algebra.big_operators.nat_antidiagonal

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

008205aa

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

327c3c0d

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) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
 -/
-import Mathbin.Data.Finset.NatAntidiagonal
-import Mathbin.Algebra.BigOperators.Basic
+import Data.Finset.NatAntidiagonal
+import Algebra.BigOperators.Basic
 
 #align_import algebra.big_operators.nat_antidiagonal from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"

327c3c0d

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) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.big_operators.nat_antidiagonal
-! leanprover-community/mathlib commit 327c3c0d9232d80e250dc8f65e7835b82b266ea5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finset.NatAntidiagonal
 import Mathbin.Algebra.BigOperators.Basic
 
+#align_import algebra.big_operators.nat_antidiagonal from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"
+
 /-!
 # Big operators for `nat_antidiagonal`

327c3c0d

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -29,15 +29,19 @@ namespace Finset
 
 namespace Nat
 
+#print Finset.Nat.prod_antidiagonal_succ /-
 theorem prod_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → M} :
     ∏ p in antidiagonal (n + 1), f p = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) := by
   rw [antidiagonal_succ, prod_cons, Prod_map]; rfl
 #align finset.nat.prod_antidiagonal_succ Finset.Nat.prod_antidiagonal_succ
+-/
 
+#print Finset.Nat.sum_antidiagonal_succ /-
 theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :
     ∑ p in antidiagonal (n + 1), f p = f (0, n + 1) + ∑ p in antidiagonal n, f (p.1 + 1, p.2) :=
   @prod_antidiagonal_succ (Multiplicative N) _ _ _
 #align finset.nat.sum_antidiagonal_succ Finset.Nat.sum_antidiagonal_succ
+-/
 
 #print Finset.Nat.prod_antidiagonal_swap /-
 @[to_additive]
@@ -48,17 +52,21 @@ theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
 -/
 
+#print Finset.Nat.prod_antidiagonal_succ' /-
 theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} :
     ∏ p in antidiagonal (n + 1), f p = f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) :=
   by
   rw [← prod_antidiagonal_swap, prod_antidiagonal_succ, ← prod_antidiagonal_swap]
   rfl
 #align finset.nat.prod_antidiagonal_succ' Finset.Nat.prod_antidiagonal_succ'
+-/
 
+#print Finset.Nat.sum_antidiagonal_succ' /-
 theorem sum_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → N} :
     ∑ p in antidiagonal (n + 1), f p = f (n + 1, 0) + ∑ p in antidiagonal n, f (p.1, p.2 + 1) :=
   @prod_antidiagonal_succ' (Multiplicative N) _ _ _
 #align finset.nat.sum_antidiagonal_succ' Finset.Nat.sum_antidiagonal_succ'
+-/
 
 #print Finset.Nat.prod_antidiagonal_subst /-
 @[to_additive]

327c3c0d

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -30,40 +30,40 @@ namespace Finset
 namespace Nat
 
 theorem prod_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal (n + 1), f p) = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) :=
-  by rw [antidiagonal_succ, prod_cons, Prod_map]; rfl
+    ∏ p in antidiagonal (n + 1), f p = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) := by
+  rw [antidiagonal_succ, prod_cons, Prod_map]; rfl
 #align finset.nat.prod_antidiagonal_succ Finset.Nat.prod_antidiagonal_succ
 
 theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :
-    (∑ p in antidiagonal (n + 1), f p) = f (0, n + 1) + ∑ p in antidiagonal n, f (p.1 + 1, p.2) :=
+    ∑ p in antidiagonal (n + 1), f p = f (0, n + 1) + ∑ p in antidiagonal n, f (p.1 + 1, p.2) :=
   @prod_antidiagonal_succ (Multiplicative N) _ _ _
 #align finset.nat.sum_antidiagonal_succ Finset.Nat.sum_antidiagonal_succ
 
