algebra.is_prime_pow
⟷
Mathlib.Algebra.IsPrimePow
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -119,7 +119,7 @@ theorem isPrimePow_nat_iff_bounded (n : ℕ) :
refine' Iff.symm ⟨fun ⟨p, _, k, _, hp, hk, hn⟩ => ⟨p, k, hp, hk, hn⟩, _⟩
rintro ⟨p, k, hp, hk, rfl⟩
refine' ⟨p, _, k, (Nat.lt_pow_self hp.one_lt _).le, hp, hk, rfl⟩
- simpa using Nat.pow_le_pow_of_le_right hp.pos hk
+ simpa using Nat.pow_le_pow_right hp.pos hk
#align is_prime_pow_nat_iff_bounded isPrimePow_nat_iff_bounded
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import Mathbin.Algebra.Associated
-import Mathbin.NumberTheory.Divisors
+import Algebra.Associated
+import NumberTheory.Divisors
#align_import algebra.is_prime_pow from "leanprover-community/mathlib"@"13a5329a8625701af92e9a96ffc90fa787fff24d"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -140,7 +140,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
-/
#print Nat.disjoint_divisors_filter_isPrimePow /-
-theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
+theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.Coprime b) :
Disjoint (a.divisors.filterₓ IsPrimePow) (b.divisors.filterₓ IsPrimePow) :=
by
simp only [Finset.disjoint_left, Finset.mem_filter, and_imp, Nat.mem_divisors, not_and]
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module algebra.is_prime_pow
-! leanprover-community/mathlib commit 13a5329a8625701af92e9a96ffc90fa787fff24d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Associated
import Mathbin.NumberTheory.Divisors
+#align_import algebra.is_prime_pow from "leanprover-community/mathlib"@"13a5329a8625701af92e9a96ffc90fa787fff24d"
+
/-!
# Prime powers
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -47,6 +47,7 @@ theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R) (k : ℕ), Prime
#align is_prime_pow_iff_pow_succ isPrimePow_iff_pow_succ
-/
+#print not_isPrimePow_zero /-
theorem not_isPrimePow_zero [NoZeroDivisors R] : ¬IsPrimePow (0 : R) :=
by
simp only [isPrimePow_def, not_exists, not_and', and_imp]
@@ -54,6 +55,7 @@ theorem not_isPrimePow_zero [NoZeroDivisors R] : ¬IsPrimePow (0 : R) :=
rw [pow_eq_zero hx]
simp
#align not_is_prime_pow_zero not_isPrimePow_zero
+-/
#print IsPrimePow.not_unit /-
theorem IsPrimePow.not_unit {n : R} (h : IsPrimePow n) : ¬IsUnit n :=
@@ -67,9 +69,11 @@ theorem IsUnit.not_isPrimePow {n : R} (h : IsUnit n) : ¬IsPrimePow n := fun h'
#align is_unit.not_is_prime_pow IsUnit.not_isPrimePow
-/
+#print not_isPrimePow_one /-
theorem not_isPrimePow_one : ¬IsPrimePow (1 : R) :=
isUnit_one.not_isPrimePow
#align not_is_prime_pow_one not_isPrimePow_one
+-/
#print Prime.isPrimePow /-
theorem Prime.isPrimePow {p : R} (hp : Prime p) : IsPrimePow p :=
@@ -84,13 +88,17 @@ theorem IsPrimePow.pow {n : R} (hn : IsPrimePow n) {k : ℕ} (hk : k ≠ 0) : Is
#align is_prime_pow.pow IsPrimePow.pow
-/
+#print IsPrimePow.ne_zero /-
theorem IsPrimePow.ne_zero [NoZeroDivisors R] {n : R} (h : IsPrimePow n) : n ≠ 0 := fun t =>
Eq.ndrec not_isPrimePow_zero t.symm h
#align is_prime_pow.ne_zero IsPrimePow.ne_zero
+-/
+#print IsPrimePow.ne_one /-
theorem IsPrimePow.ne_one {n : R} (h : IsPrimePow n) : n ≠ 1 := fun t =>
Eq.ndrec not_isPrimePow_one t.symm h
#align is_prime_pow.ne_one IsPrimePow.ne_one
+-/
section Nat
@@ -134,6 +142,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
#align is_prime_pow.dvd IsPrimePow.dvd
-/
+#print Nat.disjoint_divisors_filter_isPrimePow /-
theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
Disjoint (a.divisors.filterₓ IsPrimePow) (b.divisors.filterₓ IsPrimePow) :=
by
@@ -141,6 +150,7 @@ theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b)
