data.num.bitwise | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

f7fc89d5

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

68d1483e

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
 import Data.Num.Basic
-import Data.Bitvec.Core
+import Data.BitVec.Defs
 
 #align_import data.num.bitwise from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"

68d1483e

bump to nightly-2023-10-21-06

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

a2dc86f8

Diff

@@ -137,7 +137,7 @@ namespace Num
 def or : Num → Num → Num
   | 0, q => q
   | p, 0 => p
-  | Pos p, Pos q => pos (p.lor' q)
+  | Pos p, Pos q => pos (p.lor q)
 #align num.lor OrOp.or
 -/
 
@@ -146,7 +146,7 @@ def or : Num → Num → Num
 def land : Num → Num → Num
   | 0, q => 0
   | p, 0 => 0
-  | Pos p, Pos q => p.land' q
+  | Pos p, Pos q => p.land q
 #align num.land Num.land
 -/
 
@@ -162,7 +162,7 @@ def land : Num → Num → Num
 def ldiff : Num → Num → Num
   | 0, q => 0
   | p, 0 => p
-  | Pos p, Pos q => p.ldiff' q
+  | Pos p, Pos q => p.ldiff q
 #align num.ldiff Num.ldiff
 -/
 
@@ -171,7 +171,7 @@ def ldiff : Num → Num → Num
 def lxor : Num → Num → Num
   | 0, q => q
   | p, 0 => p
-  | Pos p, Pos q => p.lxor' q
+  | Pos p, Pos q => p.xor q
 #align num.lxor Num.lxor
 -/

68d1483e

bump to nightly-2023-10-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/19c869efa56bbb8b500f2724c0b77261edbfa28c

e9c33fc8

Diff

@@ -132,13 +132,13 @@ end PosNum
 
 namespace Num
 
-#print Num.lor /-
+#print OrOp.or /-
 /-- Bitwise "or" for `num`. -/
-def lor : Num → Num → Num
+def or : Num → Num → Num
   | 0, q => q
   | p, 0 => p
   | Pos p, Pos q => pos (p.lor' q)
-#align num.lor Num.lor
+#align num.lor OrOp.or
 -/
 
 #print Num.land /-

68d1483e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import Mathbin.Data.Num.Basic
-import Mathbin.Data.Bitvec.Core
+import Data.Num.Basic
+import Data.Bitvec.Core
 
 #align_import data.num.bitwise from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"

68d1483e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2014 Microsoft Corporation. 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.bitwise
-! leanprover-community/mathlib commit 68d1483e8a718ec63219f0e227ca3f0140361086
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Num.Basic
 import Mathbin.Data.Bitvec.Core
 
+#align_import data.num.bitwise from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
+
 /-!
 # Bitwise operations using binary representation of integers

68d1483e

bump to nightly-2023-07-03-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

ac5018f5

Diff

@@ -514,7 +514,7 @@ def bits : SNum → ∀ n, Vector Bool n
 #print SNum.cAdd /-
 def cAdd : SNum → SNum → Bool → SNum :=
   rec' (fun a p c => czAdd c a p) fun a p IH =>
-    rec' (fun b c => czAdd c b (a::p)) fun b q _ c => Bitvec.xor3 a b c::IH q (Bitvec.carry a b c)
+    rec' (fun b c => czAdd c b (a::p)) fun b q _ c => Bool.xor3 a b c::IH q (Bool.carry a b c)
 #align snum.cadd SNum.cAdd
 -/

68d1483e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -271,7 +271,6 @@ and the negation of the MSB is sign-extended to all higher bits.
 
 namespace NzsNum
 
--- mathport name: nznum.bit
 notation a "::" b => bit a b
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -294,7 +293,6 @@ def not : NzsNum → NzsNum
 #align nzsnum.not NzsNum.not
 -/
 
--- mathport name: «expr~ »
 prefix:100 "~" => not
 
 #print NzsNum.bit0 /-
@@ -353,7 +351,6 @@ def not : SNum → SNum
 #align snum.not SNum.not
 -/
 
--- mathport name: snum.not
 prefix:0 "~" => not
 
 #print SNum.bit /-
@@ -365,7 +362,6 @@ def bit : Bool → SNum → SNum
 #align snum.bit SNum.bit
 -/
 
