data.zmod.defs | Mathlib porting status

(last sync)

feat(data/fin/basic): extra instances that cover fin 0 (#18970)

These apply to fin 0, unlike the comm_ring instance which needs ne_zero n.

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

Diff

@@ -57,15 +57,27 @@ private lemma left_distrib_aux (n : ℕ) : ∀ a b c : fin n, a * (b + c) = a *
   ... ≡ (a * b) % n + (a * c) % n [MOD n] :
         (nat.mod_modeq _ _).symm.add (nat.mod_modeq _ _).symm)
 
+instance (n : ℕ) : distrib (fin n) :=
+{ left_distrib := left_distrib_aux n,
+  right_distrib := λ a b c, by rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm]; refl,
+  ..fin.add_comm_semigroup n,
+  ..fin.comm_semigroup n }
+
 /-- Commutative ring structure on `fin n`. -/
 instance (n : ℕ) [ne_zero n] : comm_ring (fin n) :=
 { one_mul := fin.one_mul,
   mul_one := fin.mul_one,
-  left_distrib := left_distrib_aux n,
-  right_distrib := λ a b c, by rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm]; refl,
   ..fin.add_monoid_with_one,
   ..fin.add_comm_group n,
-  ..fin.comm_semigroup n }
+  ..fin.comm_semigroup n,
+  ..fin.distrib n }
+
+/-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : has_distrib_neg (fin n) :=
+{ neg := has_neg.neg,
+  mul_neg := nat.cases_on n fin_zero_elim $ λ i, mul_neg,
+  neg_mul := nat.cases_on n fin_zero_elim $ λ i, neg_mul,
+  ..fin.has_involutive_neg n }
 
 end fin

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-08-08

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

e7589225

Diff

@@ -172,7 +172,7 @@ instance commRing (n : ℕ) : CommRing (ZMod n)
   natCast_zero := Nat.casesOn n (@Nat.cast_zero Int _) fun n => @Nat.cast_zero (Fin n.succ) _
   natCast_succ := Nat.casesOn n (@Nat.cast_succ Int _) fun n => @Nat.cast_succ (Fin n.succ) _
   intCast := Nat.casesOn n (coe : ℤ → ℤ) fun n => (coe : ℤ → Fin n.succ)
-  intCast_ofNat := Nat.casesOn n (@Int.cast_ofNat Int _) fun n => @Int.cast_ofNat (Fin n.succ) _
+  intCast_ofNat := Nat.casesOn n (@Int.cast_natCast Int _) fun n => @Int.cast_natCast (Fin n.succ) _
   intCast_negSucc :=
     Nat.casesOn n (@Int.cast_negSucc Int _) fun n => @Int.cast_negSucc (Fin n.succ) _
   left_distrib := Nat.casesOn n (@left_distrib Int _ _ _) fun n => @left_distrib (Fin n.succ) _ _ _

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: Eric Rodriguez
 -/
 import Algebra.NeZero
-import Data.Nat.Modeq
+import Data.Nat.ModEq
 import Data.Fintype.Lattice
 
 #align_import data.zmod.defs from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 -/
-import Mathbin.Algebra.NeZero
-import Mathbin.Data.Nat.Modeq
-import Mathbin.Data.Fintype.Lattice
+import Algebra.NeZero
+import Data.Nat.Modeq
+import Data.Fintype.Lattice
 
 #align_import data.zmod.defs from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -52,16 +52,16 @@ instance (n : ℕ) : CommSemigroup (Fin n) :=
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
       Fin.eq_of_veq
         (calc
-          a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).mul_right _
+          a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).hMul_right _
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
-          _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.mul_left _)
+          _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.hMul_left _)
     mul_comm := Fin.mul_comm }
 
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
   fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
   Fin.eq_of_veq
     (calc
-      a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).mul_left _
+      a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).hMul_left _
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]
       _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm)
 