 #print Finset.Nat.prod_antidiagonal_swap /-
 @[to_additive]
 theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal n, f p.symm) = ∏ p in antidiagonal n, f p := by
+    ∏ p in antidiagonal n, f p.symm = ∏ p in antidiagonal n, f p := by
   nth_rw 2 [← map_swap_antidiagonal]; rw [Prod_map]; rfl
 #align finset.nat.prod_antidiagonal_swap Finset.Nat.prod_antidiagonal_swap
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
 -/
 
 theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal (n + 1), f p) = f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) :=
+    ∏ p in antidiagonal (n + 1), f p = f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) :=
   by
   rw [← prod_antidiagonal_swap, prod_antidiagonal_succ, ← prod_antidiagonal_swap]
   rfl
 #align finset.nat.prod_antidiagonal_succ' Finset.Nat.prod_antidiagonal_succ'
 
 theorem sum_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → N} :
-    (∑ p in antidiagonal (n + 1), f p) = f (n + 1, 0) + ∑ p in antidiagonal n, f (p.1, p.2 + 1) :=
+    ∑ p in antidiagonal (n + 1), f p = f (n + 1, 0) + ∑ p in antidiagonal n, f (p.1, p.2 + 1) :=
   @prod_antidiagonal_succ' (Multiplicative N) _ _ _
 #align finset.nat.sum_antidiagonal_succ' Finset.Nat.sum_antidiagonal_succ'
 
 #print Finset.Nat.prod_antidiagonal_subst /-
 @[to_additive]
 theorem prod_antidiagonal_subst {n : ℕ} {f : ℕ × ℕ → ℕ → M} :
-    (∏ p in antidiagonal n, f p n) = ∏ p in antidiagonal n, f p (p.1 + p.2) :=
+    ∏ p in antidiagonal n, f p n = ∏ p in antidiagonal n, f p (p.1 + p.2) :=
   prod_congr rfl fun p hp => by rw [nat.mem_antidiagonal.1 hp]
 #align finset.nat.prod_antidiagonal_subst Finset.Nat.prod_antidiagonal_subst
 #align finset.nat.sum_antidiagonal_subst Finset.Nat.sum_antidiagonal_subst
@@ -72,7 +72,7 @@ theorem prod_antidiagonal_subst {n : ℕ} {f : ℕ × ℕ → ℕ → M} :
 #print Finset.Nat.prod_antidiagonal_eq_prod_range_succ_mk /-
 @[to_additive]
 theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type _} [CommMonoid M] (f : ℕ × ℕ → M)
-    (n : ℕ) : (∏ ij in Finset.Nat.antidiagonal n, f ij) = ∏ k in range n.succ, f (k, n - k) :=
+    (n : ℕ) : ∏ ij in Finset.Nat.antidiagonal n, f ij = ∏ k in range n.succ, f (k, n - k) :=
   by
   convert Prod_map _ ⟨fun i => (i, n - i), fun x y h => (Prod.mk.inj h).1⟩ _
   rfl
@@ -86,7 +86,7 @@ using `rw ←`. -/
 @[to_additive
       "This lemma matches more generally than\n`finset.nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ←`."]
 theorem prod_antidiagonal_eq_prod_range_succ {M : Type _} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
-    (∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2) = ∏ k in range n.succ, f k (n - k) :=
+    ∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
   prod_antidiagonal_eq_prod_range_succ_mk _ _
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ Finset.Nat.prod_antidiagonal_eq_prod_range_succ
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ Finset.Nat.sum_antidiagonal_eq_sum_range_succ

327c3c0d

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -21,7 +21,7 @@ This file contains theorems relevant to big operators over `finset.nat.antidiago
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 variable {M N : Type _} [CommMonoid M] [AddCommMonoid N]

327c3c0d

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -29,23 +29,11 @@ namespace Finset
 
 namespace Nat
 
-/- warning: finset.nat.prod_antidiagonal_succ -> Finset.Nat.prod_antidiagonal_succ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finset.nat.prod_antidiagonal_succ Finset.Nat.prod_antidiagonal_succₓ'. -/
 theorem prod_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → M} :
     (∏ p in antidiagonal (n + 1), f p) = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) :=
   by rw [antidiagonal_succ, prod_cons, Prod_map]; rfl
 #align finset.nat.prod_antidiagonal_succ Finset.Nat.prod_antidiagonal_succ
 