--- mathport name: snum.bit
 notation a "::" b => bit a b
 
 #print SNum.bit0 /-
@@ -389,8 +385,10 @@ theorem bit_zero (b) : (b::zero b) = zero b := by cases b <;> rfl
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print SNum.bit_one /-
 theorem bit_one (b) : (b::zero (not b)) = msb b := by cases b <;> rfl
 #align snum.bit_one SNum.bit_one
+-/
 
 end SNum

68d1483e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -388,12 +388,6 @@ theorem bit_zero (b) : (b::zero b) = zero b := by cases b <;> rfl
 #align snum.bit_zero SNum.bit_zero
 -/
 
-/- warning: snum.bit_one -> SNum.bit_one is a dubious translation:
-lean 3 declaration is
-  forall (b : Bool), Eq.{1} SNum (SNum.bit b (SNum.zero (not b))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NzsNum SNum (HasLiftT.mk.{1, 1} NzsNum SNum (CoeTCₓ.coe.{1, 1} NzsNum SNum (coeBase.{1, 1} NzsNum SNum SNum.hasCoe))) (NzsNum.msb b))
-but is expected to have type
-  forall (b : Bool), Eq.{1} SNum (SNum.bit b (SNum.zero (Decidable.decide (Not (Eq.{1} Bool b Bool.true)) (instDecidableNot (Eq.{1} Bool b Bool.true) (instDecidableEqBool b Bool.true))))) (SNum.nz (NzsNum.msb b))
-Case conversion may be inaccurate. Consider using '#align snum.bit_one SNum.bit_oneₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem bit_one (b) : (b::zero (not b)) = msb b := by cases b <;> rfl
 #align snum.bit_one SNum.bit_one

68d1483e

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -140,7 +140,7 @@ namespace Num
 def lor : Num → Num → Num
   | 0, q => q
   | p, 0 => p
-  | Pos p, Pos q => pos (p.lor q)
+  | Pos p, Pos q => pos (p.lor' q)
 #align num.lor Num.lor
 -/
 
@@ -149,7 +149,7 @@ def lor : Num → Num → Num
 def land : Num → Num → Num
   | 0, q => 0
   | p, 0 => 0
-  | Pos p, Pos q => p.land q
+  | Pos p, Pos q => p.land' q
 #align num.land Num.land
 -/

68d1483e

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f7fc89d5

chore: remove mathport name: <expression> lines (#11928)

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

11431c65

Diff

@@ -278,7 +278,6 @@ and the negation of the MSB is sign-extended to all higher bits.
 
 namespace NzsNum
 
--- mathport name: nznum.bit
 @[inherit_doc]
 scoped notation a "::" b => bit a b
 
@@ -295,7 +294,6 @@ def not : NzsNum → NzsNum
   | b :: p => Not b :: not p
 #align nzsnum.not NzsNum.not
 
--- mathport name: «expr~ »
 @[inherit_doc]
 scoped prefix:100 "~" => not
 
@@ -342,7 +340,6 @@ def not : SNum → SNum
 #align snum.not SNum.not
 
 -- Porting note: Defined `priority` so that `~1 : SNum` is unambiguous.
--- mathport name: snum.not
 @[inherit_doc]
 scoped prefix:100 (priority := default + 1) "~" => not
 
@@ -353,7 +350,6 @@ def bit : Bool → SNum → SNum
   | b, nz p => p.bit b
 #align snum.bit SNum.bit
 
--- mathport name: snum.bit
 @[inherit_doc]
 scoped notation a "::" b => bit a b

f7fc89d5

feat(Data/Num): use bitwise notation (#7593)

This enables the existing |||, &&&, <<<, >>>, and ^^^ notation for Num and PosNum, and makes them simp-normal form.

