (h (by decide) l).elim d⟩
 #align nat.prime_def_lt' Nat.prime_def_lt'
@@ -275,10 +273,8 @@ theorem not_prime_mul {a b : ℕ} (a1 : 1 < a) (b1 : 1 < b) : ¬Prime (a * b) :=
 -/
 
 #print Nat.not_prime_mul' /-
-theorem not_prime_mul' {a b n : ℕ} (h : a * b = n) (h₁ : 1 < a) (h₂ : 1 < b) : ¬Prime n :=
-  by
-  rw [← h]
-  exact not_prime_mul h₁ h₂
+theorem not_prime_mul' {a b n : ℕ} (h : a * b = n) (h₁ : 1 < a) (h₂ : 1 < b) : ¬Prime n := by
+  rw [← h]; exact not_prime_mul h₁ h₂
 #align nat.not_prime_mul' Nat.not_prime_mul'
 -/
 
@@ -291,10 +287,7 @@ theorem prime_mul_iff {a b : ℕ} : Nat.Prime (a * b) ↔ a.Prime ∧ b = 1 ∨
 #print Nat.Prime.dvd_iff_eq /-
 theorem Prime.dvd_iff_eq {p a : ℕ} (hp : p.Prime) (a1 : a ≠ 1) : a ∣ p ↔ p = a :=
   by
-  refine'
-    ⟨_, by
-      rintro rfl
-      rfl⟩
+  refine' ⟨_, by rintro rfl; rfl⟩
   -- rintro ⟨j, rfl⟩ does not work, due to `nat.prime` depending on the class `irreducible`
   rintro ⟨j, hj⟩
   rw [hj] at hp⊢
@@ -378,35 +371,27 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
         prime_def_le_sqrt.2
           ⟨n2, fun m m2 l d => not_lt_of_ge l <| lt_of_lt_of_le (sqrt_lt.2 h) (a m m2 d)⟩
       exact ⟨n2, dvd_rfl, fun m m2 d => le_of_eq ((dvd_prime_two_le pp m2).1 d).symm⟩
-    have k2 : 2 ≤ k := by
-      subst e
-      exact by decide
+    have k2 : 2 ≤ k := by subst e; exact by decide
     by_cases dk : k ∣ n <;> simp [dk]
     · exact ⟨k2, dk, a⟩
     · refine'
         have := min_fac_lemma n k h
         min_fac_aux_has_prop (k + 2) (i + 1) (by simp [e, left_distrib]) fun m m2 d => _
       cases' Nat.eq_or_lt_of_le (a m m2 d) with me ml
-      · subst me
-        contradiction
-      apply (Nat.eq_or_lt_of_le ml).resolve_left
-      intro me
-      rw [← me, e] at d
-      change 2 * (i + 2) ∣ n at d
+      · subst me; contradiction
+      apply (Nat.eq_or_lt_of_le ml).resolve_left; intro me
+      rw [← me, e] at d; change 2 * (i + 2) ∣ n at d
       have := a _ le_rfl (dvd_of_mul_right_dvd d)
-      rw [e] at this
-      exact absurd this (by decide)termination_by' ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
+      rw [e] at this; exact absurd this (by decide)termination_by'
+  ⟨_, measure_wf fun k => sqrt n + 2 - k⟩
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 -/
 
 #print Nat.minFac_has_prop /-
 theorem minFac_has_prop {n : ℕ} (n1 : n ≠ 1) : MinFacProp n (minFac n) :=
   by
-  by_cases n0 : n = 0
-  · simp [n0, min_fac_prop, GE.ge]
-  have n2 : 2 ≤ n := by
-    revert n0 n1
-    rcases n with (_ | _ | _) <;> exact by decide
+  by_cases n0 : n = 0; · simp [n0, min_fac_prop, GE.ge]
+  have n2 : 2 ≤ n := by revert n0 n1; rcases n with (_ | _ | _) <;> exact by decide
   simp [min_fac_eq]
   by_cases d2 : 2 ∣ n <;> simp [d2]
   · exact ⟨le_rfl, d2, fun k k2 d => k2⟩
@@ -544,8 +529,7 @@ theorem minFac_eq_one_iff {n : ℕ} : minFac n = 1 ↔ n = 1 :=
     have := min_fac_prime hn
     rw [h] at this
     exact not_prime_one this
-  · rintro rfl
-    rfl
+  · rintro rfl; rfl
 #align nat.min_fac_eq_one_iff Nat.minFac_eq_one_iff
 -/
 
@@ -755,8 +739,7 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
   by
   induction' n with n IH
   · exact pp.not_dvd_one.elim h
-  · rw [pow_succ] at h
-    exact (pp.dvd_mul.1 h).elim id IH
+  · rw [pow_succ] at h; exact (pp.dvd_mul.1 h).elim id IH
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 -/

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -367,7 +367,6 @@ theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
 
 private def min_fac_prop (n k : ℕ) :=
   2 ≤ k ∧ k ∣ n ∧ ∀ m, 2 ≤ m → m ∣ n → k ≤ m
-#align nat.min_fac_prop nat.min_fac_prop
 
 #print Nat.minFacAux_has_prop /-
 theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -432,14 +432,14 @@ theorem minFac_prime {n : ℕ} (n1 : n ≠ 1) : Prime (minFac n) :=
 
 #print Nat.minFac_le_of_dvd /-
 theorem minFac_le_of_dvd {n : ℕ} : ∀ {m : ℕ}, 2 ≤ m → m ∣ n → minFac n ≤ m := by
-  by_cases n1 : n = 1 <;> [exact fun m m2 d => n1.symm ▸ le_trans (by decide) m2,
-    exact (min_fac_has_prop n1).2.2]
+  by_cases n1 : n = 1 <;>
+    [exact fun m m2 d => n1.symm ▸ le_trans (by decide) m2;exact (min_fac_has_prop n1).2.2]
 #align nat.min_fac_le_of_dvd Nat.minFac_le_of_dvd
 -/
 
 #print Nat.minFac_pos /-
 theorem minFac_pos (n : ℕ) : 0 < minFac n := by
-  by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide, exact (min_fac_prime n1).Pos]
+  by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide;exact (min_fac_prime n1).Pos]
 #align nat.min_fac_pos Nat.minFac_pos
 -/
 
@@ -823,8 +823,8 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     have pdvdxy : p ∣ x * y := by rw [h] <;> simp [sq]
     -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
     suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
-      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip, rw [and_comm']] <;> [skip,
-            rw [mul_comm] at h pdvdxy] <;>
+      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;> [skip;rw [and_comm']] <;>
+            [skip;rw [mul_comm] at h pdvdxy] <;>
           apply this <;>
         assumption
     clear! x y

bump to nightly-2023-03-17-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

11391fe2

Diff

@@ -960,7 +960,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 lean 3 declaration is
   forall {p : Nat}, Iff (Nat.Prime p) (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.commSemiring) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) p))
 but is expected to have type
-  forall {p : Nat}, Iff (Nat.Prime p) (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.instCommSemiringInt) (Nat.cast.{0} Int Int.instNatCastInt p))
+  forall {p : Nat}, Iff (Nat.Prime p) (Prime.{0} Int (CommSemiring.toCommMonoidWithZero.{0} Int Int.instCommSemiringInt) (Nat.cast.{0} Int instNatCastInt p))
 Case conversion may be inaccurate. Consider using '#align nat.prime_iff_prime_int Nat.prime_iff_prime_intₓ'. -/
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ Prime (p : ℤ) :=
   ⟨fun hp =>

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -507,7 +507,7 @@ theorem not_prime_iff_minFac_lt {n : ℕ} (n2 : 2 ≤ n) : ¬Prime n ↔ minFac
 #print Nat.minFac_le_div /-
 theorem minFac_le_div {n : ℕ} (pos : 0 < n) (np : ¬Prime n) : minFac n ≤ n / minFac n :=
   match minFac_dvd n with
-  | ⟨0, h0⟩ => absurd Pos <| by rw [h0, mul_zero] <;> exact by decide
+  | ⟨0, h0⟩ => absurd Pos <| by rw [h0, MulZeroClass.mul_zero] <;> exact by decide
   | ⟨1, h1⟩ => by
     rw [mul_one] at h1
     rw [prime_def_min_fac, not_and_or, ← h1, eq_self_iff_true, not_true, or_false_iff, not_le] at np

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -123,7 +123,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (m «expr ∣ » p) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ∣ » p) -/
 #print Nat.prime_def_lt'' /-
 theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p :=
   by
@@ -529,7 +529,7 @@ theorem minFac_sq_le_self {n : ℕ} (w : 0 < n) (h : ¬Prime n) : minFac n ^ 2 
   have t : minFac n ≤ n / minFac n := minFac_le_div w h
   calc
     minFac n ^ 2 = minFac n * minFac n := sq (minFac n)
-    _ ≤ n / minFac n * minFac n := Nat.mul_le_mul_right (minFac n) t
+    _ ≤ n / minFac n * minFac n := (Nat.mul_le_mul_right (minFac n) t)
     _ ≤ n := div_mul_le_self n (minFac n)
     