-/- warning: finset.nat.sum_antidiagonal_succ -> Finset.Nat.sum_antidiagonal_succ is a dubious translation:
-lean 3 declaration is
-  forall {N : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} N] {n : Nat} {f : (Prod.{0, 0} Nat Nat) -> N}, Eq.{succ u1} N (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (p : Prod.{0, 0} Nat Nat) => f p)) (HAdd.hAdd.{u1, u1, u1} N N N (instHAdd.{u1} N (AddZeroClass.toHasAdd.{u1} N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_2)))) (f (Prod.mk.{0, 0} Nat Nat (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => f (Prod.mk.{0, 0} Nat Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Prod.fst.{0, 0} Nat Nat p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Prod.snd.{0, 0} Nat Nat p)))))
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-Case conversion may be inaccurate. Consider using '#align finset.nat.sum_antidiagonal_succ Finset.Nat.sum_antidiagonal_succₓ'. -/
 theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :
     (∑ p in antidiagonal (n + 1), f p) = f (0, n + 1) + ∑ p in antidiagonal n, f (p.1 + 1, p.2) :=
   @prod_antidiagonal_succ (Multiplicative N) _ _ _
@@ -60,12 +48,6 @@ theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
 -/
 
-/- warning: finset.nat.prod_antidiagonal_succ' -> Finset.Nat.prod_antidiagonal_succ' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align finset.nat.prod_antidiagonal_succ' Finset.Nat.prod_antidiagonal_succ'ₓ'. -/
 theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} :
     (∏ p in antidiagonal (n + 1), f p) = f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) :=
   by
@@ -73,12 +55,6 @@ theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} :
   rfl
 #align finset.nat.prod_antidiagonal_succ' Finset.Nat.prod_antidiagonal_succ'
 
-/- warning: finset.nat.sum_antidiagonal_succ' -> Finset.Nat.sum_antidiagonal_succ' is a dubious translation:
-lean 3 declaration is
-  forall {N : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} N] {n : Nat} {f : (Prod.{0, 0} Nat Nat) -> N}, Eq.{succ u1} N (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (p : Prod.{0, 0} Nat Nat) => f p)) (HAdd.hAdd.{u1, u1, u1} N N N (instHAdd.{u1} N (AddZeroClass.toHasAdd.{u1} N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_2)))) (f (Prod.mk.{0, 0} Nat Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => f (Prod.mk.{0, 0} Nat Nat (Prod.fst.{0, 0} Nat Nat p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (Prod.snd.{0, 0} Nat Nat p) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
-but is expected to have type
-  forall {N : Type.{u1}} [_inst_2 : AddCommMonoid.{u1} N] {n : Nat} {f : (Prod.{0, 0} Nat Nat) -> N}, Eq.{succ u1} N (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (p : Prod.{0, 0} Nat Nat) => f p)) (HAdd.hAdd.{u1, u1, u1} N N N (instHAdd.{u1} N (AddZeroClass.toAdd.{u1} N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_2)))) (f (Prod.mk.{0, 0} Nat Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Finset.sum.{u1, 0} N (Prod.{0, 0} Nat Nat) _inst_2 (Finset.Nat.antidiagonal n) (fun (p : Prod.{0, 0} Nat Nat) => f (Prod.mk.{0, 0} Nat Nat (Prod.fst.{0, 0} Nat Nat p) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (Prod.snd.{0, 0} Nat Nat p) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
-Case conversion may be inaccurate. Consider using '#align finset.nat.sum_antidiagonal_succ' Finset.Nat.sum_antidiagonal_succ'ₓ'. -/
 theorem sum_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → N} :
     (∑ p in antidiagonal (n + 1), f p) = f (n + 1, 0) + ∑ p in antidiagonal n, f (p.1, p.2 + 1) :=
   @prod_antidiagonal_succ' (Multiplicative N) _ _ _

327c3c0d

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -54,11 +54,8 @@ theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :
 #print Finset.Nat.prod_antidiagonal_swap /-
 @[to_additive]
 theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal n, f p.symm) = ∏ p in antidiagonal n, f p :=
-  by
-  nth_rw 2 [← map_swap_antidiagonal]
-  rw [Prod_map]
-  rfl
+    (∏ p in antidiagonal n, f p.symm) = ∏ p in antidiagonal n, f p := by
+  nth_rw 2 [← map_swap_antidiagonal]; rw [Prod_map]; rfl
 #align finset.nat.prod_antidiagonal_swap Finset.Nat.prod_antidiagonal_swap
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
 -/

