data.num.prime
⟷
Mathlib.Data.Num.Prime
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
@@ -50,7 +50,7 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
(minFacAux n fuel k : ℕ) = Nat.minFacAux n k.bit1 :=
by
induction' fuel with fuel ih generalizing k <;> rw [min_fac_aux, Nat.minFacAux]
- · rw [if_pos]; rwa [zero_add, Nat.sqrt_lt] at h
+ · rw [if_pos]; rwa [zero_add, Nat.sqrt_lt] at h
rw [← mul_to_nat]; simp only [cast_lt, dvd_to_nat, ite_cast]
congr 2
rw [ih] <;> [congr; convert Nat.lt_succ_of_lt h using 1] <;>
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
-import Mathbin.Data.Num.Lemmas
-import Mathbin.Data.Nat.Prime
-import Mathbin.Tactic.Ring
+import Data.Num.Lemmas
+import Data.Nat.Prime
+import Tactic.Ring
#align_import data.num.prime from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.num.prime
-! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Num.Lemmas
import Mathbin.Data.Nat.Prime
import Mathbin.Tactic.Ring
+#align_import data.num.prime from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"
+
/-!
# Primality for binary natural numbers
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -53,10 +53,10 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
(minFacAux n fuel k : ℕ) = Nat.minFacAux n k.bit1 :=
by
induction' fuel with fuel ih generalizing k <;> rw [min_fac_aux, Nat.minFacAux]
- · rw [if_pos]; rwa [zero_add, Nat.sqrt_lt] at h
+ · rw [if_pos]; rwa [zero_add, Nat.sqrt_lt] at h
rw [← mul_to_nat]; simp only [cast_lt, dvd_to_nat, ite_cast]
congr 2
- rw [ih] <;> [congr ;convert Nat.lt_succ_of_lt h using 1] <;>
+ rw [ih] <;> [congr; convert Nat.lt_succ_of_lt h using 1] <;>
simp only [_root_.bit1, _root_.bit0, cast_bit1, cast_succ, Nat.succ_eq_add_one, add_assoc,
add_left_comm]
#align pos_num.min_fac_aux_to_nat PosNum.minFacAux_to_nat
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -53,8 +53,7 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
(minFacAux n fuel k : ℕ) = Nat.minFacAux n k.bit1 :=
by
induction' fuel with fuel ih generalizing k <;> rw [min_fac_aux, Nat.minFacAux]
- · rw [if_pos]
- rwa [zero_add, Nat.sqrt_lt] at h
+ · rw [if_pos]; rwa [zero_add, Nat.sqrt_lt] at h
rw [← mul_to_nat]; simp only [cast_lt, dvd_to_nat, ite_cast]
congr 2
rw [ih] <;> [congr ;convert Nat.lt_succ_of_lt h using 1] <;>
@@ -77,18 +76,13 @@ def minFac : PosNum → PosNum
theorem minFac_to_nat (n : PosNum) : (minFac n : ℕ) = Nat.minFac n :=
by
cases n; · rfl
- · rw [min_fac, Nat.minFac_eq, if_neg]
- swap
- · simp
- rw [min_fac_aux_to_nat]
- · rfl
+ · rw [min_fac, Nat.minFac_eq, if_neg]; swap; · simp
+ rw [min_fac_aux_to_nat]; · rfl
simp only [cast_one, cast_bit1]
rw [Nat.sqrt_lt]
convert lt_add_of_pos_right _ (by decide : (0 : ℕ) < (n + 4) * n + 8)
- unfold _root_.bit1 _root_.bit0
- ring
- · rw [min_fac, Nat.minFac_eq, if_pos]
- · rfl
+ unfold _root_.bit1 _root_.bit0; ring
+ · rw [min_fac, Nat.minFac_eq, if_pos]; · rfl
simp
#align pos_num.min_fac_to_nat PosNum.minFac_to_nat
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -57,7 +57,7 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
rwa [zero_add, Nat.sqrt_lt] at h
rw [← mul_to_nat]; simp only [cast_lt, dvd_to_nat, ite_cast]
congr 2
- rw [ih] <;> [congr , convert Nat.lt_succ_of_lt h using 1] <;>
+ rw [ih] <;> [congr ;convert Nat.lt_succ_of_lt h using 1] <;>
simp only [_root_.bit1, _root_.bit0, cast_bit1, cast_succ, Nat.succ_eq_add_one, add_assoc,
add_left_comm]
#align pos_num.min_fac_aux_to_nat PosNum.minFacAux_to_nat
mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
! This file was ported from Lean 3 source module data.num.prime
-! leanprover-community/mathlib commit 58581d0fe523063f5651df0619be2bf65012a94a
+! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.Tactic.Ring
/-!