11458852

Diff

@@ -34,6 +34,10 @@ def lor : PosNum → PosNum → PosNum
   | bit1 p, bit1 q => bit1 (lor p q)
 #align pos_num.lor PosNum.lor
 
+instance : OrOp PosNum where or := PosNum.lor
+
+@[simp] lemma lor_eq_or (p q : PosNum) : p.lor q = p ||| q := rfl
+
 /-- Bitwise "and" for `PosNum`. -/
 def land : PosNum → PosNum → Num
   | 1, bit0 _ => 0
@@ -46,6 +50,10 @@ def land : PosNum → PosNum → Num
   | bit1 p, bit1 q => Num.bit1 (land p q)
 #align pos_num.land PosNum.land
 
+instance : HAnd PosNum PosNum Num where hAnd := PosNum.land
+
+@[simp] lemma land_eq_and (p q : PosNum) : p.land q = p &&& q := rfl
+
 /-- Bitwise `fun a b ↦ a && !b` for `PosNum`. For example, `ldiff 5 9 = 4`:
 ```
  101
@@ -78,6 +86,10 @@ def lxor : PosNum → PosNum → Num
   | bit1 p, bit1 q => Num.bit0 (lxor p q)
 #align pos_num.lxor PosNum.lxor
 
+instance : HXor PosNum PosNum Num where hXor := PosNum.lxor
+
+@[simp] lemma lxor_eq_xor (p q : PosNum) : p.lxor q = p ^^^ q := rfl
+
 /-- `a.testBit n` is `true` iff the `n`-th bit (starting from the LSB) in the binary representation
       of `a` is active. If the size of `a` is less than `n`, this evaluates to `false`. -/
 def testBit : PosNum → Nat → Bool
@@ -102,9 +114,14 @@ def shiftl : PosNum → Nat → PosNum
   | p, n + 1 => shiftl p.bit0 n
 #align pos_num.shiftl PosNum.shiftl
 
+instance : HShiftLeft PosNum Nat PosNum where hShiftLeft := PosNum.shiftl
+
+@[simp] lemma shiftl_eq_shiftLeft (p : PosNum) (n : Nat) : p.shiftl n = p <<< n := rfl
+
+
 -- Porting note: `PosNum.shiftl` is defined as tail-recursive in Lean4.
 --               This theorem ensures the definition is same to one in Lean3.
-theorem shiftl_succ_eq_bit0_shiftl : ∀ (p : PosNum) (n : Nat), shiftl p n.succ = bit0 (shiftl p n)
+theorem shiftl_succ_eq_bit0_shiftl : ∀ (p : PosNum) (n : Nat), p <<< n.succ = bit0 (p <<< n)
   | _, 0       => rfl
   | p, .succ n => shiftl_succ_eq_bit0_shiftl p.bit0 n
 
@@ -116,24 +133,36 @@ def shiftr : PosNum → Nat → Num
   | bit1 p, n + 1 => shiftr p n
 #align pos_num.shiftr PosNum.shiftr
 
+instance : HShiftRight PosNum Nat Num where hShiftRight := PosNum.shiftr
+
+@[simp] lemma shiftr_eq_shiftRight (p : PosNum) (n : Nat) : p.shiftr n = p >>> n := rfl
+
 end PosNum
 
 namespace Num
 
 /-- Bitwise "or" for `Num`. -/
-def lor : Num → Num → Num
+protected def lor : Num → Num → Num
   | 0, q => q
   | p, 0 => p
-  | pos p, pos q => pos (p.lor q)
-#align num.lor Num.lor
+  | pos p, pos q => pos (p ||| q)
+#align num.lor OrOp.or
+
+instance : OrOp Num where or := Num.lor
+
+@[simp] lemma lor_eq_or (p q : Num) : p.lor q = p ||| q := rfl
 
 /-- Bitwise "and" for `Num`. -/
 def land : Num → Num → Num
   | 0, _ => 0
   | _, 0 => 0
-  | pos p, pos q => p.land q
+  | pos p, pos q => p &&& q
 #align num.land Num.land
 
+instance : AndOp Num where and := Num.land
+
+@[simp] lemma land_eq_and (p q : Num) : p.land q = p &&& q := rfl
+
 /-- Bitwise `fun a b ↦ a && !b` for `Num`. For example, `ldiff 5 9 = 4`:
 ```
  101
@@ -152,21 +181,33 @@ def ldiff : Num → Num → Num
 def lxor : Num → Num → Num
   | 0, q => q
   | p, 0 => p
-  | pos p, pos q => p.lxor q
+  | pos p, pos q => p ^^^ q
 #align num.lxor Num.lxor
 