@@ -83,8 +83,8 @@ instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
 instance (n : ℕ) : HasDistribNeg (Fin n) :=
   { Fin.hasInvolutiveNeg n with
     neg := Neg.neg
-    mul_neg := Nat.casesOn n finZeroElim fun i => mul_neg
-    neg_mul := Nat.casesOn n finZeroElim fun i => neg_mul }
+    hMul_neg := Nat.casesOn n finZeroElim fun i => mul_neg
+    neg_hMul := Nat.casesOn n finZeroElim fun i => neg_mul }
 
 end Fin

bump to nightly-2023-08-02-01

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

7aca3f15

Diff

@@ -76,8 +76,8 @@ instance (n : ℕ) : Distrib (Fin n) :=
 instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
   { Fin.instAddMonoidWithOne, Fin.addCommGroup n, Fin.instCommSemigroup n,
     Fin.instDistrib n with
-    one_mul := Fin.one_mul
-    mul_one := Fin.mul_one }
+    one_mul := Fin.one_mul'
+    mul_one := Fin.mul_one' }
 
 /-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/
 instance (n : ℕ) : HasDistribNeg (Fin n) :=

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module data.zmod.defs
-! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.NeZero
 import Mathbin.Data.Nat.Modeq
 import Mathbin.Data.Fintype.Lattice
 
+#align_import data.zmod.defs from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"
+
 /-!
 # Definition of `zmod n` + basic results.

bump to nightly-2023-07-18-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

a4aa5276

Diff

@@ -70,15 +70,15 @@ private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a
 
 instance (n : ℕ) : Distrib (Fin n) :=
   { Fin.addCommSemigroup n,
-    Fin.commSemigroup n with
+    Fin.instCommSemigroup n with
     left_distrib := left_distrib_aux n
     right_distrib := fun a b c => by
       rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm] <;> rfl }
 
 /-- Commutative ring structure on `fin n`. -/
 instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
-  { Fin.addMonoidWithOne, Fin.addCommGroup n, Fin.commSemigroup n,
-    Fin.distrib n with
+  { Fin.instAddMonoidWithOne, Fin.addCommGroup n, Fin.instCommSemigroup n,
+    Fin.instDistrib n with
     one_mul := Fin.one_mul
     mul_one := Fin.mul_one }

bump to nightly-2023-07-13-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/b01d6eb9d0a308807af54319b264d0994b91774b

7e6e2608

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module data.zmod.defs
-! leanprover-community/mathlib commit 63f84d91dd847f50bae04a01071f3a5491934e36
+! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -68,16 +68,27 @@ private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]
       _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm)
 
-/-- Commutative ring structure on `fin n`. -/
-instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
-  { Fin.addMonoidWithOne, Fin.addCommGroup n,
+instance (n : ℕ) : Distrib (Fin n) :=
+  { Fin.addCommSemigroup n,
     Fin.commSemigroup n with
-    one_mul := Fin.one_mul
-    mul_one := Fin.mul_one
     left_distrib := left_distrib_aux n
     right_distrib := fun a b c => by
       rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm] <;> rfl }
 
+/-- Commutative ring structure on `fin n`. -/
+instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
+  { Fin.addMonoidWithOne, Fin.addCommGroup n, Fin.commSemigroup n,
+    Fin.distrib n with
+    one_mul := Fin.one_mul
+    mul_one := Fin.mul_one }
+
+/-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/
+instance (n : ℕ) : HasDistribNeg (Fin n) :=
+  { Fin.hasInvolutiveNeg n with
+    neg := Neg.neg
+    mul_neg := Nat.casesOn n finZeroElim fun i => mul_neg
+    neg_mul := Nat.casesOn n finZeroElim fun i => neg_mul }
+
 end Fin
 
 #print ZMod /-

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -57,8 +57,7 @@ instance (n : ℕ) : CommSemigroup (Fin n) :=
         (calc
           a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).mul_right _
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
-          _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.mul_left _
-          )
+          _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.mul_left _)
     mul_comm := Fin.mul_comm }
 
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
@@ -67,8 +66,7 @@ private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a
     (calc
       a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).mul_left _
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]
-      _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm
-      )
+      _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm)
 