327c3c0d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

008205aa

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -66,9 +66,9 @@ theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type*} [CommMonoid M] (f :
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ_mk Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk
 
 /-- This lemma matches more generally than `Finset.Nat.prod_antidiagonal_eq_prod_range_succ_mk` when
-using `rw ←`. -/
+using `rw ← `. -/
 @[to_additive "This lemma matches more generally than
-`Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ←`."]
+`Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ← `."]
 theorem prod_antidiagonal_eq_prod_range_succ {M : Type*} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
     ∏ ij in antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
   prod_antidiagonal_eq_prod_range_succ_mk _ _

008205aa

style: cleanup by putting by on the same line as := (#8407)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

5e9b46ed

Diff

@@ -23,8 +23,9 @@ namespace Finset
 namespace Nat
 
 theorem prod_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal (n + 1), f p) = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) :=
-  by rw [antidiagonal_succ, prod_cons, prod_map]; rfl
+    (∏ p in antidiagonal (n + 1), f p)
+      = f (0, n + 1) * ∏ p in antidiagonal n, f (p.1 + 1, p.2) := by
+  rw [antidiagonal_succ, prod_cons, prod_map]; rfl
 #align finset.nat.prod_antidiagonal_succ Finset.Nat.prod_antidiagonal_succ
 
 theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :

008205aa

feat(Data.Finset.Antidiagonal): generalize Finset.Nat.antidiagonal (#7486)

We define a type class Finset.HasAntidiagonal A which contains a function antidiagonal : A → Finset (A × A) such that antidiagonal n is the Finset of all pairs adding to n, as witnessed by mem_antidiagonal.

When A is a canonically ordered add monoid with locally finite order this typeclass can be instantiated with Finset.antidiagonalOfLocallyFinite. This applies in particular when A is ℕ, more generally or σ →₀ ℕ, or even ι →₀ A under the additional assumption OrderedSub A that make it a canonically ordered add monoid. (In fact, we would just need an AddMonoid with a compatible order, finite Iic, such that if a + b = n, then a, b ≤ n, and any finiteness condition would be OK.)

For computational reasons it is better to manually provide instances for ℕ and σ →₀ ℕ, to avoid quadratic runtime performance. These instances are provided as Finset.Nat.instHasAntidiagonal and Finsupp.instHasAntidiagonal. This is why Finset.antidiagonalOfLocallyFinite is an abbrev and not an instance.

This definition does not exactly match with that of Multiset.antidiagonal defined in Mathlib.Data.Multiset.Antidiagonal, because of the multiplicities. Indeed, by counting multiplicities, Multiset α is equivalent to α →₀ ℕ, but Finset.antidiagonal and Multiset.antidiagonal will return different objects. For example, for s : Multiset ℕ := {0,0,0}, Multiset.antidiagonal s has 8 elements but Finset.antidiagonal s has only 4.

def s : Multiset ℕ := {0, 0, 0}
#eval (Finset.antidiagonal s).card -- 4
#eval Multiset.card (Multiset.antidiagonal s) -- 8

TODO

Define HasMulAntidiagonal (for monoids). For PNat, we will recover the set of divisors of a strictly positive integer.

This closes #7917

Co-authored by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> and Eric Wieser <efw27@cam.ac.uk>

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

85a1f28f

Diff

@@ -53,13 +53,13 @@ theorem sum_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → N} :
 @[to_additive]
 theorem prod_antidiagonal_subst {n : ℕ} {f : ℕ × ℕ → ℕ → M} :
     ∏ p in antidiagonal n, f p n = ∏ p in antidiagonal n, f p (p.1 + p.2) :=
-  prod_congr rfl fun p hp ↦ by rw [Nat.mem_antidiagonal.1 hp]
+  prod_congr rfl fun p hp ↦ by rw [mem_antidiagonal.mp hp]
 #align finset.nat.prod_antidiagonal_subst Finset.Nat.prod_antidiagonal_subst
 #align finset.nat.sum_antidiagonal_subst Finset.Nat.sum_antidiagonal_subst
 