 #align nat.min_fac_sq_le_self Nat.minFac_sq_le_self
@@ -768,7 +768,7 @@ theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
     lt_irrefl x <|
       calc
         x = x ^ 1 := (pow_one _).symm
-        _ < x ^ n := Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn
+        _ < x ^ n := (Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn)
         _ = x := hxn.symm
         
 #align nat.prime.pow_not_prime Nat.Prime.pow_not_prime

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: replace refine' that already have a ?_ (#12261)

Co-authored-by: Moritz Firsching <firsching@google.com>

94b44d32

Diff

@@ -656,7 +656,7 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     simp only [sq, mul_right_inj' hp.ne_zero] at h
     subst h
     exact ⟨rfl, rfl⟩
-  · refine' (hy ?_).elim
+  · refine (hy ?_).elim
     subst hap
     subst ha
     rw [sq, Nat.mul_right_eq_self_iff (Nat.mul_pos hp.pos hp.pos : 0 < a * a)] at h

feat(Data/Nat/Prime): add 2 theorems (#11620)

7e8cd2b7

Diff

@@ -454,6 +454,18 @@ theorem exists_dvd_of_not_prime2 {n : ℕ} (n2 : 2 ≤ n) (np : ¬Prime n) :
     (not_prime_iff_minFac_lt n2).1 np⟩
 #align nat.exists_dvd_of_not_prime2 Nat.exists_dvd_of_not_prime2
 
+theorem not_prime_of_dvd_of_ne {m n : ℕ} (h1 : m ∣ n) (h2 : m ≠ 1) (h3 : m ≠ n) : ¬Prime n :=
+  fun h => Or.elim (h.eq_one_or_self_of_dvd m h1) h2 h3
+
+theorem not_prime_of_dvd_of_lt {m n : ℕ} (h1 : m ∣ n) (h2 : 2 ≤ m) (h3 : m < n) : ¬Prime n :=
+  not_prime_of_dvd_of_ne h1 (ne_of_gt h2) (ne_of_lt h3)
+
+theorem not_prime_iff_exists_dvd_ne {n : ℕ} (h : 2 ≤ n) : (¬Prime n) ↔ ∃ m, m ∣ n ∧ m ≠ 1 ∧ m ≠ n :=
+  ⟨exists_dvd_of_not_prime h, fun ⟨_, h1, h2, h3⟩ => not_prime_of_dvd_of_ne h1 h2 h3⟩
+
+theorem not_prime_iff_exists_dvd_lt {n : ℕ} (h : 2 ≤ n) : (¬Prime n) ↔ ∃ m, m ∣ n ∧ 2 ≤ m ∧ m < n :=
+  ⟨exists_dvd_of_not_prime2 h, fun ⟨_, h1, h2, h3⟩ => not_prime_of_dvd_of_lt h1 h2 h3⟩
+
 theorem exists_prime_and_dvd {n : ℕ} (hn : n ≠ 1) : ∃ p, Prime p ∧ p ∣ n :=
   ⟨minFac n, minFac_prime hn, minFac_dvd _⟩
 #align nat.exists_prime_and_dvd Nat.exists_prime_and_dvd

chore: exact by decide -> decide (#12067)

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

1e53d4f0

Diff

@@ -389,7 +389,7 @@ theorem not_prime_iff_minFac_lt {n : ℕ} (n2 : 2 ≤ n) : ¬Prime n ↔ minFac
 
 theorem minFac_le_div {n : ℕ} (pos : 0 < n) (np : ¬Prime n) : minFac n ≤ n / minFac n :=
   match minFac_dvd n with
-  | ⟨0, h0⟩ => absurd pos <| by rw [h0, mul_zero]; exact by decide
+  | ⟨0, h0⟩ => absurd pos <| by rw [h0, mul_zero]; decide
   | ⟨1, h1⟩ => by
     rw [mul_one] at h1
     rw [prime_def_minFac, not_and_or, ← h1, eq_self_iff_true, _root_.not_true, or_false_iff,

chore(Data/Nat/Defs): Integrate Nat.sqrt material (#11866)

Move the content of Data.Nat.ForSqrt and Data.Nat.Sqrt to Data.Nat.Defs by using Nat-specific Std lemmas rather than the mathlib general ones. This makes it ready to move to Std if wanted.

d4b9a267

Diff

@@ -9,7 +9,6 @@ import Mathlib.Data.Int.Units
 import Mathlib.Data.Nat.Factorial.Basic
 import Mathlib.Data.Nat.GCD.Basic
 import Mathlib.Data.Nat.Parity
-import Mathlib.Data.Nat.Sqrt
 import Mathlib.Order.Bounds.Basic
 
 #align_import data.nat.prime from "leanprover-community/mathlib"@"8631e2d5ea77f6c13054d9151d82b83069680cb1"

chore(Data/Int): Rename coe_nat to natCast (#11637)

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

392a24a9

Diff

@@ -739,14 +739,14 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ _root_.Prime (p : ℤ) :=
   ⟨fun hp =>
-    ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
-      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h
-      rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
+    ⟨Int.natCast_ne_zero_iff_pos.2 hp.pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
+      rw [← Int.dvd_natAbs, Int.natCast_dvd_natCast, Int.natAbs_mul, hp.dvd_mul] at h
+      rwa [← Int.dvd_natAbs, Int.natCast_dvd_natCast, ← Int.dvd_natAbs, Int.natCast_dvd_natCast]⟩,
     fun hp =>
     Nat.prime_iff.2
-      ⟨Int.coe_nat_ne_zero.1 hp.1,
+      ⟨Int.natCast_ne_zero.1 hp.1,
         (mt Nat.isUnit_iff.1) fun h => by simp [h, not_prime_one] at hp, fun a b => by
-        simpa only [Int.coe_nat_dvd, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
+        simpa only [Int.natCast_dvd_natCast, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
 #align nat.prime_iff_prime_int Nat.prime_iff_prime_int
 
 /-- Two prime powers with positive exponents are equal only when the primes and the

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -713,7 +713,7 @@ theorem ne_one_iff_exists_prime_dvd : ∀ {n}, n ≠ 1 ↔ ∃ p : ℕ, p.Prime
   | n + 2 => by
     let a := n + 2
     let ha : a ≠ 1 := Nat.succ_succ_ne_one n
-    simp only [true_iff_iff, Ne.def, not_false_iff, ha]
+    simp only [true_iff_iff, Ne, not_false_iff, ha]
     exact ⟨a.minFac, Nat.minFac_prime ha, a.minFac_dvd⟩
 #align nat.ne_one_iff_exists_prime_dvd Nat.ne_one_iff_exists_prime_dvd

change the order of operation in zsmulRec and nsmulRec (#11451)

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.

9a3feeae

Diff

@@ -732,7 +732,7 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
   have hpd4 : p ∣ m / p ^ k * (n / p ^ l) := by simpa [Nat.div_mul_div_comm hpm hpn] using hpd3
   have hpd5 : p ∣ m / p ^ k ∨ p ∣ n / p ^ l :=
     (Prime.dvd_mul p_prime).1 hpd4
-  suffices p ^ k * p ∣ m ∨ p ^ l * p ∣ n by rwa [_root_.pow_succ', _root_.pow_succ']
+  suffices p ^ k * p ∣ m ∨ p ^ l * p ∣ n by rwa [_root_.pow_succ, _root_.pow_succ]
   exact hpd5.elim (fun h : p ∣ m / p ^ k => Or.inl <| mul_dvd_of_dvd_div hpm h)
     fun h : p ∣ n / p ^ l => Or.inr <| mul_dvd_of_dvd_div hpn h
 #align nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul Nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul

chore: classify removed @[pp_nodot] porting notes (#11181)

Classifies by adding issue number #11180 to porting notes claiming:

removed @[pp_nodot]

76aa1eb1

Diff

@@ -43,7 +43,7 @@ variable {n : ℕ}
 
 /-- `Nat.Prime p` means that `p` is a prime number, that is, a natural number
   at least 2 whose only divisors are `p` and `1`. -/
--- Porting note: removed @[pp_nodot]
+-- Porting note (#11180): removed @[pp_nodot]
 def Prime (p : ℕ) :=
   Irreducible p
 #align nat.prime Nat.Prime

feat: the ring of integers of the p-th cyclotomic field is a PID if p = 3 or p = 5 (#10683)

We prove that the ring of integers of the p-th cyclotomic field is a PID if p = 3 or p = 5.