 /-- Commutative ring structure on `fin n`. -/
 instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -155,7 +155,7 @@ instance commRing (n : ℕ) : CommRing (ZMod n)
     Nat.casesOn n (@CommRing.nsmul_zero' Int _) fun n => @CommRing.nsmul_zero' (Fin n.succ) _
   nsmul_succ :=
     Nat.casesOn n (@CommRing.nsmul_succ' Int _) fun n => @CommRing.nsmul_succ' (Fin n.succ) _
-  add_left_neg := by cases n; exacts[@add_left_neg Int _, @add_left_neg (Fin n.succ) _]
+  add_left_neg := by cases n; exacts [@add_left_neg Int _, @add_left_neg (Fin n.succ) _]
   add_comm := Nat.casesOn n (@add_comm Int _) fun n => @add_comm (Fin n.succ) _
   mul := Nat.casesOn n (@Mul.mul Int _) fun n => @Mul.mul (Fin n.succ) _
   mul_assoc := Nat.casesOn n (@mul_assoc Int _) fun n => @mul_assoc (Fin n.succ) _

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -155,9 +155,7 @@ instance commRing (n : ℕ) : CommRing (ZMod n)
     Nat.casesOn n (@CommRing.nsmul_zero' Int _) fun n => @CommRing.nsmul_zero' (Fin n.succ) _
   nsmul_succ :=
     Nat.casesOn n (@CommRing.nsmul_succ' Int _) fun n => @CommRing.nsmul_succ' (Fin n.succ) _
-  add_left_neg := by
-    cases n
-    exacts[@add_left_neg Int _, @add_left_neg (Fin n.succ) _]
+  add_left_neg := by cases n; exacts[@add_left_neg Int _, @add_left_neg (Fin n.succ) _]
   add_comm := Nat.casesOn n (@add_comm Int _) fun n => @add_comm (Fin n.succ) _
   mul := Nat.casesOn n (@Mul.mul Int _) fun n => @Mul.mul (Fin n.succ) _
   mul_assoc := Nat.casesOn n (@mul_assoc Int _) fun n => @mul_assoc (Fin n.succ) _

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -69,7 +69,6 @@ private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]
       _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm
       )
-#align fin.left_distrib_aux fin.left_distrib_aux
 
 /-- Commutative ring structure on `fin n`. -/
 instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(Data/Int/Cast): fix confusion between OfNat and Nat.cast lemmas (#11861)

This renames

Int.cast_ofNat to Int.cast_natCast
Int.int_cast_ofNat to Int.cast_ofNat

I think the history here is that this lemma was previously about Int.ofNat, before we globally fixed the simp-normal form to be Nat.cast.

Since the Int.cast_ofNat name is repurposed, it can't be deprecated. Int.int_cast_ofNat is such a wonky name that it was probably never used.

a7ffab83

Diff

@@ -169,7 +169,7 @@ instance commRing (n : ℕ) : CommRing (ZMod n) where
   natCast_zero := Nat.casesOn n (@Nat.cast_zero Int _) fun n => @Nat.cast_zero (Fin n.succ) _
   natCast_succ := Nat.casesOn n (@Nat.cast_succ Int _) fun n => @Nat.cast_succ (Fin n.succ) _
   intCast := Nat.casesOn n ((↑) : ℤ → ℤ) fun n => ((↑) : ℤ → Fin n.succ)
-  intCast_ofNat := Nat.casesOn n (@Int.cast_ofNat Int _) fun n => @Int.cast_ofNat (Fin n.succ) _
+  intCast_ofNat := Nat.casesOn n (@Int.cast_natCast Int _) fun n => @Int.cast_natCast (Fin n.succ) _
   intCast_negSucc :=
     Nat.casesOn n (@Int.cast_negSucc Int _) fun n => @Int.cast_negSucc (Fin n.succ) _
   left_distrib := Nat.casesOn n (@left_distrib Int _ _ _) fun n => @left_distrib (Fin n.succ) _ _ _