 @[to_additive]
 theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type*} [CommMonoid M] (f : ℕ × ℕ → M)
-    (n : ℕ) : ∏ ij in Finset.Nat.antidiagonal n, f ij = ∏ k in range n.succ, f (k, n - k) :=
+    (n : ℕ) : ∏ ij in antidiagonal n, f ij = ∏ k in range n.succ, f (k, n - k) :=
   Finset.prod_map (range n.succ) ⟨fun i ↦ (i, n - i), fun _ _ h ↦ (Prod.mk.inj h).1⟩ f
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ_mk Finset.Nat.prod_antidiagonal_eq_prod_range_succ_mk
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ_mk Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk
@@ -69,7 +69,7 @@ using `rw ←`. -/
 @[to_additive "This lemma matches more generally than
 `Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ←`."]
 theorem prod_antidiagonal_eq_prod_range_succ {M : Type*} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
-    ∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
+    ∏ ij in antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
   prod_antidiagonal_eq_prod_range_succ_mk _ _
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ Finset.Nat.prod_antidiagonal_eq_prod_range_succ
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ Finset.Nat.sum_antidiagonal_eq_sum_range_succ

008205aa

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

@@ -16,7 +16,7 @@ This file contains theorems relevant to big operators over `Finset.NatAntidiagon
 
 open BigOperators
 
-variable {M N : Type _} [CommMonoid M] [AddCommMonoid N]
+variable {M N : Type*} [CommMonoid M] [AddCommMonoid N]
 
 namespace Finset
 
@@ -58,7 +58,7 @@ theorem prod_antidiagonal_subst {n : ℕ} {f : ℕ × ℕ → ℕ → M} :
 #align finset.nat.sum_antidiagonal_subst Finset.Nat.sum_antidiagonal_subst
 
 @[to_additive]
-theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type _} [CommMonoid M] (f : ℕ × ℕ → M)
+theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type*} [CommMonoid M] (f : ℕ × ℕ → M)
     (n : ℕ) : ∏ ij in Finset.Nat.antidiagonal n, f ij = ∏ k in range n.succ, f (k, n - k) :=
   Finset.prod_map (range n.succ) ⟨fun i ↦ (i, n - i), fun _ _ h ↦ (Prod.mk.inj h).1⟩ f
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ_mk Finset.Nat.prod_antidiagonal_eq_prod_range_succ_mk
@@ -68,7 +68,7 @@ theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type _} [CommMonoid M] (f :
 using `rw ←`. -/
 @[to_additive "This lemma matches more generally than
 `Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ←`."]
-theorem prod_antidiagonal_eq_prod_range_succ {M : Type _} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
+theorem prod_antidiagonal_eq_prod_range_succ {M : Type*} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
     ∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
   prod_antidiagonal_eq_prod_range_succ_mk _ _
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ Finset.Nat.prod_antidiagonal_eq_prod_range_succ

008205aa

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module algebra.big_operators.nat_antidiagonal
-! leanprover-community/mathlib commit 008205aa645b3f194c1da47025c5f110c8406eab
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finset.NatAntidiagonal
 import Mathlib.Algebra.BigOperators.Basic
 
+#align_import algebra.big_operators.nat_antidiagonal from "leanprover-community/mathlib"@"008205aa645b3f194c1da47025c5f110c8406eab"
+
 /-!
 # Big operators for `NatAntidiagonal`

008205aa

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -37,7 +37,7 @@ theorem sum_antidiagonal_succ {n : ℕ} {f : ℕ × ℕ → N} :
 
 @[to_additive]
 theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal n, f p.swap) = ∏ p in antidiagonal n, f p := by
+    ∏ p in antidiagonal n, f p.swap = ∏ p in antidiagonal n, f p := by
   conv_lhs => rw [← map_swap_antidiagonal, Finset.prod_map]
 #align finset.nat.prod_antidiagonal_swap Finset.Nat.prod_antidiagonal_swap
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
@@ -55,14 +55,14 @@ theorem sum_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → N} :
 