From flt-regular

depends on: #10492
depends on: #10502

5f834b3b

Diff

@@ -175,6 +175,8 @@ theorem prime_two : Prime 2 := by decide
 theorem prime_three : Prime 3 := by decide
 #align nat.prime_three Nat.prime_three
 
+theorem prime_five : Prime 5 := by decide
+
 theorem Prime.five_le_of_ne_two_of_ne_three {p : ℕ} (hp : p.Prime) (h_two : p ≠ 2)
     (h_three : p ≠ 3) : 5 ≤ p := by
   by_contra! h

chore: classify was decide! porting notes (#11044)

Classifies by adding issue number #11043 to porting notes claiming:

was decide!

bc380937

Diff

@@ -179,7 +179,7 @@ theorem Prime.five_le_of_ne_two_of_ne_three {p : ℕ} (hp : p.Prime) (h_two : p
     (h_three : p ≠ 3) : 5 ≤ p := by
   by_contra! h
   revert h_two h_three hp
-  -- Porting note: was `decide!`
+  -- Porting note (#11043): was `decide!`
   match p with
   | 0 => decide
   | 1 => decide

chore: prepare Lean version bump with explicit simp (#10999)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

38bce757

Diff

@@ -293,7 +293,7 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
     · exact ⟨k2, dk, a⟩
     · refine'
         have := minFac_lemma n k h
-        minFacAux_has_prop n2 (k + 2) (i + 1) (by simp [e, left_distrib]) fun m m2 d => _
+        minFacAux_has_prop n2 (k + 2) (i + 1) (by simp [k, e, left_distrib]) fun m m2 d => _
       rcases Nat.eq_or_lt_of_le (a m m2 d) with me | ml
       · subst me
         contradiction

feat: A natural is odd iff it's coprime with 2 (#10222)

From LeanAPAP

66ad5718

Diff

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 -/
 import Mathlib.Algebra.Associated
-import Mathlib.Algebra.Parity
 import Mathlib.Data.Int.Dvd.Basic
 import Mathlib.Data.Int.Units
 import Mathlib.Data.Nat.Factorial.Basic
 import Mathlib.Data.Nat.GCD.Basic
+import Mathlib.Data.Nat.Parity
 import Mathlib.Data.Nat.Sqrt
 import Mathlib.Order.Bounds.Basic
 
@@ -39,6 +39,7 @@ open Bool Subtype
 open Nat
 
 namespace Nat
+variable {n : ℕ}
 
 /-- `Nat.Prime p` means that `p` is a prime number, that is, a natural number
   at least 2 whose only divisors are `p` and `1`. -/
@@ -564,6 +565,14 @@ theorem Prime.not_dvd_mul {p m n : ℕ} (pp : Prime p) (Hm : ¬p ∣ m) (Hn : ¬
   mt pp.dvd_mul.1 <| by simp [Hm, Hn]
 #align nat.prime.not_dvd_mul Nat.Prime.not_dvd_mul
 
+@[simp] lemma coprime_two_left : Coprime 2 n ↔ Odd n := by
+  rw [prime_two.coprime_iff_not_dvd, odd_iff_not_even, even_iff_two_dvd]
+
+@[simp] lemma coprime_two_right : n.Coprime 2 ↔ Odd n := coprime_comm.trans coprime_two_left
+
+alias ⟨Coprime.odd_of_left, _root_.Odd.coprime_two_left⟩ := coprime_two_left
+alias ⟨Coprime.odd_of_right, _root_.Odd.coprime_two_right⟩ := coprime_two_right
+
 theorem prime_iff {p : ℕ} : p.Prime ↔ _root_.Prime p :=
   ⟨fun h => ⟨h.ne_zero, h.not_unit, fun _ _ => h.dvd_mul.mp⟩, Prime.irreducible⟩
 #align nat.prime_iff Nat.prime_iff

chore: bump dependencies (#10315)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

ba9f2e5b

Diff

@@ -433,7 +433,7 @@ theorem minFac_eq_two_iff (n : ℕ) : minFac n = 2 ↔ 2 ∣ n := by
     have ub := minFac_le_of_dvd (le_refl 2) h
     have lb := minFac_pos n
     refine ub.eq_or_lt.resolve_right fun h' => ?_
-    have := le_antisymm (Nat.succ_le_of_lt lb) (lt_succ_iff.mp h')
+    have := le_antisymm (Nat.succ_le_of_lt lb) (Nat.lt_succ_iff.mp h')
     rw [eq_comm, Nat.minFac_eq_one_iff] at this
     subst this
     exact not_lt_of_le (le_of_dvd zero_lt_one h) one_lt_two

chore: move to v4.6.0-rc1, merging adaptations from bump/v4.6.0 (#10176)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

490d2d48

Diff

@@ -252,7 +252,7 @@ def minFacAux (n : ℕ) : ℕ → ℕ
       else
         have := minFac_lemma n k h
         minFacAux n (k + 2)
-termination_by _ n k => sqrt n + 2 - k
+termination_by k => sqrt n + 2 - k
 #align nat.min_fac_aux Nat.minFacAux
 
 /-- Returns the smallest prime factor of `n ≠ 1`. -/
@@ -303,7 +303,7 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
       have := a _ le_rfl (dvd_of_mul_right_dvd d')
       rw [e] at this
       exact absurd this (by contradiction)
-  termination_by _ n _ k => sqrt n + 2 - k
+  termination_by k => sqrt n + 2 - k
 #align nat.min_fac_aux_has_prop Nat.minFacAux_has_prop
 
 theorem minFac_has_prop {n : ℕ} (n1 : n ≠ 1) : minFacProp n (minFac n) := by

feat(Data/Nat/Prime): some lemmas on primes and powers (#10025)

This is the first PR in a sequence that adds auxiliary lemmas from the EulerProducts project to Mathlib.

It adds two lemmas on prime numbers and powers:

lemma Nat.Prime.one_le {p : ℕ} (hp : p.Prime) : 1 ≤ p

lemma Nat.Prime.pow_injective {p q m n : ℕ} (hp : p.Prime) (hq : q.Prime)
    (h : p ^ (m + 1) = q ^ (n + 1)) : p = q ∧ m = n

(The first one is for discoverability by exact? in cases one needs 1 ≤ p.)

76b26e84

Diff

@@ -77,6 +77,8 @@ theorem Prime.one_lt {p : ℕ} : Prime p → 1 < p :=
   Prime.two_le
 #align nat.prime.one_lt Nat.Prime.one_lt
 
+lemma Prime.one_le {p : ℕ} (hp : p.Prime) : 1 ≤ p := hp.one_lt.le
+
 instance Prime.one_lt' (p : ℕ) [hp : Fact p.Prime] : Fact (1 < p) :=
   ⟨hp.1.one_lt⟩
 #align nat.prime.one_lt' Nat.Prime.one_lt'
@@ -736,6 +738,14 @@ theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ _root_.Prime (p : ℤ) :=
         simpa only [Int.coe_nat_dvd, (Int.ofNat_mul _ _).symm] using hp.2.2 a b⟩⟩
 #align nat.prime_iff_prime_int Nat.prime_iff_prime_int
 
+/-- Two prime powers with positive exponents are equal only when the primes and the
+exponents are equal. -/
+lemma Prime.pow_inj {p q m n : ℕ} (hp : p.Prime) (hq : q.Prime)
+    (h : p ^ (m + 1) = q ^ (n + 1)) : p = q ∧ m = n := by
+  have H := dvd_antisymm (Prime.dvd_of_dvd_pow hp <| h ▸ dvd_pow_self p (succ_ne_zero m))
+    (Prime.dvd_of_dvd_pow hq <| h.symm ▸ dvd_pow_self q (succ_ne_zero n))
+  exact ⟨H, succ_inj'.mp <| Nat.pow_right_injective hq.two_le (H ▸ h)⟩
+
 /-- The type of prime numbers -/
 def Primes :=
   { p : ℕ // p.Prime }

feat(Nat/Prime): weaken assumptions in Nat.not_prime_mul (#9901)

Assume _ ≠ 1 instead of 1 < _ in Nat.not_prime_mul, Nat.not_prime_mul', Int.not_prime_of_int_mul.

8cab1b0a

Diff

@@ -213,25 +213,20 @@ theorem Prime.not_dvd_one {p : ℕ} (pp : Prime p) : ¬p ∣ 1 :=
   Irreducible.not_dvd_one pp
 #align nat.prime.not_dvd_one Nat.Prime.not_dvd_one
 
-theorem not_prime_mul {a b : ℕ} (a1 : 1 < a) (b1 : 1 < b) : ¬Prime (a * b) := fun h =>
-  ne_of_lt (Nat.mul_lt_mul_of_pos_left b1 (lt_of_succ_lt a1)) <| by
-    simpa using (dvd_prime_two_le h a1).1 (dvd_mul_right _ _)
-#align nat.not_prime_mul Nat.not_prime_mul
-
-theorem not_prime_mul' {a b n : ℕ} (h : a * b = n) (h₁ : 1 < a) (h₂ : 1 < b) : ¬Prime n := by
-  rw [← h]
-  exact not_prime_mul h₁ h₂
-#align nat.not_prime_mul' Nat.not_prime_mul'
-
 theorem prime_mul_iff {a b : ℕ} : Nat.Prime (a * b) ↔ a.Prime ∧ b = 1 ∨ b.Prime ∧ a = 1 := by
   simp only [iff_self_iff, irreducible_mul_iff, ← irreducible_iff_nat_prime, Nat.isUnit_iff]
 #align nat.prime_mul_iff Nat.prime_mul_iff
 