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -75,7 +75,7 @@ instance instCommRing (n : ℕ) [NeZero n] : CommRing (Fin n) :=
   { Fin.instAddMonoidWithOne n, Fin.addCommGroup n, Fin.instCommSemigroup n, Fin.instDistrib n with
     one_mul := Fin.one_mul'
     mul_one := Fin.mul_one',
-    -- porting note: new, see
+    -- Porting note: new, see
     -- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/ring.20vs.20Ring/near/322876462
     zero_mul := Fin.zero_mul'
     mul_zero := Fin.mul_zero' }
@@ -157,7 +157,7 @@ instance commRing (n : ℕ) : CommRing (ZMod n) where
   nsmul_succ := Nat.casesOn n
     (inferInstanceAs (CommRing ℤ)).nsmul_succ
     fun n => (inferInstanceAs (CommRing (Fin n.succ))).nsmul_succ
-  -- porting note: `match` didn't work here
+  -- Porting note: `match` didn't work here
   add_left_neg := Nat.casesOn n (@add_left_neg Int _) fun n => @add_left_neg (Fin n.succ) _
   add_comm := Nat.casesOn n (@add_comm Int _) fun n => @add_comm (Fin n.succ) _
   mul := Nat.casesOn n (@Mul.mul Int _) fun n => @Mul.mul (Fin n.succ) _
@@ -176,11 +176,11 @@ instance commRing (n : ℕ) : CommRing (ZMod n) where
   right_distrib :=
     Nat.casesOn n (@right_distrib Int _ _ _) fun n => @right_distrib (Fin n.succ) _ _ _
   mul_comm := Nat.casesOn n (@mul_comm Int _) fun n => @mul_comm (Fin n.succ) _
-  -- porting note: new, see
+  -- Porting note: new, see
   -- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/ring.20vs.20Ring/near/322876462
   zero_mul := Nat.casesOn n (@zero_mul Int _) fun n => @zero_mul (Fin n.succ) _
   mul_zero := Nat.casesOn n (@mul_zero Int _) fun n => @mul_zero (Fin n.succ) _
-  -- porting note: all npow fields are new, but probably should be backported
+  -- Porting note: all npow fields are new, but probably should be backported
   npow := Nat.casesOn n
     (inferInstanceAs (CommRing ℤ)).npow fun n => (inferInstanceAs (CommRing (Fin n.succ))).npow
   npow_zero := Nat.casesOn n

chore(Init/Fin): deprecate Fin.eq_of_veq and Fin.veq_of_eq (#10626)

We have Fin.eq_of_val_eq and Fin.val_eq_of_eq in Lean core now. Also slightly shake the tree.

9a944835

Diff

@@ -46,7 +46,7 @@ open Nat.ModEq Int
 instance instCommSemigroup (n : ℕ) : CommSemigroup (Fin n) :=
   { inferInstanceAs (Mul (Fin n)) with
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
-      Fin.eq_of_veq <|
+      Fin.eq_of_val_eq <|
         calc
           a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).mul_right _
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
@@ -56,7 +56,7 @@ instance instCommSemigroup (n : ℕ) : CommSemigroup (Fin n) :=
 
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
   fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
-  Fin.eq_of_veq <|
+  Fin.eq_of_val_eq <|
     calc
       a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).mul_left _
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]

chore: reduce imports (#9830)

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

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

f4c4ca61

Diff

@@ -5,7 +5,7 @@ Authors: Eric Rodriguez
 -/
 import Mathlib.Algebra.NeZero
 import Mathlib.Data.Nat.ModEq
-import Mathlib.Data.Fintype.Lattice
+import Mathlib.Data.Fintype.Card
 
 #align_import data.zmod.defs from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"

refactor(Logic/Unique): remove dependency on Fin (#8510)

Unique should be available earlier than results about Fin n, by virtue of being a very basic logic typeclass with no dependencies on Nat or algebra.

This also generalizes some of the moved instances and lemmas. There are no new declarations in this PR, only renames of existing ones.

