data.finset.nat_antidiagonal | 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

9003f287

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

cc70d914

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -140,7 +140,7 @@ theorem Finset.filter_fst_eq_antidiagonal (n m : ℕ) :
   ext ⟨x, y⟩
   simp only [mem_filter, nat.mem_antidiagonal]
   split_ifs with h h
-  · simp (config := { contextual := true }) [and_comm', eq_tsub_iff_add_eq_of_le h, add_comm]
+  · simp (config := { contextual := true }) [and_comm, eq_tsub_iff_add_eq_of_le h, add_comm]
   · rw [not_le] at h
     simp only [not_mem_empty, iff_false_iff, not_and]
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)

cc70d914

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -110,7 +110,7 @@ theorem Finset.antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antid
     (hq : q ∈ antidiagonal n) : p = q ↔ p.fst = q.fst :=
   by
   refine' ⟨congr_arg Prod.fst, fun h => Prod.ext h ((add_right_inj q.fst).mp _)⟩
-  rw [mem_antidiagonal] at hp hq 
+  rw [mem_antidiagonal] at hp hq
   rw [hq, ← h, hp]
 #align finset.nat.antidiagonal_congr Finset.antidiagonal_congr
 -/
@@ -120,7 +120,7 @@ theorem Finset.antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ ant
   by
   rw [le_iff_exists_add]
   use kl.2
-  rwa [mem_antidiagonal, eq_comm] at hlk 
+  rwa [mem_antidiagonal, eq_comm] at hlk
 #align finset.nat.antidiagonal.fst_le Finset.antidiagonal.fst_le
 -/
 
@@ -129,7 +129,7 @@ theorem Finset.antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ ant
   by
   rw [le_iff_exists_add]
   use kl.1
-  rwa [mem_antidiagonal, eq_comm, add_comm] at hlk 
+  rwa [mem_antidiagonal, eq_comm, add_comm] at hlk
 #align finset.nat.antidiagonal.snd_le Finset.antidiagonal.snd_le
 -/
 
@@ -141,7 +141,7 @@ theorem Finset.filter_fst_eq_antidiagonal (n m : ℕ) :
   simp only [mem_filter, nat.mem_antidiagonal]
   split_ifs with h h
   · simp (config := { contextual := true }) [and_comm', eq_tsub_iff_add_eq_of_le h, add_comm]
-  · rw [not_le] at h 
+  · rw [not_le] at h
     simp only [not_mem_empty, iff_false_iff, not_and]
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
 #align finset.nat.filter_fst_eq_antidiagonal Finset.filter_fst_eq_antidiagonal
@@ -169,7 +169,7 @@ def Finset.sigmaAntidiagonalEquivProd : (Σ n : ℕ, antidiagonal n) ≃ ℕ ×
   invFun x := ⟨x.1 + x.2, x, mem_antidiagonal.mpr rfl⟩
   left_inv := by
     rintro ⟨n, ⟨k, l⟩, h⟩
-    rw [mem_antidiagonal] at h 
+    rw [mem_antidiagonal] at h
     exact Sigma.subtype_ext h rfl
   right_inv x := rfl
 #align finset.nat.sigma_antidiagonal_equiv_prod Finset.sigmaAntidiagonalEquivProd

cc70d914

bump to nightly-2023-11-01-06

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

13aa39b0

Diff

@@ -28,21 +28,17 @@ namespace Finset
 
 namespace Nat
 
-#print Finset.Nat.antidiagonal /-
 /-- The antidiagonal of a natural number `n` is
     the finset of pairs `(i, j)` such that `i + j = n`. -/
 def antidiagonal (n : ℕ) : Finset (ℕ × ℕ) :=
   ⟨Multiset.Nat.antidiagonal n, Multiset.Nat.nodup_antidiagonal n⟩
 #align finset.nat.antidiagonal Finset.Nat.antidiagonal
--/
 
-#print Finset.Nat.mem_antidiagonal /-
 /-- A pair (i, j) is contained in the antidiagonal of `n` if and only if `i + j = n`. -/
 @[simp]
 theorem mem_antidiagonal {n : ℕ} {x : ℕ × ℕ} : x ∈ antidiagonal n ↔ x.1 + x.2 = n := by
   rw [antidiagonal, mem_def, Multiset.Nat.mem_antidiagonal]
 #align finset.nat.mem_antidiagonal Finset.Nat.mem_antidiagonal
--/
 
 #print Finset.Nat.card_antidiagonal /-
 /-- The cardinality of the antidiagonal of `n` is `n + 1`. -/
@@ -101,44 +97,44 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
 #align finset.nat.antidiagonal_succ_succ' Finset.Nat.antidiagonal_succ_succ'
 -/
 