rintro n han ha hn hbn hb -
exact hn.ne_one (Nat.eq_one_of_dvd_coprimes hab han hbn)
#align nat.disjoint_divisors_filter_prime_pow Nat.disjoint_divisors_filter_isPrimePow
+-/
#print IsPrimePow.two_le /-
theorem IsPrimePow.two_le : ∀ {n : ℕ}, IsPrimePow n → 2 ≤ n
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -27,12 +27,12 @@ variable {R : Type _} [CommMonoidWithZero R] (n p : R) (k : ℕ)
/-- `n` is a prime power if there is a prime `p` and a positive natural `k` such that `n` can be
written as `p^k`. -/
def IsPrimePow : Prop :=
- ∃ (p : R)(k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n
+ ∃ (p : R) (k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n
#align is_prime_pow IsPrimePow
-/
#print isPrimePow_def /-
-theorem isPrimePow_def : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n :=
+theorem isPrimePow_def : IsPrimePow n ↔ ∃ (p : R) (k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n :=
Iff.rfl
#align is_prime_pow_def isPrimePow_def
-/
@@ -40,7 +40,7 @@ theorem isPrimePow_def : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p ∧ 0 <
#print isPrimePow_iff_pow_succ /-
/-- An equivalent definition for prime powers: `n` is a prime power iff there is a prime `p` and a
natural `k` such that `n` can be written as `p^(k+1)`. -/
-theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p ∧ p ^ (k + 1) = n :=
+theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R) (k : ℕ), Prime p ∧ p ^ (k + 1) = n :=
(isPrimePow_def _).trans
⟨fun ⟨p, k, hp, hk, hn⟩ => ⟨_, _, hp, by rwa [Nat.sub_add_cancel hk]⟩, fun ⟨p, k, hp, hn⟩ =>
⟨_, _, hp, Nat.succ_pos', hn⟩⟩
@@ -124,7 +124,7 @@ instance {n : ℕ} : Decidable (IsPrimePow n) :=
#print IsPrimePow.dvd /-
theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m ≠ 1) : IsPrimePow m :=
by
- rw [isPrimePow_nat_iff] at hn⊢
+ rw [isPrimePow_nat_iff] at hn ⊢
rcases hn with ⟨p, k, hp, hk, rfl⟩
obtain ⟨i, hik, rfl⟩ := (Nat.dvd_prime_pow hp).1 hm
refine' ⟨p, i, hp, _, rfl⟩
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -47,12 +47,6 @@ theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p
#align is_prime_pow_iff_pow_succ isPrimePow_iff_pow_succ
-/
-/- warning: not_is_prime_pow_zero -> not_isPrimePow_zero is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))], Not (IsPrimePow.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R _inst_1)], Not (IsPrimePow.{u1} R _inst_1 (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align not_is_prime_pow_zero not_isPrimePow_zeroₓ'. -/
theorem not_isPrimePow_zero [NoZeroDivisors R] : ¬IsPrimePow (0 : R) :=
by
simp only [isPrimePow_def, not_exists, not_and', and_imp]
@@ -73,12 +67,6 @@ theorem IsUnit.not_isPrimePow {n : R} (h : IsUnit n) : ¬IsPrimePow n := fun h'
#align is_unit.not_is_prime_pow IsUnit.not_isPrimePow
-/
-/- warning: not_is_prime_pow_one -> not_isPrimePow_one is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R], Not (IsPrimePow.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R], Not (IsPrimePow.{u1} R _inst_1 (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align not_is_prime_pow_one not_isPrimePow_oneₓ'. -/
theorem not_isPrimePow_one : ¬IsPrimePow (1 : R) :=
isUnit_one.not_isPrimePow
#align not_is_prime_pow_one not_isPrimePow_one
@@ -96,22 +84,10 @@ theorem IsPrimePow.pow {n : R} (hn : IsPrimePow n) {k : ℕ} (hk : k ≠ 0) : Is
#align is_prime_pow.pow IsPrimePow.pow
-/