8b144faa

Diff

@@ -108,7 +108,7 @@ instance ZMod.repr : ∀ n : ℕ, Repr (ZMod n)
 
 namespace ZMod
 
-instance instUnique : Unique (ZMod 1) := Fin.unique
+instance instUnique : Unique (ZMod 1) := Fin.uniqueFinOne
 
 instance fintype : ∀ (n : ℕ) [NeZero n], Fintype (ZMod n)
   | 0, h => (h.ne rfl).elim

feat: Simple results about ZMod (#8205)

1d775649

Diff

@@ -108,6 +108,8 @@ instance ZMod.repr : ∀ n : ℕ, Repr (ZMod n)
 
 namespace ZMod
 
+instance instUnique : Unique (ZMod 1) := Fin.unique
+
 instance fintype : ∀ (n : ℕ) [NeZero n], Fintype (ZMod n)
   | 0, h => (h.ne rfl).elim
   | n + 1, _ => Fin.fintype (n + 1)

chore: tidy various files (#6393)

3697da16

Diff

@@ -70,7 +70,7 @@ instance instDistrib (n : ℕ) : Distrib (Fin n) :=
       rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm] }
 #align fin.distrib Fin.instDistrib
 
-/-- Commutative ring structure on `fin n`. -/
+/-- Commutative ring structure on `Fin n`. -/
 instance instCommRing (n : ℕ) [NeZero n] : CommRing (Fin n) :=
   { Fin.instAddMonoidWithOne n, Fin.addCommGroup n, Fin.instCommSemigroup n, Fin.instDistrib n with
     one_mul := Fin.one_mul'
@@ -81,7 +81,7 @@ instance instCommRing (n : ℕ) [NeZero n] : CommRing (Fin n) :=
     mul_zero := Fin.mul_zero' }
 #align fin.comm_ring Fin.instCommRing
 
-/-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/
+/-- Note this is more general than `Fin.instCommRing` as it applies (vacuously) to `Fin 0` too. -/
 instance instHasDistribNeg (n : ℕ) : HasDistribNeg (Fin n) :=
   { toInvolutiveNeg := Fin.instInvolutiveNeg n
     mul_neg := Nat.casesOn n finZeroElim fun _i => mul_neg

chore: bump to nightly-2023-07-15 (#5992)

Various adaptations to changes when Fin API was moved to Std. One notable change is that many lemmas are now stated in terms of i ≠ 0 (for i : Fin n) rather then i.1 ≠ 0, and as a consequence many Fin.vne_of_ne applications have been added or removed, mostly removed.

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

24924f96

Diff

@@ -73,12 +73,12 @@ instance instDistrib (n : ℕ) : Distrib (Fin n) :=
 /-- Commutative ring structure on `fin n`. -/
 instance instCommRing (n : ℕ) [NeZero n] : CommRing (Fin n) :=
   { Fin.instAddMonoidWithOne n, Fin.addCommGroup n, Fin.instCommSemigroup n, Fin.instDistrib n with
-    one_mul := Fin.one_mul
-    mul_one := Fin.mul_one,
+    one_mul := Fin.one_mul'
+    mul_one := Fin.mul_one',
     -- porting note: new, see
     -- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/ring.20vs.20Ring/near/322876462
-    zero_mul := Fin.zero_mul
-    mul_zero := Fin.mul_zero }
+    zero_mul := Fin.zero_mul'
+    mul_zero := Fin.mul_zero' }
 #align fin.comm_ring Fin.instCommRing
 
 /-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/

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) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module data.zmod.defs
-! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.NeZero
 import Mathlib.Data.Nat.ModEq
 import Mathlib.Data.Fintype.Lattice
 
+#align_import data.zmod.defs from "leanprover-community/mathlib"@"3a2b5524a138b5d0b818b858b516d4ac8a484b03"
+
 /-!
 # Definition of `ZMod n` + basic results.

chore: forward-port leanprover-community/mathlib#18970 (#5852)

This also #aligns some nearby instance names

4f2aaaf3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module data.zmod.defs
-! leanprover-community/mathlib commit 1126441d6bccf98c81214a0780c73d499f6721fe
+! leanprover-community/mathlib commit 3a2b5524a138b5d0b818b858b516d4ac8a484b03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -46,7 +46,7 @@ to register the ring structure on `ZMod n` as type class instance.
 open Nat.ModEq Int
 