+instance : Xor Num where xor := Num.lxor
+
+@[simp] lemma lxor_eq_xor (p q : Num) : p.lxor q = p ^^^ q := rfl
+
 /-- Left-shift the binary representation of a `Num`. -/
 def shiftl : Num → Nat → Num
   | 0, _ => 0
-  | pos p, n => pos (p.shiftl n)
+  | pos p, n => pos (p <<< n)
 #align num.shiftl Num.shiftl
 
+instance : HShiftLeft Num Nat Num where hShiftLeft := Num.shiftl
+
+@[simp] lemma shiftl_eq_shiftLeft (p : Num) (n : Nat) : p.shiftl n = p <<< n := rfl
+
 /-- Right-shift the binary representation of a `Num`. -/
 def shiftr : Num → Nat → Num
   | 0, _ => 0
-  | pos p, n => p.shiftr n
+  | pos p, n => p >>> n
 #align num.shiftr Num.shiftr
 
+instance : HShiftRight Num Nat Num where hShiftRight := Num.shiftr
+
+@[simp] lemma shiftr_eq_shiftRight (p : Num) (n : Nat) : p.shiftr n = p >>> n := rfl
+
 /-- `a.testBit n` is `true` iff the `n`-th bit (starting from the LSB) in the binary representation
       of `a` is active. If the size of `a` is less than `n`, this evaluates to `false`. -/
 def testBit : Num → Nat → Bool

f7fc89d5

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

@@ -340,7 +340,7 @@ open SNum
 
 /-- A dependent induction principle for `NzsNum`, with base cases
       `0 : SNum` and `(-1) : SNum`. -/
-def drec' {C : SNum → Sort _} (z : ∀ b, C (SNum.zero b)) (s : ∀ b p, C p → C (b :: p)) :
+def drec' {C : SNum → Sort*} (z : ∀ b, C (SNum.zero b)) (s : ∀ b p, C p → C (b :: p)) :
     ∀ p : NzsNum, C p
   | msb b => by rw [← bit_one]; exact s b (SNum.zero (Not b)) (z (Not b))
   | bit b p => s b p (drec' z s p)
@@ -366,7 +366,7 @@ def tail : SNum → SNum
 #align snum.tail SNum.tail
 
 /-- A dependent induction principle for `SNum` which avoids relying on `NzsNum`. -/
-def drec' {C : SNum → Sort _} (z : ∀ b, C (SNum.zero b)) (s : ∀ b p, C p → C (b :: p)) : ∀ p, C p
+def drec' {C : SNum → Sort*} (z : ∀ b, C (SNum.zero b)) (s : ∀ b p, C p → C (b :: p)) : ∀ p, C p
   | zero b => z b
   | nz p => p.drec' z s
 #align snum.drec' SNum.drec'

f7fc89d5

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

@@ -2,16 +2,13 @@
 Copyright (c) 2014 Microsoft Corporation. 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.bitwise
-! 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.Data.Num.Basic
 import Mathlib.Data.Bool.Basic
 import Mathlib.Data.Vector.Basic
 
+#align_import data.num.bitwise from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
 /-!
 # Bitwise operations using binary representation of integers

f7fc89d5

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

@@ -345,7 +345,7 @@ open SNum
       `0 : SNum` and `(-1) : SNum`. -/
 def drec' {C : SNum → Sort _} (z : ∀ b, C (SNum.zero b)) (s : ∀ b p, C p → C (b :: p)) :
     ∀ p : NzsNum, C p
-  | msb b => by rw [← bit_one] ; exact s b (SNum.zero (Not b)) (z (Not b))
+  | msb b => by rw [← bit_one]; exact s b (SNum.zero (Not b)) (z (Not b))
   | bit b p => s b p (drec' z s p)
 #align nzsnum.drec' NzsNum.drec'

f7fc89d5

fix: move two trivial theorems over booleans to Bool/Basic (#5630)

This eliminates an unnecessary dependency from Num.Bitwise to Bitvec.Defs.