+theorem not_prime_mul {a b : ℕ} (a1 : a ≠ 1) (b1 : b ≠ 1) : ¬Prime (a * b) := by
+  simp [prime_mul_iff, _root_.not_or, *]
+#align nat.not_prime_mul Nat.not_prime_mul
+
+theorem not_prime_mul' {a b n : ℕ} (h : a * b = n) (h₁ : a ≠ 1) (h₂ : b ≠ 1) : ¬Prime n :=
+  h ▸ not_prime_mul h₁ h₂
+#align nat.not_prime_mul' Nat.not_prime_mul'
+
 theorem Prime.dvd_iff_eq {p a : ℕ} (hp : p.Prime) (a1 : a ≠ 1) : a ∣ p ↔ p = a := by
-  refine'
-    ⟨_, by
-      rintro rfl
-      rfl⟩
+  refine ⟨?_, by rintro rfl; rfl⟩
   rintro ⟨j, rfl⟩
   rcases prime_mul_iff.mp hp with (⟨_, rfl⟩ | ⟨_, rfl⟩)
   · exact mul_one _

chore(*): use ∀ s ⊆ t, _ etc (#9276)

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

be0b59d2

Diff

@@ -95,7 +95,7 @@ theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m 
   rw [hn, mul_one]
 #align nat.prime.eq_one_or_self_of_dvd Nat.Prime.eq_one_or_self_of_dvd
 
-theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ (m) (_ : m ∣ p), m = 1 ∨ m = p := by
+theorem prime_def_lt'' {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, m ∣ p → m = 1 ∨ m = p := by
   refine' ⟨fun h => ⟨h.two_le, h.eq_one_or_self_of_dvd⟩, fun h => _⟩
   -- Porting note: needed to make ℕ explicit
   have h1 := (@one_lt_two ℕ ..).trans_le h.1

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -136,7 +136,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
         have : ∀ {m k : ℕ}, m ≤ k → 1 < m → p ≠ m * k := fun {m k} mk m1 e =>
           a m m1 (le_sqrt.2 (e.symm ▸ Nat.mul_le_mul_left m mk)) ⟨k, e⟩
         fun m m2 l ⟨k, e⟩ => by
-        cases' le_total m k with mk km
+        rcases le_total m k with mk | km
         · exact this mk m2 e
         · rw [mul_comm] at e
           refine' this km (lt_of_mul_lt_mul_right _ (zero_le m)) e
@@ -296,7 +296,7 @@ theorem minFacAux_has_prop {n : ℕ} (n2 : 2 ≤ n) :
     · refine'
         have := minFac_lemma n k h
         minFacAux_has_prop n2 (k + 2) (i + 1) (by simp [e, left_distrib]) fun m m2 d => _
-      cases' Nat.eq_or_lt_of_le (a m m2 d) with me ml
+      rcases Nat.eq_or_lt_of_le (a m m2 d) with me | ml
       · subst me
         contradiction
       apply (Nat.eq_or_lt_of_le ml).resolve_left

chore: rename by_contra' to by_contra! (#8797)

To fit with the "please try harder" convention of ! tactics.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

738b1a97

Diff

@@ -174,7 +174,7 @@ theorem prime_three : Prime 3 := by decide
 
 theorem Prime.five_le_of_ne_two_of_ne_three {p : ℕ} (hp : p.Prime) (h_two : p ≠ 2)
     (h_three : p ≠ 3) : 5 ≤ p := by
-  by_contra' h
+  by_contra! h
   revert h_two h_three hp
   -- Porting note: was `decide!`
   match p with

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -430,7 +430,7 @@ theorem minFac_eq_one_iff {n : ℕ} : minFac n = 1 ↔ n = 1 := by
 theorem minFac_eq_two_iff (n : ℕ) : minFac n = 2 ↔ 2 ∣ n := by
   constructor
   · intro h
-    rw [←h]
+    rw [← h]
     exact minFac_dvd n
   · intro h
     have ub := minFac_le_of_dvd (le_refl 2) h

feat: add and use not_irreducible_pow (#8452)

Also rename pow_not_prime theorems to match.

not_irreducible_pow is extracted from flt-regular.

7c1536fc

Diff

@@ -585,16 +585,16 @@ theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p
   pp.prime.dvd_of_dvd_pow h
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 
-theorem Prime.pow_not_prime' {x n : ℕ} (hn : n ≠ 1) : ¬(x ^ n).Prime :=
-  pow_not_prime hn ∘ Nat.Prime.prime
-#align nat.prime.pow_not_prime' Nat.Prime.pow_not_prime'
+theorem Prime.not_prime_pow' {x n : ℕ} (hn : n ≠ 1) : ¬(x ^ n).Prime :=
+  not_irreducible_pow hn
+#align nat.prime.pow_not_prime' Nat.Prime.not_prime_pow'
 
-theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime :=
-  pow_not_prime' ((two_le_iff _).mp hn).2
-#align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
+theorem Prime.not_prime_pow {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime :=
+  not_prime_pow' ((two_le_iff _).mp hn).2
+#align nat.prime.pow_not_prime Nat.Prime.not_prime_pow
 
 theorem Prime.eq_one_of_pow {x n : ℕ} (h : (x ^ n).Prime) : n = 1 :=
-  not_imp_not.mp Prime.pow_not_prime' h
+  not_imp_not.mp Prime.not_prime_pow' h
 #align nat.prime.eq_one_of_pow Nat.Prime.eq_one_of_pow
 
 theorem Prime.pow_eq_iff {p a k : ℕ} (hp : p.Prime) : a ^ k = p ↔ a = p ∧ k = 1 := by

feat: add aesop attribute to Nat.not_prime_one (#8332)

@Yaël Dillies's recent proof at #8164 uses aesop in a way that relies on simp using decide := true by default, which we have now disabled, and hence this breaks on nightly-testing.

I propose we add @[aesop safe destruct] to Nat.not_prime_one (and Nat.not_prime_zero while we're there).

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

4cb02b43

Diff

@@ -51,11 +51,11 @@ theorem irreducible_iff_nat_prime (a : ℕ) : Irreducible a ↔ Nat.Prime a :=
   Iff.rfl
 #align irreducible_iff_nat_prime Nat.irreducible_iff_nat_prime
 
-theorem not_prime_zero : ¬Prime 0
+@[aesop safe destruct] theorem not_prime_zero : ¬Prime 0
   | h => h.ne_zero rfl
 #align nat.not_prime_zero Nat.not_prime_zero
 
-theorem not_prime_one : ¬Prime 1
+@[aesop safe destruct] theorem not_prime_one : ¬Prime 1
   | h => h.ne_one rfl
 #align nat.not_prime_one Nat.not_prime_one

fix: patch for std4#194 (more order lemmas for Nat) (#8077)

5f84b04f

Diff

@@ -671,7 +671,7 @@ theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 
 theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
-  (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
+  (coprime_or_dvd_of_prime pp n).resolve_right fun h => Nat.lt_le_asymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 
 theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Prime p) :

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -315,7 +315,7 @@ theorem minFac_has_prop {n : ℕ} (n1 : n ≠ 1) : minFacProp n (minFac n) := by
   have n2 : 2 ≤ n := by
     revert n0 n1
     rcases n with (_ | _ | _) <;> simp [succ_le_succ]
-  simp [minFac_eq]
+  simp only [minFac_eq, Nat.isUnit_iff]
   by_cases d2 : 2 ∣ n <;> simp [d2]
   · exact ⟨le_rfl, d2, fun k k2 _ => k2⟩
   · refine'

chore: golf some Nat.Prime proofs (#7452)

Also correct indentation for another.

89df0a5a

Diff

@@ -581,29 +581,18 @@ theorem irreducible_iff_prime {p : ℕ} : Irreducible p ↔ _root_.Prime p :=
   prime_iff
 #align nat.irreducible_iff_prime Nat.irreducible_iff_prime
 
-theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p ∣ m := by
-  induction' n with n IH
-  · exact pp.not_dvd_one.elim h
-  · rw [pow_succ] at h
-    exact (pp.dvd_mul.1 h).elim IH id
+theorem Prime.dvd_of_dvd_pow {p m n : ℕ} (pp : Prime p) (h : p ∣ m ^ n) : p ∣ m :=
+  pp.prime.dvd_of_dvd_pow h
 #align nat.prime.dvd_of_dvd_pow Nat.Prime.dvd_of_dvd_pow
 
-theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun hp =>
-  (hp.eq_one_or_self_of_dvd x <| dvd_trans ⟨x, sq _⟩ (pow_dvd_pow _ hn)).elim
-    (fun hx1 => hp.ne_one <| hx1.symm ▸ one_pow _) fun hxn =>
-    lt_irrefl x <|
-      calc
-        x = x ^ 1 := (pow_one _).symm
-        _ < x ^ n := Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn
-        _ = x := hxn.symm
-#align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
-
-theorem Prime.pow_not_prime' {x : ℕ} : ∀ {n : ℕ}, n ≠ 1 → ¬(x ^ n).Prime
-  | 0 => fun _ => not_prime_one
-  | 1 => fun h => (h rfl).elim
-  | _ + 2 => fun _ => Prime.pow_not_prime le_add_self
+theorem Prime.pow_not_prime' {x n : ℕ} (hn : n ≠ 1) : ¬(x ^ n).Prime :=
+  pow_not_prime hn ∘ Nat.Prime.prime
 #align nat.prime.pow_not_prime' Nat.Prime.pow_not_prime'
 
+theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime :=
+  pow_not_prime' ((two_le_iff _).mp hn).2
+#align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
+
 theorem Prime.eq_one_of_pow {x n : ℕ} (h : (x ^ n).Prime) : n = 1 :=
   not_imp_not.mp Prime.pow_not_prime' h
 #align nat.prime.eq_one_of_pow Nat.Prime.eq_one_of_pow
@@ -630,29 +619,29 @@ theorem Prime.pow_minFac {p k : ℕ} (hp : p.Prime) (hk : k ≠ 0) : (p ^ k).min
 
 theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (hy : y ≠ 1) :
     x * y = p ^ 2 ↔ x = p ∧ y = p := by
-    refine' ⟨fun h => _, fun ⟨h₁, h₂⟩ => h₁.symm ▸ h₂.symm ▸ (sq _).symm⟩
-    have pdvdxy : p ∣ x * y := by rw [h]; simp [sq]
-    -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
-    suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
-      obtain hx | hy := hp.dvd_mul.1 pdvdxy <;>
-        [skip; rw [And.comm]] <;>
-        [skip; rw [mul_comm] at h pdvdxy] <;>
-        apply this <;>
-        assumption
-    rintro x y hx hy h ⟨a, ha⟩
-    have : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h⟩
-    obtain ha1 | hap := (Nat.dvd_prime hp).mp ‹a ∣ p›
-    · subst ha1
-      rw [mul_one] at ha
-      subst ha
-      simp only [sq, mul_right_inj' hp.ne_zero] at h
-      subst h
-      exact ⟨rfl, rfl⟩
-    · refine' (hy ?_).elim
-      subst hap
-      subst ha
-      rw [sq, Nat.mul_right_eq_self_iff (Nat.mul_pos hp.pos hp.pos : 0 < a * a)] at h
-      exact h
+  refine' ⟨fun h => _, fun ⟨h₁, h₂⟩ => h₁.symm ▸ h₂.symm ▸ (sq _).symm⟩
+  have pdvdxy : p ∣ x * y := by rw [h]; simp [sq]
+  -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
+  suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
+    obtain hx | hy := hp.dvd_mul.1 pdvdxy <;>
+      [skip; rw [And.comm]] <;>
+      [skip; rw [mul_comm] at h pdvdxy] <;>
+      apply this <;>
+      assumption
+  rintro x y hx hy h ⟨a, ha⟩
+  have : a ∣ p := ⟨y, by rwa [ha, sq, mul_assoc, mul_right_inj' hp.ne_zero, eq_comm] at h⟩
+  obtain ha1 | hap := (Nat.dvd_prime hp).mp ‹a ∣ p›
+  · subst ha1
+    rw [mul_one] at ha
+    subst ha
+    simp only [sq, mul_right_inj' hp.ne_zero] at h
+    subst h
+    exact ⟨rfl, rfl⟩
+  · refine' (hy ?_).elim
+    subst hap
+    subst ha
+    rw [sq, Nat.mul_right_eq_self_iff (Nat.mul_pos hp.pos hp.pos : 0 < a * a)] at h
+    exact h
 #align nat.prime.mul_eq_prime_sq_iff Nat.Prime.mul_eq_prime_sq_iff
 
 theorem Prime.dvd_factorial : ∀ {n p : ℕ} (_ : Prime p), p ∣ n ! ↔ p ≤ n

chore: bump to v4.1.0-rc1 (2nd attempt) (#7216)

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

bfaffcf1

Diff

@@ -143,7 +143,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
           rwa [one_mul, ← e]⟩
 #align nat.prime_def_le_sqrt Nat.prime_def_le_sqrt
 
-theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.coprime m) : Prime n := by
+theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.Coprime m) : Prime n := by
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
     rintro rfl
@@ -517,7 +517,7 @@ theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔
   simp at h
 #align nat.prime.mod_two_eq_one_iff_ne_two Nat.Prime.mod_two_eq_one_iff_ne_two
 
-theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : coprime m n := by
+theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : Coprime m n := by
   rw [coprime_iff_gcd_eq_one]
   by_contra g2
   obtain ⟨p, hp, hpdvd⟩ := exists_prime_and_dvd g2
@@ -526,7 +526,7 @@ theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n
   · exact gcd_dvd_right _ _
 #align nat.coprime_of_dvd Nat.coprime_of_dvd
 
-theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : coprime m n :=
+theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : Coprime m n :=
   coprime_of_dvd fun k kp km kn => not_le_of_gt kp.one_lt <| le_of_dvd zero_lt_one <| H k kp km kn
 #align nat.coprime_of_dvd' Nat.coprime_of_dvd'
 
@@ -538,16 +538,16 @@ theorem factors_lemma {k} : (k + 2) / minFac (k + 2) < k + 2 :=
       )).one_lt
 #align nat.factors_lemma Nat.factors_lemma
 
-theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : coprime p n ↔ ¬p ∣ n :=
+theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : Coprime p n ↔ ¬p ∣ n :=
   ⟨fun co d => pp.not_dvd_one <| co.dvd_of_dvd_mul_left (by simp [d]), fun nd =>
     coprime_of_dvd fun m m2 mp => ((prime_dvd_prime_iff_eq m2 pp).1 mp).symm ▸ nd⟩
 #align nat.prime.coprime_iff_not_dvd Nat.Prime.coprime_iff_not_dvd
 
-theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬coprime p n :=
+theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬Coprime p n :=
   iff_not_comm.2 pp.coprime_iff_not_dvd
 #align nat.prime.dvd_iff_not_coprime Nat.Prime.dvd_iff_not_coprime
 
-theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
+theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬Coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
   apply Iff.intro
   · intro h
     exact
@@ -664,29 +664,29 @@ theorem Prime.dvd_factorial : ∀ {n p : ℕ} (_ : Prime p), p ∣ n ! ↔ p ≤
         (_root_.lt_or_eq_of_le h).elim (Or.inr ∘ le_of_lt_succ) fun h => Or.inl <| by rw [h]⟩
 #align nat.prime.dvd_factorial Nat.Prime.dvd_factorial
 
-theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : coprime a (p ^ m) :=
+theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : Coprime a (p ^ m) :=
   (pp.coprime_iff_not_dvd.2 h).symm.pow_right _
 #align nat.prime.coprime_pow_of_not_dvd Nat.Prime.coprime_pow_of_not_dvd
 
-theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : coprime p q ↔ p ≠ q :=
+theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : Coprime p q ↔ p ≠ q :=
   pp.coprime_iff_not_dvd.trans <| not_congr <| dvd_prime_two_le pq pp.two_le
 #align nat.coprime_primes Nat.coprime_primes
 
 theorem coprime_pow_primes {p q : ℕ} (n m : ℕ) (pp : Prime p) (pq : Prime q) (h : p ≠ q) :
-    coprime (p ^ n) (q ^ m) :=
+    Coprime (p ^ n) (q ^ m) :=
   ((coprime_primes pp pq).2 h).pow _ _
 #align nat.coprime_pow_primes Nat.coprime_pow_primes
 
-theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : coprime p i ∨ p ∣ i := by
+theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p ∣ i := by
   rw [pp.dvd_iff_not_coprime]; apply em
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 
-theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : coprime p n :=
+theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
   (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 
 theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Prime p) :
-    p = n ∨ coprime p n :=
+    p = n ∨ Coprime p n :=
   hle.eq_or_lt.imp Eq.symm fun h => coprime_of_lt_prime n_pos h pp
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 
@@ -696,7 +696,7 @@ theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃
 
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)
     (h1 : p1 ∣ n) (h2 : p2 ∣ n) : p1 * p2 ∣ n :=
-  coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
+  Coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
 #align nat.prime.dvd_mul_of_dvd_ne Nat.Prime.dvd_mul_of_dvd_ne
 
 /-- If `p` is prime,

Revert "chore: bump to v4.1.0-rc1 (#7174)" (#7198)

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.