 /-- Multiplicative commutative semigroup structure on `Fin n`. -/
-instance (n : ℕ) : CommSemigroup (Fin n) :=
+instance instCommSemigroup (n : ℕ) : CommSemigroup (Fin n) :=
   { inferInstanceAs (Mul (Fin n)) with
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
       Fin.eq_of_veq <|
@@ -55,6 +55,7 @@ instance (n : ℕ) : CommSemigroup (Fin n) :=
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
           _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.mul_left _
     mul_comm := Fin.mul_comm }
+#align fin.comm_semigroup Fin.instCommSemigroup
 
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
   fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
@@ -65,18 +66,30 @@ private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a
       _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm
 
 /-- Commutative ring structure on `Fin n`. -/
-instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=
-  { Fin.instAddMonoidWithOneFin n, Fin.addCommGroup n,
-    Fin.instCommSemigroupFin n with
-    one_mul := Fin.one_mul
-    mul_one := Fin.mul_one
+instance instDistrib (n : ℕ) : Distrib (Fin n) :=
+  { Fin.addCommSemigroup n, Fin.instCommSemigroup n with
     left_distrib := left_distrib_aux n
     right_distrib := fun a b c => by
-      rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm],
+      rw [mul_comm, left_distrib_aux, mul_comm _ b, mul_comm] }
+#align fin.distrib Fin.instDistrib
+
+/-- Commutative ring structure on `fin n`. -/
+instance instCommRing (n : ℕ) [NeZero n] : CommRing (Fin n) :=
+  { Fin.instAddMonoidWithOne n, Fin.addCommGroup n, Fin.instCommSemigroup n, Fin.instDistrib n with
+    one_mul := Fin.one_mul
+    mul_one := Fin.mul_one,
     -- porting note: new, see
     -- https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/ring.20vs.20Ring/near/322876462
     zero_mul := Fin.zero_mul
     mul_zero := Fin.mul_zero }
+#align fin.comm_ring Fin.instCommRing
+
+/-- Note this is more general than `fin.comm_ring` as it applies (vacuously) to `fin 0` too. -/
+instance instHasDistribNeg (n : ℕ) : HasDistribNeg (Fin n) :=
+  { toInvolutiveNeg := Fin.instInvolutiveNeg n
+    mul_neg := Nat.casesOn n finZeroElim fun _i => mul_neg
+    neg_mul := Nat.casesOn n finZeroElim fun _i => neg_mul }
+#align fin.has_distrib_neg Fin.instHasDistribNeg
 
 end Fin

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -38,7 +38,7 @@ namespace Fin
 ## Ring structure on `Fin n`
 
 We define a commutative ring structure on `Fin n`.
-Afterwords, when we define `ZMod n` in terms of `Fin n`, we use these definitions
+Afterwards, when we define `ZMod n` in terms of `Fin n`, we use these definitions
 to register the ring structure on `ZMod n` as type class instance.
 -/

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -45,7 +45,7 @@ to register the ring structure on `ZMod n` as type class instance.
 
 open Nat.ModEq Int
 
-/-- Multiplicative commutative semigroup structure on `fin n`. -/
+/-- Multiplicative commutative semigroup structure on `Fin n`. -/
 instance (n : ℕ) : CommSemigroup (Fin n) :=
   { inferInstanceAs (Mul (Fin n)) with
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -111,7 +111,7 @@ instance infinite : Infinite (ZMod 0) :=
 theorem card (n : ℕ) [Fintype (ZMod n)] : Fintype.card (ZMod n) = n := by
   cases n with
   | zero => exact (not_finite (ZMod 0)).elim
-  | succ n => convert Fintype.card_fin (n + 1)
+  | succ n => convert Fintype.card_fin (n + 1) using 2
 #align zmod.card ZMod.card
 
 /- We define each field by cases, to ensure that the eta-expanded `ZMod.commRing` is defeq to the

feat: tactic congr! and improvement to convert (#2566)

This introduces a tactic congr! that is an analogue to mathlib 3's congr'. It is a more insistent version of congr that makes use of more congruence lemmas (including user congruence lemmas), propext, funext, and Subsingleton instances. It also has a feature to lift reflexive relations to equalities. Along with funext, the tactic does intros, allowing congr! to get access to function bodies; the introduced variables can be named using rename_i if needed.