# Primality for binary natural numbers
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file defines versions of `nat.min_fac` and `nat.prime` for `num` and `pos_num`. As with other
`num` definitions, they are not intended for general use (`nat` should be used instead of `num` in
most cases) but they can be used in contexts where kernel computation is required, such as proofs
mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0
@@ -31,6 +31,7 @@ Nevertheless, sometimes proof by computational reflection requires natural numbe
namespace PosNum
+#print PosNum.minFacAux /-
/-- Auxiliary function for computing the smallest prime factor of a `pos_num`. Unlike
`nat.min_fac_aux`, we use a natural number `fuel` variable that is set to an upper bound on the
number of iterations. It is initialized to the number `n` we are determining primality for. Even
@@ -42,7 +43,9 @@ def minFacAux (n : PosNum) : ℕ → PosNum → PosNum
| fuel + 1, k =>
if h : n < k.bit1 * k.bit1 then n else if k.bit1 ∣ n then k.bit1 else min_fac_aux fuel k.succ
#align pos_num.min_fac_aux PosNum.minFacAux
+-/
+#print PosNum.minFacAux_to_nat /-
theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.bit1) :
(minFacAux n fuel k : ℕ) = Nat.minFacAux n k.bit1 :=
by
@@ -55,14 +58,18 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
simp only [_root_.bit1, _root_.bit0, cast_bit1, cast_succ, Nat.succ_eq_add_one, add_assoc,
add_left_comm]
#align pos_num.min_fac_aux_to_nat PosNum.minFacAux_to_nat
+-/
+#print PosNum.minFac /-
/-- Returns the smallest prime factor of `n ≠ 1`. -/
def minFac : PosNum → PosNum
| 1 => 1
| bit0 n => 2
| bit1 n => minFacAux (bit1 n) n 1
#align pos_num.min_fac PosNum.minFac
+-/
+#print PosNum.minFac_to_nat /-
@[simp]
theorem minFac_to_nat (n : PosNum) : (minFac n : ℕ) = Nat.minFac n :=
by
@@ -81,13 +88,17 @@ theorem minFac_to_nat (n : PosNum) : (minFac n : ℕ) = Nat.minFac n :=
· rfl
simp
#align pos_num.min_fac_to_nat PosNum.minFac_to_nat
+-/
+#print PosNum.Prime /-
/-- Primality predicate for a `pos_num`. -/
@[simp]
def Prime (n : PosNum) : Prop :=
Nat.Prime n
#align pos_num.prime PosNum.Prime
+-/
+#print PosNum.decidablePrime /-
instance decidablePrime : DecidablePred PosNum.Prime
| 1 => Decidable.isFalse Nat.not_prime_one
| bit0 n =>
@@ -104,33 +115,42 @@ instance decidablePrime : DecidablePred PosNum.Prime
· exact Nat.bit0_le_bit1_iff.2 (to_nat_pos _)
rw [← min_fac_to_nat, to_nat_inj]; rfl)
#align pos_num.decidable_prime PosNum.decidablePrime
+-/
end PosNum
namespace Num
+#print Num.minFac /-
/-- Returns the smallest prime factor of `n ≠ 1`. -/
def minFac : Num → PosNum
| 0 => 2
| Pos n => n.minFac
#align num.min_fac Num.minFac
+-/
+#print Num.minFac_to_nat /-
@[simp]
theorem minFac_to_nat : ∀ n : Num, (minFac n : ℕ) = Nat.minFac n
| 0 => rfl
| Pos n => PosNum.minFac_to_nat _
#align num.min_fac_to_nat Num.minFac_to_nat
+-/
+#print Num.Prime /-
/-- Primality predicate for a `num`. -/
@[simp]
def Prime (n : Num) : Prop :=
Nat.Prime n
#align num.prime Num.Prime
+-/
+#print Num.decidablePrime /-
instance decidablePrime : DecidablePred Num.Prime
| 0 => Decidable.isFalse Nat.not_prime_zero
| Pos n => PosNum.decidablePrime n
#align num.decidable_prime Num.decidablePrime
+-/
end Num
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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>
@@ -76,7 +76,8 @@ theorem minFac_to_nat (n : PosNum) : (minFac n : ℕ) = Nat.minFac n := by
calc
(n : ℕ) + (n : ℕ) + 1 ≤ (n : ℕ) + (n : ℕ) + (n : ℕ) := by simp
_ = (n : ℕ) * (1 + 1 + 1) := by simp only [mul_add, mul_one]
- _ < _ := by simp [mul_lt_mul]
+ _ < _ := by
+ set_option simprocs false in simp [mul_lt_mul]
· rw [minFac, Nat.minFac_eq, if_pos]
· rfl
simp
@@ -2,16 +2,13 @@
Copyright (c) 2020 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.num.prime
-! leanprover-community/mathlib commit 58581d0fe523063f5651df0619be2bf65012a94a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Num.Lemmas
import Mathlib.Data.Nat.Prime
import Mathlib.Tactic.Ring
+#align_import data.num.prime from "leanprover-community/mathlib"@"58581d0fe523063f5651df0619be2bf65012a94a"
+
/-!
# Primality for binary natural numbers
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.
@@ -52,7 +52,7 @@ theorem minFacAux_to_nat {fuel : ℕ} {n k : PosNum} (h : Nat.sqrt n < fuel + k.
simp_rw [← mul_to_nat]
simp only [cast_lt, dvd_to_nat]
split_ifs <;> try rfl
- rw [ih] <;> [congr , convert Nat.lt_succ_of_lt h using 1] <;>
+ rw [ih] <;> [congr; convert Nat.lt_succ_of_lt h using 1] <;>
simp only [_root_.bit1, _root_.bit0, cast_bit1, cast_succ, Nat.succ_eq_add_one, add_assoc,
add_left_comm, ← one_add_one_eq_two]
#align pos_num.min_fac_aux_to_nat PosNum.minFacAux_to_nat
@@ -18,7 +18,7 @@ import Mathlib.Tactic.Ring
This file defines versions of `Nat.minFac` and `Nat.Prime` for `Num` and `PosNum`. As with other
`Num` definitions, they are not intended for general use (`Nat` should be used instead of `Num` in
most cases) but they can be used in contexts where kernel computation is required, such as proofs
-by `rfl` and `dec_trivial`, as well as in `#reduce`.
+by `rfl` and `decide`, as well as in `#reduce`.
The default decidable instance for `Nat.Prime` is optimized for VM evaluation, so it should be
preferred within `#eval` or in tactic execution, while for proofs the `norm_num` tactic can be used
The unported dependencies are