40b58304

Diff

@@ -143,7 +143,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
           rwa [one_mul, ← e]⟩
 #align nat.prime_def_le_sqrt Nat.prime_def_le_sqrt
 
-theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.Coprime m) : Prime n := by
+theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.coprime m) : Prime n := by
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
     rintro rfl
@@ -517,7 +517,7 @@ theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔
   simp at h
 #align nat.prime.mod_two_eq_one_iff_ne_two Nat.Prime.mod_two_eq_one_iff_ne_two
 
-theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : Coprime m n := by
+theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : coprime m n := by
   rw [coprime_iff_gcd_eq_one]
   by_contra g2
   obtain ⟨p, hp, hpdvd⟩ := exists_prime_and_dvd g2
@@ -526,7 +526,7 @@ theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n
   · exact gcd_dvd_right _ _
 #align nat.coprime_of_dvd Nat.coprime_of_dvd
 
-theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : Coprime m n :=
+theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : coprime m n :=
   coprime_of_dvd fun k kp km kn => not_le_of_gt kp.one_lt <| le_of_dvd zero_lt_one <| H k kp km kn
 #align nat.coprime_of_dvd' Nat.coprime_of_dvd'
 
@@ -538,16 +538,16 @@ theorem factors_lemma {k} : (k + 2) / minFac (k + 2) < k + 2 :=
       )).one_lt
 #align nat.factors_lemma Nat.factors_lemma
 
-theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : Coprime p n ↔ ¬p ∣ n :=
+theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : coprime p n ↔ ¬p ∣ n :=
   ⟨fun co d => pp.not_dvd_one <| co.dvd_of_dvd_mul_left (by simp [d]), fun nd =>
     coprime_of_dvd fun m m2 mp => ((prime_dvd_prime_iff_eq m2 pp).1 mp).symm ▸ nd⟩
 #align nat.prime.coprime_iff_not_dvd Nat.Prime.coprime_iff_not_dvd
 
-theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬Coprime p n :=
+theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬coprime p n :=
   iff_not_comm.2 pp.coprime_iff_not_dvd
 #align nat.prime.dvd_iff_not_coprime Nat.Prime.dvd_iff_not_coprime
 
-theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬Coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
+theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
   apply Iff.intro
   · intro h
     exact
@@ -664,29 +664,29 @@ theorem Prime.dvd_factorial : ∀ {n p : ℕ} (_ : Prime p), p ∣ n ! ↔ p ≤
         (_root_.lt_or_eq_of_le h).elim (Or.inr ∘ le_of_lt_succ) fun h => Or.inl <| by rw [h]⟩
 #align nat.prime.dvd_factorial Nat.Prime.dvd_factorial
 
-theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : Coprime a (p ^ m) :=
+theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : coprime a (p ^ m) :=
   (pp.coprime_iff_not_dvd.2 h).symm.pow_right _
 #align nat.prime.coprime_pow_of_not_dvd Nat.Prime.coprime_pow_of_not_dvd
 
-theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : Coprime p q ↔ p ≠ q :=
+theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : coprime p q ↔ p ≠ q :=
   pp.coprime_iff_not_dvd.trans <| not_congr <| dvd_prime_two_le pq pp.two_le
 #align nat.coprime_primes Nat.coprime_primes
 
 theorem coprime_pow_primes {p q : ℕ} (n m : ℕ) (pp : Prime p) (pq : Prime q) (h : p ≠ q) :
-    Coprime (p ^ n) (q ^ m) :=
+    coprime (p ^ n) (q ^ m) :=
   ((coprime_primes pp pq).2 h).pow _ _
 #align nat.coprime_pow_primes Nat.coprime_pow_primes
 
-theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p ∣ i := by
+theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : coprime p i ∨ p ∣ i := by
   rw [pp.dvd_iff_not_coprime]; apply em
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 
-theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
+theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : coprime p n :=
   (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 
 theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Prime p) :
-    p = n ∨ Coprime p n :=
+    p = n ∨ coprime p n :=
   hle.eq_or_lt.imp Eq.symm fun h => coprime_of_lt_prime n_pos h pp
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 
@@ -696,7 +696,7 @@ theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃
 
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)
     (h1 : p1 ∣ n) (h2 : p2 ∣ n) : p1 * p2 ∣ n :=
-  Coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
+  coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
 #align nat.prime.dvd_mul_of_dvd_ne Nat.Prime.dvd_mul_of_dvd_ne
 
 /-- If `p` is prime,

chore: bump to v4.1.0-rc1 (#7174)

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>

6f8e8104

Diff

@@ -143,7 +143,7 @@ theorem prime_def_le_sqrt {p : ℕ} : Prime p ↔ 2 ≤ p ∧ ∀ m, 2 ≤ m →
           rwa [one_mul, ← e]⟩
 #align nat.prime_def_le_sqrt Nat.prime_def_le_sqrt
 
-theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.coprime m) : Prime n := by
+theorem prime_of_coprime (n : ℕ) (h1 : 1 < n) (h : ∀ m < n, m ≠ 0 → n.Coprime m) : Prime n := by
   refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩
   have hm : m ≠ 0 := by
     rintro rfl
@@ -517,7 +517,7 @@ theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔
   simp at h
 #align nat.prime.mod_two_eq_one_iff_ne_two Nat.Prime.mod_two_eq_one_iff_ne_two
 
-theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : coprime m n := by
+theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n) : Coprime m n := by
   rw [coprime_iff_gcd_eq_one]
   by_contra g2
   obtain ⟨p, hp, hpdvd⟩ := exists_prime_and_dvd g2
@@ -526,7 +526,7 @@ theorem coprime_of_dvd {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → ¬k ∣ n
   · exact gcd_dvd_right _ _
 #align nat.coprime_of_dvd Nat.coprime_of_dvd
 
-theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : coprime m n :=
+theorem coprime_of_dvd' {m n : ℕ} (H : ∀ k, Prime k → k ∣ m → k ∣ n → k ∣ 1) : Coprime m n :=
   coprime_of_dvd fun k kp km kn => not_le_of_gt kp.one_lt <| le_of_dvd zero_lt_one <| H k kp km kn
 #align nat.coprime_of_dvd' Nat.coprime_of_dvd'
 
@@ -538,16 +538,16 @@ theorem factors_lemma {k} : (k + 2) / minFac (k + 2) < k + 2 :=
       )).one_lt
 #align nat.factors_lemma Nat.factors_lemma
 
-theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : coprime p n ↔ ¬p ∣ n :=
+theorem Prime.coprime_iff_not_dvd {p n : ℕ} (pp : Prime p) : Coprime p n ↔ ¬p ∣ n :=
   ⟨fun co d => pp.not_dvd_one <| co.dvd_of_dvd_mul_left (by simp [d]), fun nd =>
     coprime_of_dvd fun m m2 mp => ((prime_dvd_prime_iff_eq m2 pp).1 mp).symm ▸ nd⟩
 #align nat.prime.coprime_iff_not_dvd Nat.Prime.coprime_iff_not_dvd
 
-theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬coprime p n :=
+theorem Prime.dvd_iff_not_coprime {p n : ℕ} (pp : Prime p) : p ∣ n ↔ ¬Coprime p n :=
   iff_not_comm.2 pp.coprime_iff_not_dvd
 #align nat.prime.dvd_iff_not_coprime Nat.Prime.dvd_iff_not_coprime
 
-theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
+theorem Prime.not_coprime_iff_dvd {m n : ℕ} : ¬Coprime m n ↔ ∃ p, Prime p ∧ p ∣ m ∧ p ∣ n := by
   apply Iff.intro
   · intro h
     exact
@@ -664,29 +664,29 @@ theorem Prime.dvd_factorial : ∀ {n p : ℕ} (_ : Prime p), p ∣ n ! ↔ p ≤
         (_root_.lt_or_eq_of_le h).elim (Or.inr ∘ le_of_lt_succ) fun h => Or.inl <| by rw [h]⟩
 #align nat.prime.dvd_factorial Nat.Prime.dvd_factorial
 
-theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : coprime a (p ^ m) :=
+theorem Prime.coprime_pow_of_not_dvd {p m a : ℕ} (pp : Prime p) (h : ¬p ∣ a) : Coprime a (p ^ m) :=
   (pp.coprime_iff_not_dvd.2 h).symm.pow_right _
 #align nat.prime.coprime_pow_of_not_dvd Nat.Prime.coprime_pow_of_not_dvd
 
-theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : coprime p q ↔ p ≠ q :=
+theorem coprime_primes {p q : ℕ} (pp : Prime p) (pq : Prime q) : Coprime p q ↔ p ≠ q :=
   pp.coprime_iff_not_dvd.trans <| not_congr <| dvd_prime_two_le pq pp.two_le
 #align nat.coprime_primes Nat.coprime_primes
 
 theorem coprime_pow_primes {p q : ℕ} (n m : ℕ) (pp : Prime p) (pq : Prime q) (h : p ≠ q) :
-    coprime (p ^ n) (q ^ m) :=
+    Coprime (p ^ n) (q ^ m) :=
   ((coprime_primes pp pq).2 h).pow _ _
 #align nat.coprime_pow_primes Nat.coprime_pow_primes
 
-theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : coprime p i ∨ p ∣ i := by
+theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : Coprime p i ∨ p ∣ i := by
   rw [pp.dvd_iff_not_coprime]; apply em
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 
-theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : coprime p n :=
+theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : Coprime p n :=
   (coprime_or_dvd_of_prime pp n).resolve_right fun h => lt_le_antisymm hlt (le_of_dvd n_pos h)
 #align nat.coprime_of_lt_prime Nat.coprime_of_lt_prime
 
 theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Prime p) :
-    p = n ∨ coprime p n :=
+    p = n ∨ Coprime p n :=
   hle.eq_or_lt.imp Eq.symm fun h => coprime_of_lt_prime n_pos h pp
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 
@@ -696,7 +696,7 @@ theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃
 
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)
     (h1 : p1 ∣ n) (h2 : p2 ∣ n) : p1 * p2 ∣ n :=
-  coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
+  Coprime.mul_dvd_of_dvd_of_dvd ((coprime_primes pp1 pp2).mpr h_neq) h1 h2
 #align nat.prime.dvd_mul_of_dvd_ne Nat.Prime.dvd_mul_of_dvd_ne
 