 @[to_additive]
 theorem prod_antidiagonal_subst {n : ℕ} {f : ℕ × ℕ → ℕ → M} :
-    (∏ p in antidiagonal n, f p n) = ∏ p in antidiagonal n, f p (p.1 + p.2) :=
+    ∏ p in antidiagonal n, f p n = ∏ p in antidiagonal n, f p (p.1 + p.2) :=
   prod_congr rfl fun p hp ↦ by rw [Nat.mem_antidiagonal.1 hp]
 #align finset.nat.prod_antidiagonal_subst Finset.Nat.prod_antidiagonal_subst
 #align finset.nat.sum_antidiagonal_subst Finset.Nat.sum_antidiagonal_subst
 
 @[to_additive]
 theorem prod_antidiagonal_eq_prod_range_succ_mk {M : Type _} [CommMonoid M] (f : ℕ × ℕ → M)
-    (n : ℕ) : (∏ ij in Finset.Nat.antidiagonal n, f ij) = ∏ k in range n.succ, f (k, n - k) :=
+    (n : ℕ) : ∏ ij in Finset.Nat.antidiagonal n, f ij = ∏ k in range n.succ, f (k, n - k) :=
   Finset.prod_map (range n.succ) ⟨fun i ↦ (i, n - i), fun _ _ h ↦ (Prod.mk.inj h).1⟩ f
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ_mk Finset.Nat.prod_antidiagonal_eq_prod_range_succ_mk
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ_mk Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk
@@ -72,7 +72,7 @@ using `rw ←`. -/
 @[to_additive "This lemma matches more generally than
 `Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk` when using `rw ←`."]
 theorem prod_antidiagonal_eq_prod_range_succ {M : Type _} [CommMonoid M] (f : ℕ → ℕ → M) (n : ℕ) :
-    (∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2) = ∏ k in range n.succ, f k (n - k) :=
+    ∏ ij in Finset.Nat.antidiagonal n, f ij.1 ij.2 = ∏ k in range n.succ, f k (n - k) :=
   prod_antidiagonal_eq_prod_range_succ_mk _ _
 #align finset.nat.prod_antidiagonal_eq_prod_range_succ Finset.Nat.prod_antidiagonal_eq_prod_range_succ
 #align finset.nat.sum_antidiagonal_eq_sum_range_succ Finset.Nat.sum_antidiagonal_eq_sum_range_succ

008205aa

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -42,9 +42,8 @@ theorem prod_antidiagonal_swap {n : ℕ} {f : ℕ × ℕ → M} :
 #align finset.nat.prod_antidiagonal_swap Finset.Nat.prod_antidiagonal_swap
 #align finset.nat.sum_antidiagonal_swap Finset.Nat.sum_antidiagonal_swap
 
-theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} :
-    (∏ p in antidiagonal (n + 1), f p) = f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) :=
-  by
+theorem prod_antidiagonal_succ' {n : ℕ} {f : ℕ × ℕ → M} : (∏ p in antidiagonal (n + 1), f p) =
+    f (n + 1, 0) * ∏ p in antidiagonal n, f (p.1, p.2 + 1) := by
   rw [← prod_antidiagonal_swap, prod_antidiagonal_succ, ← prod_antidiagonal_swap]
   rfl
 #align finset.nat.prod_antidiagonal_succ' Finset.Nat.prod_antidiagonal_succ'

008205aa

chore: scoped BigOperators notation (#1952)

e707fa67

Diff

@@ -17,8 +17,7 @@ import Mathlib.Algebra.BigOperators.Basic
 This file contains theorems relevant to big operators over `Finset.NatAntidiagonal`.
 -/
 
--- Porting note: commented out the next line
--- open BigOperators
+open BigOperators
 
 variable {M N : Type _} [CommMonoid M] [AddCommMonoid N]

008205aa

feat port: Algebra.BigOperators.NatAntidiagonal (#1656)

Co-authored-by: Johan Commelin <johan@commelin.net>

da5db4bb

`algebra.big_operators.nat_antidiagonal` ⟷ `Mathlib.Algebra.BigOperators.NatAntidiagonal`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 3 + 192

algebra.big_operators.nat_antidiagonal ⟷ Mathlib.Algebra.BigOperators.NatAntidiagonal

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 3 + 192

`algebra.big_operators.nat_antidiagonal` ⟷ `Mathlib.Algebra.BigOperators.NatAntidiagonal`