-#print Finset.Nat.map_swap_antidiagonal /-
-theorem map_swap_antidiagonal {n : ℕ} :
+#print Finset.map_swap_antidiagonal /-
+theorem Finset.map_swap_antidiagonal {n : ℕ} :
     (antidiagonal n).map ⟨Prod.swap, Prod.swap_rightInverse.Injective⟩ = antidiagonal n :=
   eq_of_veq <| by simp [antidiagonal, Multiset.Nat.map_swap_antidiagonal]
-#align finset.nat.map_swap_antidiagonal Finset.Nat.map_swap_antidiagonal
+#align finset.nat.map_swap_antidiagonal Finset.map_swap_antidiagonal
 -/
 
-#print Finset.Nat.antidiagonal_congr /-
+#print Finset.antidiagonal_congr /-
 /-- A point in the antidiagonal is determined by its first co-ordinate. -/
-theorem antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal n)
+theorem Finset.antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal n)
     (hq : q ∈ antidiagonal n) : p = q ↔ p.fst = q.fst :=
   by
   refine' ⟨congr_arg Prod.fst, fun h => Prod.ext h ((add_right_inj q.fst).mp _)⟩
   rw [mem_antidiagonal] at hp hq 
   rw [hq, ← h, hp]
-#align finset.nat.antidiagonal_congr Finset.Nat.antidiagonal_congr
+#align finset.nat.antidiagonal_congr Finset.antidiagonal_congr
 -/
 
-#print Finset.Nat.antidiagonal.fst_le /-
-theorem antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 ≤ n :=
+#print Finset.antidiagonal.fst_le /-
+theorem Finset.antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 ≤ n :=
   by
   rw [le_iff_exists_add]
   use kl.2
   rwa [mem_antidiagonal, eq_comm] at hlk 
-#align finset.nat.antidiagonal.fst_le Finset.Nat.antidiagonal.fst_le
+#align finset.nat.antidiagonal.fst_le Finset.antidiagonal.fst_le
 -/
 
-#print Finset.Nat.antidiagonal.snd_le /-
-theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 ≤ n :=
+#print Finset.antidiagonal.snd_le /-
+theorem Finset.antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 ≤ n :=
   by
   rw [le_iff_exists_add]
   use kl.1
   rwa [mem_antidiagonal, eq_comm, add_comm] at hlk 
-#align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
+#align finset.nat.antidiagonal.snd_le Finset.antidiagonal.snd_le
 -/
 
-#print Finset.Nat.filter_fst_eq_antidiagonal /-
-theorem filter_fst_eq_antidiagonal (n m : ℕ) :
+#print Finset.filter_fst_eq_antidiagonal /-
+theorem Finset.filter_fst_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅ :=
   by
   ext ⟨x, y⟩
@@ -148,26 +144,26 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
   · rw [not_le] at h 
     simp only [not_mem_empty, iff_false_iff, not_and]
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
-#align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonal
+#align finset.nat.filter_fst_eq_antidiagonal Finset.filter_fst_eq_antidiagonal
 -/
 
-#print Finset.Nat.filter_snd_eq_antidiagonal /-
-theorem filter_snd_eq_antidiagonal (n m : ℕ) :
+#print Finset.filter_snd_eq_antidiagonal /-
+theorem Finset.filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ :=
   by
   have : (fun x : ℕ × ℕ => x.snd = m) ∘ Prod.swap = fun x : ℕ × ℕ => x.fst = m := by ext; simp
   rw [← map_swap_antidiagonal]
   simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
-#align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal
+#align finset.nat.filter_snd_eq_antidiagonal Finset.filter_snd_eq_antidiagonal
 -/
 
 section EquivProd
 
-#print Finset.Nat.sigmaAntidiagonalEquivProd /-
+#print Finset.sigmaAntidiagonalEquivProd /-
 /-- The disjoint union of antidiagonals `Σ (n : ℕ), antidiagonal n` is equivalent to the product
     `ℕ × ℕ`. This is such an equivalence, obtained by mapping `(n, (k, l))` to `(k, l)`. -/
 @[simps]
-def sigmaAntidiagonalEquivProd : (Σ n : ℕ, antidiagonal n) ≃ ℕ × ℕ
+def Finset.sigmaAntidiagonalEquivProd : (Σ n : ℕ, antidiagonal n) ≃ ℕ × ℕ
     where
   toFun x := x.2
   invFun x := ⟨x.1 + x.2, x, mem_antidiagonal.mpr rfl⟩
@@ -176,7 +172,7 @@ def sigmaAntidiagonalEquivProd : (Σ n : ℕ, antidiagonal n) ≃ ℕ × ℕ
     rw [mem_antidiagonal] at h 
     exact Sigma.subtype_ext h rfl
   right_inv x := rfl
-#align finset.nat.sigma_antidiagonal_equiv_prod Finset.Nat.sigmaAntidiagonalEquivProd
+#align finset.nat.sigma_antidiagonal_equiv_prod Finset.sigmaAntidiagonalEquivProd
 -/
 
 end EquivProd

cc70d914

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) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.Data.Finset.Card
-import Mathbin.Data.Multiset.NatAntidiagonal
+import Data.Finset.Card
+import Data.Multiset.NatAntidiagonal
 