This also modifies convert to use congr! rather than congr, which makes it work more like the mathlib3 version of the tactic.

b46c2e36

Diff

@@ -111,7 +111,7 @@ instance infinite : Infinite (ZMod 0) :=
 theorem card (n : ℕ) [Fintype (ZMod n)] : Fintype.card (ZMod n) = n := by
   cases n with
   | zero => exact (not_finite (ZMod 0)).elim
-  | succ n => convert Fintype.card_fin (n + 1); apply Subsingleton.elim
+  | succ n => convert Fintype.card_fin (n + 1)
 #align zmod.card ZMod.card
 
 /- We define each field by cases, to ensure that the eta-expanded `ZMod.commRing` is defeq to the

chore: bump to nightly-2023-02-03 (#1999)

78fc778d

Diff

@@ -50,7 +50,6 @@ instance (n : ℕ) : CommSemigroup (Fin n) :=
   { inferInstanceAs (Mul (Fin n)) with
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
       Fin.eq_of_veq <|
-        show _ ≡ _ [MOD _] from -- lean4#2073
         calc
           a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).mul_right _
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
@@ -60,7 +59,6 @@ instance (n : ℕ) : CommSemigroup (Fin n) :=
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
   fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
   Fin.eq_of_veq <|
-    show _ ≡ _ [MOD _] from -- lean4#2073
     calc
       a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).mul_left _
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]

chore: use inferInstanceAs (#2074)

Drop

by delta mydef; infer_instance. This generates id _ in the proof.
show _, by infer_instance. This generates let in let; not sure if it's bad for defeq but a reducible inferInstanceAs should not be worse.

f9f9320a

Diff

@@ -89,8 +89,8 @@ def ZMod : ℕ → Type
 #align zmod ZMod
 
 instance ZMod.decidableEq : ∀ n : ℕ, DecidableEq (ZMod n)
-  | 0 => by dsimp [ZMod]; infer_instance
-  | n + 1 => by dsimp [ZMod]; infer_instance
+  | 0 => inferInstanceAs (DecidableEq ℤ)
+  | n + 1 => inferInstanceAs (DecidableEq (Fin (n + 1)))
 #align zmod.decidable_eq ZMod.decidableEq
 
 instance ZMod.repr : ∀ n : ℕ, Repr (ZMod n)

chore: bump lean 01-29 (#1927)

1abd74a8

Diff

@@ -49,22 +49,22 @@ open Nat.ModEq Int
 instance (n : ℕ) : CommSemigroup (Fin n) :=
   { inferInstanceAs (Mul (Fin n)) with
     mul_assoc := fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
-      Fin.eq_of_veq
-        (calc
+      Fin.eq_of_veq <|
+        show _ ≡ _ [MOD _] from -- lean4#2073
+        calc
           a * b % n * c ≡ a * b * c [MOD n] := (Nat.mod_modEq _ _).mul_right _
           _ ≡ a * (b * c) [MOD n] := by rw [mul_assoc]
           _ ≡ a * (b * c % n) [MOD n] := (Nat.mod_modEq _ _).symm.mul_left _
-          )
     mul_comm := Fin.mul_comm }
 
 private theorem left_distrib_aux (n : ℕ) : ∀ a b c : Fin n, a * (b + c) = a * b + a * c :=
   fun ⟨a, ha⟩ ⟨b, hb⟩ ⟨c, hc⟩ =>
-  Fin.eq_of_veq
-    (calc
+  Fin.eq_of_veq <|
+    show _ ≡ _ [MOD _] from -- lean4#2073
+    calc
       a * ((b + c) % n) ≡ a * (b + c) [MOD n] := (Nat.mod_modEq _ _).mul_left _
       _ ≡ a * b + a * c [MOD n] := by rw [mul_add]
       _ ≡ a * b % n + a * c % n [MOD n] := (Nat.mod_modEq _ _).symm.add (Nat.mod_modEq _ _).symm
-      )
 
 /-- Commutative ring structure on `Fin n`. -/
 instance (n : ℕ) [NeZero n] : CommRing (Fin n) :=