-/- warning: is_prime_pow.ne_zero -> IsPrimePow.ne_zero is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))] {n : R}, (IsPrimePow.{u1} R _inst_1 n) -> (Ne.{succ u1} R n (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] [_inst_2 : NoZeroDivisors.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1)))) (CommMonoidWithZero.toZero.{u1} R _inst_1)] {n : R}, (IsPrimePow.{u1} R _inst_1 n) -> (Ne.{succ u1} R n (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align is_prime_pow.ne_zero IsPrimePow.ne_zeroₓ'. -/
theorem IsPrimePow.ne_zero [NoZeroDivisors R] {n : R} (h : IsPrimePow n) : n ≠ 0 := fun t =>
Eq.ndrec not_isPrimePow_zero t.symm h
#align is_prime_pow.ne_zero IsPrimePow.ne_zero
-/- warning: is_prime_pow.ne_one -> IsPrimePow.ne_one is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] {n : R}, (IsPrimePow.{u1} R _inst_1 n) -> (Ne.{succ u1} R n (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))))
-but is expected to have type
- forall {R : Type.{u1}} [_inst_1 : CommMonoidWithZero.{u1} R] {n : R}, (IsPrimePow.{u1} R _inst_1 n) -> (Ne.{succ u1} R n (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Monoid.toOne.{u1} R (MonoidWithZero.toMonoid.{u1} R (CommMonoidWithZero.toMonoidWithZero.{u1} R _inst_1))))))
-Case conversion may be inaccurate. Consider using '#align is_prime_pow.ne_one IsPrimePow.ne_oneₓ'. -/
theorem IsPrimePow.ne_one {n : R} (h : IsPrimePow n) : n ≠ 1 := fun t =>
Eq.ndrec not_isPrimePow_one t.symm h
#align is_prime_pow.ne_one IsPrimePow.ne_one
@@ -158,12 +134,6 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
#align is_prime_pow.dvd IsPrimePow.dvd
-/
-/- warning: nat.disjoint_divisors_filter_prime_pow -> Nat.disjoint_divisors_filter_isPrimePow is a dubious translation:
-lean 3 declaration is
- forall {a : Nat} {b : Nat}, (Nat.coprime a b) -> (Disjoint.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat) (Finset.orderBot.{0} Nat) (Finset.filter.{0} Nat (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (a : Nat) => IsPrimePow.decidable a) (Nat.divisors a)) (Finset.filter.{0} Nat (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (a : Nat) => IsPrimePow.decidable a) (Nat.divisors b)))
-but is expected to have type
- forall {a : Nat} {b : Nat}, (Nat.coprime a b) -> (Disjoint.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{0} Nat) (Finset.filter.{0} Nat (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (a : Nat) => instDecidableIsPrimePowNatToCommMonoidWithZeroLinearOrderedCommMonoidWithZero a) (Nat.divisors a)) (Finset.filter.{0} Nat (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (a : Nat) => instDecidableIsPrimePowNatToCommMonoidWithZeroLinearOrderedCommMonoidWithZero a) (Nat.divisors b)))
-Case conversion may be inaccurate. Consider using '#align nat.disjoint_divisors_filter_prime_pow Nat.disjoint_divisors_filter_isPrimePowₓ'. -/
theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
Disjoint (a.divisors.filterₓ IsPrimePow) (b.divisors.filterₓ IsPrimePow) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
The names for lemmas about monotonicity of (a ^ ·)
and (· ^ n)
were a mess. This PR tidies up everything related by following the naming convention for (a * ·)
and (· * b)
. Namely, (a ^ ·)
is pow_right
and (· ^ n)
is pow_left
in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.
Algebra.GroupPower.Order
pow_mono
→ pow_right_mono
pow_le_pow
→ pow_le_pow_right
pow_le_pow_of_le_left
→ pow_le_pow_left
pow_lt_pow_of_lt_left
→ pow_lt_pow_left
strictMonoOn_pow
→ pow_left_strictMonoOn
pow_strictMono_right
→ pow_right_strictMono
pow_lt_pow
→ pow_lt_pow_right
pow_lt_pow_iff
→ pow_lt_pow_iff_right
pow_le_pow_iff
→ pow_le_pow_iff_right
self_lt_pow
→ lt_self_pow
strictAnti_pow
→ pow_right_strictAnti
pow_lt_pow_iff_of_lt_one
→ pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one
→ pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow
→ lt_of_pow_lt_pow_left
le_of_pow_le_pow
→ le_of_pow_le_pow_left
pow_lt_pow₀
→ pow_lt_pow_right₀
Algebra.GroupPower.CovariantClass
pow_le_pow_of_le_left'
→ pow_le_pow_left'
nsmul_le_nsmul_of_le_right
→ nsmul_le_nsmul_right
pow_lt_pow'
→ pow_lt_pow_right'
nsmul_lt_nsmul
→ nsmul_lt_nsmul_left
pow_strictMono_left
→ pow_right_strictMono'
nsmul_strictMono_right
→ nsmul_left_strictMono
StrictMono.pow_right'
→ StrictMono.pow_const
StrictMono.nsmul_left
→ StrictMono.const_nsmul
pow_strictMono_right'
→ pow_left_strictMono
nsmul_strictMono_left
→ nsmul_right_strictMono
Monotone.pow_right
→ Monotone.pow_const
Monotone.nsmul_left
→ Monotone.const_nsmul
lt_of_pow_lt_pow'
→ lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul
→ lt_of_nsmul_lt_nsmul_right
pow_le_pow'
→ pow_le_pow_right'
nsmul_le_nsmul
→ nsmul_le_nsmul_left
pow_le_pow_of_le_one'
→ pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos
→ nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow'
→ le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul'
→ le_of_nsmul_le_nsmul_right'
pow_le_pow_iff'
→ pow_le_pow_iff_right'
nsmul_le_nsmul_iff
→ nsmul_le_nsmul_iff_left
pow_lt_pow_iff'
→ pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff
→ nsmul_lt_nsmul_iff_left
Data.Nat.Pow
Nat.pow_lt_pow_of_lt_left
→ Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left
→ Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left
→ Nat.pow_lt_pow_iff_left
pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left
to have the correct name since Nat.pow_le_pow_of_le_left
is in Std.Nat.pow_le_pow_right
to have the correct name since Nat.pow_le_pow_of_le_right
is in Std.self_le_pow
was a duplicate of le_self_pow
.Nat.pow_lt_pow_of_lt_right
is defeq to pow_lt_pow_right
.Nat.pow_right_strictMono
is defeq to pow_right_strictMono
.Nat.pow_le_iff_le_right
is defeq to pow_le_pow_iff_right
.Nat.pow_lt_iff_lt_right
is defeq to pow_lt_pow_iff_right
.0 < n
or 1 ≤ n
to n ≠ 0
.Nat
lemmas have been protected
.@@ -88,7 +88,7 @@ theorem isPrimePow_nat_iff_bounded (n : ℕ) :
rintro ⟨p, k, hp, hk, rfl⟩
refine' ⟨p, _, k, (Nat.lt_pow_self hp.one_lt _).le, hp, hk, rfl⟩
conv => { lhs; rw [← (pow_one p)] }
- exact (Nat.pow_le_iff_le_right hp.two_le).mpr hk
+ exact pow_le_pow_right hp.one_lt.le hk
#align is_prime_pow_nat_iff_bounded isPrimePow_nat_iff_bounded
instance {n : ℕ} : Decidable (IsPrimePow n) :=
@@ -87,7 +87,7 @@ theorem isPrimePow_nat_iff_bounded (n : ℕ) :
refine' Iff.symm ⟨fun ⟨p, _, k, _, hp, hk, hn⟩ => ⟨p, k, hp, hk, hn⟩, _⟩
rintro ⟨p, k, hp, hk, rfl⟩
refine' ⟨p, _, k, (Nat.lt_pow_self hp.one_lt _).le, hp, hk, rfl⟩
- conv => { lhs; rw [←(pow_one p)] }
+ conv => { lhs; rw [← (pow_one p)] }
exact (Nat.pow_le_iff_le_right hp.two_le).mpr hk
#align is_prime_pow_nat_iff_bounded isPrimePow_nat_iff_bounded
This is the supremum of
along with some minor fixes from failures on nightly-testing as Mathlib master
is merged into it.
Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.
I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0
branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.
In particular this includes adjustments for the Lean PRs
We can get rid of all the
local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)
macros across Mathlib (and in any projects that want to write natural number powers of reals).
Changes the default behaviour of simp
to (config := {decide := false})
. This makes simp
(and consequentially norm_num
) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp
or norm_num
to decide
or rfl
, or adding (config := {decide := true})
.