56e243fb

Diff

@@ -9,7 +9,8 @@ Authors: Mario Carneiro
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Num.Basic
-import Mathlib.Data.Bitvec.Defs
+import Mathlib.Data.Bool.Basic
+import Mathlib.Data.Vector.Basic
 
 /-!
 # Bitwise operations using binary representation of integers
@@ -426,7 +427,7 @@ def bits : SNum → ∀ n, Vector Bool n
       `a` represents a carry bit. -/
 def cAdd : SNum → SNum → Bool → SNum :=
   rec' (fun a p c ↦ czAdd c a p) fun a p IH ↦
-    rec' (fun b c ↦ czAdd c b (a :: p)) fun b q _ c ↦ Bitvec.xor3 a b c :: IH q (Bitvec.carry a b c)
+    rec' (fun b c ↦ czAdd c b (a :: p)) fun b q _ c ↦ Bool.xor3 a b c :: IH q (Bool.carry a b c)
 #align snum.cadd SNum.cAdd
 
 /-- Add two `SNum`s. -/

f7fc89d5

refactor: Defs and Lemmas files for Bitvec (#4899)

The Core file was just dumped from Lean3 core. I've split it into Defs and Lemmas in the style of the List folder for example.

a55642fc

Diff

@@ -9,7 +9,7 @@ Authors: Mario Carneiro
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Num.Basic
-import Mathlib.Data.Bitvec.Core
+import Mathlib.Data.Bitvec.Defs
 
 /-!
 # Bitwise operations using binary representation of integers

f7fc89d5

refactor: Add a new theorem for PosNum.shiftl (#2783)

59b0a41e

Diff

@@ -104,6 +104,12 @@ def shiftl : PosNum → Nat → PosNum
   | p, n + 1 => shiftl p.bit0 n
 #align pos_num.shiftl PosNum.shiftl
 
+-- Porting note: `PosNum.shiftl` is defined as tail-recursive in Lean4.
+--               This theorem ensures the definition is same to one in Lean3.
+theorem shiftl_succ_eq_bit0_shiftl : ∀ (p : PosNum) (n : Nat), shiftl p n.succ = bit0 (shiftl p n)
+  | _, 0       => rfl
+  | p, .succ n => shiftl_succ_eq_bit0_shiftl p.bit0 n
+
 /-- Right-shift the binary representation of a `PosNum`. -/
 def shiftr : PosNum → Nat → Num
   | p, 0 => Num.pos p

f7fc89d5

fix: avoid global notation overloading (#1951)

This is currently breaking mathport.

d0c49172

Diff

@@ -235,7 +235,7 @@ namespace NzsNum
 
 -- mathport name: nznum.bit
 @[inherit_doc]
-notation a "::" b => bit a b
+scoped notation a "::" b => bit a b
 
 /-- Sign of a `NzsNum`. -/
 def sign : NzsNum → Bool
@@ -252,7 +252,7 @@ def not : NzsNum → NzsNum
 
 -- mathport name: «expr~ »
 @[inherit_doc]
-prefix:100 "~" => not
+scoped prefix:100 "~" => not
 
 /-- Add an inactive bit at the end of a `NzsNum`. This mimics `PosNum.bit0`. -/
 def bit0 : NzsNum → NzsNum :=
@@ -299,7 +299,7 @@ def not : SNum → SNum
 -- Porting note: Defined `priority` so that `~1 : SNum` is unambiguous.
 -- mathport name: snum.not
 @[inherit_doc]
-prefix:100 (priority := default + 1) "~" => not
+scoped prefix:100 (priority := default + 1) "~" => not
 
 /-- Add a bit at the end of a `SNum`. This mimics `NzsNum.bit`. -/
 @[match_pattern]
@@ -310,7 +310,7 @@ def bit : Bool → SNum → SNum
 
 -- mathport name: snum.bit
 @[inherit_doc]
-notation a "::" b => bit a b
+scoped notation a "::" b => bit a b
 
 /-- Add an inactive bit at the end of a `SNum`. This mimics `ZNum.bit0`. -/
 def bit0 : SNum → SNum :=

f7fc89d5

feat: port Data.Num.Bitwise (#1919)

0988583c

`data.num.bitwise` ⟷ `Mathlib.Data.Num.Bitwise`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 146

data.num.bitwise ⟷ Mathlib.Data.Num.Bitwise

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 6 + 146

`data.num.bitwise` ⟷ `Mathlib.Data.Num.Bitwise`