 /-- If `p` is prime,

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -571,7 +571,7 @@ theorem prime_iff {p : ℕ} : p.Prime ↔ _root_.Prime p :=
   ⟨fun h => ⟨h.ne_zero, h.not_unit, fun _ _ => h.dvd_mul.mp⟩, Prime.irreducible⟩
 #align nat.prime_iff Nat.prime_iff
 
-alias prime_iff ↔ Prime.prime _root_.Prime.nat_prime
+alias ⟨Prime.prime, _root_.Prime.nat_prime⟩ := prime_iff
 #align nat.prime.prime Nat.Prime.prime
 #align prime.nat_prime Prime.nat_prime

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -782,7 +782,7 @@ theorem coe_nat_inj (p q : Nat.Primes) : (p : ℕ) = (q : ℕ) ↔ p = q :=
 
 end Primes
 
-instance monoid.primePow {α : Type _} [Monoid α] : Pow α Primes :=
+instance monoid.primePow {α : Type*} [Monoid α] : Pow α Primes :=
   ⟨fun x p => x ^ (p : ℕ)⟩
 #align nat.monoid.prime_pow Nat.monoid.primePow

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -246,7 +246,7 @@ theorem minFac_lemma (n k : ℕ) (h : ¬n < k * k) : sqrt n - k < sqrt n + 2 - k
 
 /-- If `n < k * k`, then `minFacAux n k = n`, if `k | n`, then `minFacAux n k = k`.
   Otherwise, `minFacAux n k = minFacAux n (k+2)` using well-founded recursion.
-  If `n` is odd and `1 < n`, then then `minFacAux n 3` is the smallest prime factor of `n`. -/
+  If `n` is odd and `1 < n`, then `minFacAux n 3` is the smallest prime factor of `n`. -/
 def minFacAux (n : ℕ) : ℕ → ℕ
   | k =>
     if h : n < k * k then n

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2015 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.nat.prime
-! leanprover-community/mathlib commit 8631e2d5ea77f6c13054d9151d82b83069680cb1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Associated
 import Mathlib.Algebra.Parity
@@ -17,6 +12,8 @@ import Mathlib.Data.Nat.GCD.Basic
 import Mathlib.Data.Nat.Sqrt
 import Mathlib.Order.Bounds.Basic
 
+#align_import data.nat.prime from "leanprover-community/mathlib"@"8631e2d5ea77f6c13054d9151d82b83069680cb1"
+
 /-!
 # Prime numbers

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

12343aa5

Diff

@@ -694,7 +694,7 @@ theorem eq_or_coprime_of_le_prime {n p} (n_pos : 0 < n) (hle : n ≤ p) (pp : Pr
 #align nat.eq_or_coprime_of_le_prime Nat.eq_or_coprime_of_le_prime
 
 theorem dvd_prime_pow {p : ℕ} (pp : Prime p) {m i : ℕ} : i ∣ p ^ m ↔ ∃ k ≤ m, i = p ^ k := by
-  simp_rw [_root_.dvd_prime_pow  (prime_iff.mp pp)  m, associated_eq_eq]
+  simp_rw [_root_.dvd_prime_pow (prime_iff.mp pp) m, associated_eq_eq]
 #align nat.dvd_prime_pow Nat.dvd_prime_pow
 
 theorem Prime.dvd_mul_of_dvd_ne {p1 p2 n : ℕ} (h_neq : p1 ≠ p2) (pp1 : Prime p1) (pp2 : Prime p2)

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -357,7 +357,7 @@ theorem le_minFac {m n : ℕ} : n = 1 ∨ m ≤ minFac n ↔ ∀ p, Prime p →
 
 theorem le_minFac' {m n : ℕ} : n = 1 ∨ m ≤ minFac n ↔ ∀ p, 2 ≤ p → p ∣ n → m ≤ p :=
   ⟨fun h p (pp : 1 < p) d =>
-    h.elim (by rintro rfl ; cases not_le_of_lt pp (le_of_dvd (by decide) d)) fun h =>
+    h.elim (by rintro rfl; cases not_le_of_lt pp (le_of_dvd (by decide) d)) fun h =>
       le_trans h <| minFac_le_of_dvd pp d,
     fun H => le_minFac.2 fun p pp d => H p pp.two_le d⟩
 #align nat.le_min_fac' Nat.le_minFac'
@@ -681,7 +681,7 @@ theorem coprime_pow_primes {p q : ℕ} (n m : ℕ) (pp : Prime p) (pq : Prime q)
 #align nat.coprime_pow_primes Nat.coprime_pow_primes
 
 theorem coprime_or_dvd_of_prime {p} (pp : Prime p) (i : ℕ) : coprime p i ∨ p ∣ i := by
-  rw [pp.dvd_iff_not_coprime] ; apply em
+  rw [pp.dvd_iff_not_coprime]; apply em
 #align nat.coprime_or_dvd_of_prime Nat.coprime_or_dvd_of_prime
 
 theorem coprime_of_lt_prime {n p} (n_pos : 0 < n) (hlt : n < p) (pp : Prime p) : coprime p n :=
@@ -746,8 +746,8 @@ theorem succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul {p : ℕ} (p_prime : Prime p) {
 theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ _root_.Prime (p : ℤ) :=
   ⟨fun hp =>
     ⟨Int.coe_nat_ne_zero_iff_pos.2 hp.pos, mt Int.isUnit_iff_natAbs_eq.1 hp.ne_one, fun a b h => by
-      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h ;
-        rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
+      rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h
+      rwa [← Int.dvd_natAbs, Int.coe_nat_dvd, ← Int.dvd_natAbs, Int.coe_nat_dvd]⟩,
     fun hp =>
     Nat.prime_iff.2
       ⟨Int.coe_nat_ne_zero.1 hp.1,

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -336,12 +336,12 @@ theorem minFac_prime {n : ℕ} (n1 : n ≠ 1) : Prime (minFac n) :=
 #align nat.min_fac_prime Nat.minFac_prime
 
 theorem minFac_le_of_dvd {n : ℕ} : ∀ {m : ℕ}, 2 ≤ m → m ∣ n → minFac n ≤ m := by
-  by_cases n1 : n = 1 <;> [exact fun m2 _ => n1.symm ▸ le_trans (by decide) m2,
+  by_cases n1 : n = 1 <;> [exact fun m2 _ => n1.symm ▸ le_trans (by decide) m2;
     apply (minFac_has_prop n1).2.2]
 #align nat.min_fac_le_of_dvd Nat.minFac_le_of_dvd
 
 theorem minFac_pos (n : ℕ) : 0 < minFac n := by
-  by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide, exact (minFac_prime n1).pos]
+  by_cases n1 : n = 1 <;> [exact n1.symm ▸ (by decide); exact (minFac_prime n1).pos]
 #align nat.min_fac_pos Nat.minFac_pos
 
 theorem minFac_le {n : ℕ} (H : 0 < n) : minFac n ≤ n :=
@@ -638,8 +638,8 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
     -- Could be `wlog := hp.dvd_mul.1 pdvdxy using x y`, but that imports more than we want.
     suffices ∀ x' y' : ℕ, x' ≠ 1 → y' ≠ 1 → x' * y' = p ^ 2 → p ∣ x' → x' = p ∧ y' = p by
       obtain hx | hy := hp.dvd_mul.1 pdvdxy <;>
-        [skip, rw [And.comm]] <;>
-        [skip, rw [mul_comm] at h pdvdxy] <;>
+        [skip; rw [And.comm]] <;>
+        [skip; rw [mul_comm] at h pdvdxy] <;>
         apply this <;>
         assumption
     rintro x y hx hy h ⟨a, ha⟩

feat: port Data.Nat.PrimeNormNum (#3892)

Excluding computing Nat.factors, which requires a little bit of generalization of NormNum.Result.
It's a lot faster than in Lean 3:

2 ^ 19 - 1 is prime: Lean 3: 330ms, Lean 4: 36ms
2 ^ 25 - 39 is prime: Lean 3: 3300ms + multiple seconds type-checking, Lean 4 165ms + <100ms type-checking
(2 ^ 19 - 1) * (2 ^ 25 - 39) is not prime: Lean 3: 300ms, Lean 4: 90ms

Simplify the definition of Nat.minFac a bit
Added some remarks in the code, explaining why some parts are a bit more verbose than necessary. In these cases, simplifying the code would cause a significant slow-down (my first version of this port was 100x slower).
Note: Calling the function on larger numbers currently does cause panics/stack overflows in Lean 4

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

cf6dcb52

Diff

@@ -262,10 +262,8 @@ termination_by _ n k => sqrt n + 2 - k
 #align nat.min_fac_aux Nat.minFacAux
 
 /-- Returns the smallest prime factor of `n ≠ 1`. -/
-def minFac : ℕ → ℕ
-  | 0 => 2
-  | 1 => 1
-  | n + 2 => if 2 ∣ n then 2 else minFacAux (n + 2) 3
+def minFac (n : ℕ) : ℕ :=
+  if 2 ∣ n then 2 else minFacAux n 3
 #align nat.min_fac Nat.minFac
 
 @[simp]
@@ -278,11 +276,7 @@ theorem minFac_one : minFac 1 = 1 :=
   rfl
 #align nat.min_fac_one Nat.minFac_one
 