This changed the behaviour of simp
so that simp [f]
will only unfold "fully applied" occurrences of f
. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true })
. We may in future add a syntax for this, e.g. simp [!f]
; please provide feedback! In the meantime, we have made the following changes:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[eqns]
to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp
and Function.flip
.This change in Lean may require further changes down the line (e.g. adding the !f
syntax, and/or upstreaming the special treatment for Function.comp
and Function.flip
, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>
@@ -101,7 +101,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
refine' ⟨p, i, hp, _, rfl⟩
apply Nat.pos_of_ne_zero
rintro rfl
- simp only [pow_zero, ne_eq] at hm₁
+ simp only [pow_zero, ne_eq, not_true_eq_false] at hm₁
#align is_prime_pow.dvd IsPrimePow.dvd
theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.Coprime b) :
@@ -104,7 +104,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
simp only [pow_zero, ne_eq] at hm₁
#align is_prime_pow.dvd IsPrimePow.dvd
-theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
+theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.Coprime b) :
Disjoint (a.divisors.filter IsPrimePow) (b.divisors.filter IsPrimePow) := by
simp only [Finset.disjoint_left, Finset.mem_filter, and_imp, Nat.mem_divisors, not_and]
rintro n han _ha hn hbn _hb -
@@ -104,7 +104,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
simp only [pow_zero, ne_eq] at hm₁
#align is_prime_pow.dvd IsPrimePow.dvd
-theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.Coprime b) :
+theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
Disjoint (a.divisors.filter IsPrimePow) (b.divisors.filter IsPrimePow) := by
simp only [Finset.disjoint_left, Finset.mem_filter, and_imp, Nat.mem_divisors, not_and]
rintro n han _ha hn hbn _hb -
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>
@@ -104,7 +104,7 @@ theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m
simp only [pow_zero, ne_eq] at hm₁
#align is_prime_pow.dvd IsPrimePow.dvd
-theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.coprime b) :
+theorem Nat.disjoint_divisors_filter_isPrimePow {a b : ℕ} (hab : a.Coprime b) :
Disjoint (a.divisors.filter IsPrimePow) (b.divisors.filter IsPrimePow) := by
simp only [Finset.disjoint_left, Finset.mem_filter, and_imp, Nat.mem_divisors, not_and]
rintro n han _ha hn hbn _hb -
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -15,7 +15,7 @@ This file deals with prime powers: numbers which are positive integer powers of
-/
-variable {R : Type _} [CommMonoidWithZero R] (n p : R) (k : ℕ)
+variable {R : Type*} [CommMonoidWithZero R] (n p : R) (k : ℕ)
/-- `n` is a prime power if there is a prime `p` and a positive natural `k` such that `n` can be
written as `p^k`. -/
@@ -2,15 +2,12 @@
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module algebra.is_prime_pow
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Associated
import Mathlib.NumberTheory.Divisors
+#align_import algebra.is_prime_pow from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
/-!
# Prime powers
at
and goals (#5387)
Changes are of the form
some_tactic at h⊢
-> some_tactic at h ⊢
some_tactic at h
-> some_tactic at h
@@ -98,7 +98,7 @@ instance {n : ℕ} : Decidable (IsPrimePow n) :=
decidable_of_iff' _ (isPrimePow_nat_iff_bounded n)
theorem IsPrimePow.dvd {n m : ℕ} (hn : IsPrimePow n) (hm : m ∣ n) (hm₁ : m ≠ 1) : IsPrimePow m := by
- rw [isPrimePow_nat_iff] at hn⊢
+ rw [isPrimePow_nat_iff] at hn ⊢
rcases hn with ⟨p, k, hp, _hk, rfl⟩
obtain ⟨i, hik, rfl⟩ := (Nat.dvd_prime_pow hp).1 hm
refine' ⟨p, i, hp, _, rfl⟩
@@ -23,16 +23,16 @@ variable {R : Type _} [CommMonoidWithZero R] (n p : R) (k : ℕ)
/-- `n` is a prime power if there is a prime `p` and a positive natural `k` such that `n` can be
written as `p^k`. -/
def IsPrimePow : Prop :=
- ∃ (p : R)(k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n
+ ∃ (p : R) (k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n
#align is_prime_pow IsPrimePow
-theorem isPrimePow_def : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n :=
+theorem isPrimePow_def : IsPrimePow n ↔ ∃ (p : R) (k : ℕ), Prime p ∧ 0 < k ∧ p ^ k = n :=
Iff.rfl
#align is_prime_pow_def isPrimePow_def
/-- An equivalent definition for prime powers: `n` is a prime power iff there is a prime `p` and a
natural `k` such that `n` can be written as `p^(k+1)`. -/
-theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R)(k : ℕ), Prime p ∧ p ^ (k + 1) = n :=
+theorem isPrimePow_iff_pow_succ : IsPrimePow n ↔ ∃ (p : R) (k : ℕ), Prime p ∧ p ^ (k + 1) = n :=
(isPrimePow_def _).trans
⟨fun ⟨p, k, hp, hk, hn⟩ => ⟨_, _, hp, by rwa [Nat.sub_add_cancel hk]⟩, fun ⟨p, k, hp, hn⟩ =>
⟨_, _, hp, Nat.succ_pos', hn⟩⟩
@@ -129,4 +129,3 @@ theorem IsPrimePow.one_lt {n : ℕ} (h : IsPrimePow n) : 1 < n :=
#align is_prime_pow.one_lt IsPrimePow.one_lt
end Nat
-
The unported dependencies are