-theorem minFac_eq : ∀ n, minFac n = if 2 ∣ n then 2 else minFacAux n 3
-  | 0 => by simp
-  | 1 => by simp [show 2 ≠ 1 by decide]
-  | n + 2 => by
-    simp [minFac]
+theorem minFac_eq (n : ℕ) : minFac n = if 2 ∣ n then 2 else minFacAux n 3 := rfl
 #align nat.min_fac_eq Nat.minFac_eq
 
 private def minFacProp (n k : ℕ) :=

feat: add Mathlib.Tactic.Common, and import (#4056)

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

a4eaf1c4

Diff

@@ -16,7 +16,6 @@ import Mathlib.Data.Nat.Factorial.Basic
 import Mathlib.Data.Nat.GCD.Basic
 import Mathlib.Data.Nat.Sqrt
 import Mathlib.Order.Bounds.Basic
-import Mathlib.Tactic.ByContra
 
 /-!
 # Prime numbers

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -422,7 +422,6 @@ theorem minFac_sq_le_self {n : ℕ} (w : 0 < n) (h : ¬Prime n) : minFac n ^ 2 
     minFac n ^ 2 = minFac n * minFac n := sq (minFac n)
     _ ≤ n / minFac n * minFac n := Nat.mul_le_mul_right (minFac n) t
     _ ≤ n := div_mul_le_self n (minFac n)
-
 #align nat.min_fac_sq_le_self Nat.minFac_sq_le_self
 
 @[simp]
@@ -607,7 +606,6 @@ theorem Prime.pow_not_prime {x n : ℕ} (hn : 2 ≤ n) : ¬(x ^ n).Prime := fun
         x = x ^ 1 := (pow_one _).symm
         _ < x ^ n := Nat.pow_right_strictMono (hxn.symm ▸ hp.two_le) hn
         _ = x := hxn.symm
-
 #align nat.prime.pow_not_prime Nat.Prime.pow_not_prime
 
 theorem Prime.pow_not_prime' {x : ℕ} : ∀ {n : ℕ}, n ≠ 1 → ¬(x ^ n).Prime
@@ -665,7 +663,6 @@ theorem Prime.mul_eq_prime_sq_iff {x y p : ℕ} (hp : p.Prime) (hx : x ≠ 1) (h
       subst ha
       rw [sq, Nat.mul_right_eq_self_iff (Nat.mul_pos hp.pos hp.pos : 0 < a * a)] at h
       exact h
-
 #align nat.prime.mul_eq_prime_sq_iff Nat.Prime.mul_eq_prime_sq_iff
 
 theorem Prime.dvd_factorial : ∀ {n p : ℕ} (_ : Prime p), p ∣ n ! ↔ p ≤ n

feat: port Data.PNat.Factors (#1830)

Co-authored-by: qawbecrdtey <qawbecrdtey@naver.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Lukas Miaskiwskyi <lukas.mias@gmail.com>

948f2ea7

Diff

@@ -768,6 +768,7 @@ theorem prime_iff_prime_int {p : ℕ} : p.Prime ↔ _root_.Prime (p : ℤ) :=
 /-- The type of prime numbers -/
 def Primes :=
   { p : ℕ // p.Prime }
+  deriving DecidableEq
 #align nat.primes Nat.Primes
 
 namespace Primes

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -476,6 +476,7 @@ theorem dvd_of_forall_prime_mul_dvd {a b : ℕ}
   · apply one_dvd
   obtain ⟨p, hp⟩ := exists_prime_and_dvd ha
   exact _root_.trans (dvd_mul_left a p) (hdvd p hp.1 hp.2)
+#align nat.dvd_of_forall_prime_mul_dvd Nat.dvd_of_forall_prime_mul_dvd
 
 /-- Euclid's theorem on the **infinitude of primes**.
 Here given in the form: for every `n`, there exists a prime number `p ≥ n`. -/
@@ -582,6 +583,8 @@ theorem prime_iff {p : ℕ} : p.Prime ↔ _root_.Prime p :=
 #align nat.prime_iff Nat.prime_iff
 
 alias prime_iff ↔ Prime.prime _root_.Prime.nat_prime
+#align nat.prime.prime Nat.Prime.prime
+#align prime.nat_prime Prime.nat_prime
 
 -- Porting note: attributes `protected`, `nolint dup_namespace` removed

feat: port Data.Nat.Parity (#1661)

Backported in leanprover-community/mathlib#18221.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

234131a3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.prime
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
+! leanprover-community/mathlib commit 8631e2d5ea77f6c13054d9151d82b83069680cb1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -516,6 +516,10 @@ theorem Prime.odd_of_ne_two {p : ℕ} (hp : p.Prime) (h_two : p ≠ 2) : Odd p :
   hp.eq_two_or_odd'.resolve_left h_two
 #align nat.prime.odd_of_ne_two Nat.Prime.odd_of_ne_two
 
+theorem Prime.even_sub_one {p : ℕ} (hp : p.Prime) (h2 : p ≠ 2) : Even (p - 1) :=
+  let ⟨n, hn⟩ := hp.odd_of_ne_two h2; ⟨n, by rw [hn, Nat.add_sub_cancel, two_mul]⟩
+#align nat.prime.even_sub_one Nat.Prime.even_sub_one
+
 /-- A prime `p` satisfies `p % 2 = 1` if and only if `p ≠ 2`. -/
 theorem Prime.mod_two_eq_one_iff_ne_two {p : ℕ} [Fact p.Prime] : p % 2 = 1 ↔ p ≠ 2 := by
   refine' ⟨fun h hf => _, (Nat.Prime.eq_two_or_odd <| @Fact.out p.Prime _).resolve_left⟩

chore: fix most phantom #aligns (#1794)

3d3fb046

Diff

@@ -349,7 +349,7 @@ theorem minFac_le_of_dvd {n : ℕ} : ∀ {m : ℕ}, 2 ≤ m → m ∣ n → minF
 
 theorem minFac_pos (n : ℕ) : 0 < minFac n := by
   by_cases n1 : n = 1 <;> [exact n1.symm ▸ by decide, exact (minFac_prime n1).pos]
-#align nat.minFac_pos Nat.minFac_pos
+#align nat.min_fac_pos Nat.minFac_pos
 
 theorem minFac_le {n : ℕ} (H : 0 < n) : minFac n ≤ n :=
   le_of_dvd H (minFac_dvd n)

chore: format by line breaks with long lines (#1529)

This was done semi-automatically with some regular expressions in vim in contrast to the fully automatic https://github.com/leanprover-community/mathlib4/pull/1523.

Co-authored-by: Moritz Firsching <firsching@google.com>

1050066f

Diff

@@ -89,8 +89,8 @@ theorem Prime.ne_one {p : ℕ} (hp : p.Prime) : p ≠ 1 :=
   hp.one_lt.ne'
 #align nat.prime.ne_one Nat.Prime.ne_one
 
-theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m ∣ p) : m = 1 ∨ m = p :=
-  by
+theorem Prime.eq_one_or_self_of_dvd {p : ℕ} (pp : p.Prime) (m : ℕ) (hm : m ∣ p) :
+    m = 1 ∨ m = p := by
   obtain ⟨n, hn⟩ := hm
   have := pp.isUnit_or_isUnit hn
   rw [Nat.isUnit_iff, Nat.isUnit_iff] at this

chore: update SHA of Data.Nat.Prime (#1389)

... to the latest mathlib3 commit modifying the file. The changes have been ported in 412b151 has been ported in #1156.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

805f185a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.nat.prime
-! leanprover-community/mathlib commit 0743cc5d9d86bcd1bba10f480e948a257d65056f
+! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

feat: port Algebra.GCDMonoid.Basic (#1135)

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

bfe06a77

Diff

@@ -475,7 +475,7 @@ theorem dvd_of_forall_prime_mul_dvd {a b : ℕ}
   obtain rfl | ha := eq_or_ne a 1
   · apply one_dvd
   obtain ⟨p, hp⟩ := exists_prime_and_dvd ha
-  exact trans (dvd_mul_left a p) (hdvd p hp.1 hp.2)
+  exact _root_.trans (dvd_mul_left a p) (hdvd p hp.1 hp.2)
 
 /-- Euclid's theorem on the **infinitude of primes**.
 Here given in the form: for every `n`, there exists a prime number `p ≥ n`. -/

chore: fix casing per naming scheme (#1183)

Fix a lot of wrong casing mostly in the docstrings but also sometimes in def/theorem names. E.g. fin 2 --> Fin 2, add_monoid_hom --> AddMonoidHom

Remove \n from to_additive docstrings that were inserted by mathport.

Move files and directories with Gcd and Smul to GCD and SMul

71723d8b

Diff

@@ -13,7 +13,7 @@ import Mathlib.Algebra.Parity
 import Mathlib.Data.Int.Dvd.Basic
 import Mathlib.Data.Int.Units
 import Mathlib.Data.Nat.Factorial.Basic
-import Mathlib.Data.Nat.Gcd.Basic
+import Mathlib.Data.Nat.GCD.Basic
 import Mathlib.Data.Nat.Sqrt
 import Mathlib.Order.Bounds.Basic
 import Mathlib.Tactic.ByContra