 #align_import data.finset.nat_antidiagonal from "leanprover-community/mathlib"@"cc70d9141824ea8982d1562ce009952f2c3ece30"

cc70d914

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) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.finset.nat_antidiagonal
-! leanprover-community/mathlib commit cc70d9141824ea8982d1562ce009952f2c3ece30
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Finset.Card
 import Mathbin.Data.Multiset.NatAntidiagonal
 
+#align_import data.finset.nat_antidiagonal from "leanprover-community/mathlib"@"cc70d9141824ea8982d1562ce009952f2c3ece30"
+
 /-!
 # Antidiagonals in ℕ × ℕ as finsets

cc70d914

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -140,6 +140,7 @@ theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagon
 #align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
 -/
 
+#print Finset.Nat.filter_fst_eq_antidiagonal /-
 theorem filter_fst_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅ :=
   by
@@ -151,7 +152,9 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
     simp only [not_mem_empty, iff_false_iff, not_and]
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
 #align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonal
+-/
 
+#print Finset.Nat.filter_snd_eq_antidiagonal /-
 theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ :=
   by
@@ -159,6 +162,7 @@ theorem filter_snd_eq_antidiagonal (n m : ℕ) :
   rw [← map_swap_antidiagonal]
   simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
 #align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal
+-/
 
 section EquivProd

cc70d914

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -117,7 +117,7 @@ theorem antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal
     (hq : q ∈ antidiagonal n) : p = q ↔ p.fst = q.fst :=
   by
   refine' ⟨congr_arg Prod.fst, fun h => Prod.ext h ((add_right_inj q.fst).mp _)⟩
-  rw [mem_antidiagonal] at hp hq
+  rw [mem_antidiagonal] at hp hq 
   rw [hq, ← h, hp]
 #align finset.nat.antidiagonal_congr Finset.Nat.antidiagonal_congr
 -/
@@ -127,7 +127,7 @@ theorem antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagon
   by
   rw [le_iff_exists_add]
   use kl.2
-  rwa [mem_antidiagonal, eq_comm] at hlk
+  rwa [mem_antidiagonal, eq_comm] at hlk 
 #align finset.nat.antidiagonal.fst_le Finset.Nat.antidiagonal.fst_le
 -/
 
@@ -136,7 +136,7 @@ theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagon
   by
   rw [le_iff_exists_add]
   use kl.1
-  rwa [mem_antidiagonal, eq_comm, add_comm] at hlk
+  rwa [mem_antidiagonal, eq_comm, add_comm] at hlk 
 #align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
 -/
 
@@ -147,7 +147,7 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
   simp only [mem_filter, nat.mem_antidiagonal]
   split_ifs with h h
   · simp (config := { contextual := true }) [and_comm', eq_tsub_iff_add_eq_of_le h, add_comm]
-  · rw [not_le] at h
+  · rw [not_le] at h 
     simp only [not_mem_empty, iff_false_iff, not_and]
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
 #align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonal
@@ -166,13 +166,13 @@ section EquivProd
 /-- The disjoint union of antidiagonals `Σ (n : ℕ), antidiagonal n` is equivalent to the product
     `ℕ × ℕ`. This is such an equivalence, obtained by mapping `(n, (k, l))` to `(k, l)`. -/
 @[simps]
-def sigmaAntidiagonalEquivProd : (Σn : ℕ, antidiagonal n) ≃ ℕ × ℕ
+def sigmaAntidiagonalEquivProd : (Σ n : ℕ, antidiagonal n) ≃ ℕ × ℕ
     where
   toFun x := x.2
   invFun x := ⟨x.1 + x.2, x, mem_antidiagonal.mpr rfl⟩
   left_inv := by
     rintro ⟨n, ⟨k, l⟩, h⟩
-    rw [mem_antidiagonal] at h
+    rw [mem_antidiagonal] at h 
     exact Sigma.subtype_ext h rfl
   right_inv x := rfl
 #align finset.nat.sigma_antidiagonal_equiv_prod Finset.Nat.sigmaAntidiagonalEquivProd

cc70d914

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -140,12 +140,6 @@ theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagon
 #align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
 -/
 
-/- warning: finset.nat.filter_fst_eq_antidiagonal -> Finset.Nat.filter_fst_eq_antidiagonal is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat) (m : Nat), Eq.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.filter.{0} (Prod.{0, 0} Nat Nat) (fun (x : Prod.{0, 0} Nat Nat) => Eq.{1} Nat (Prod.fst.{0, 0} Nat Nat x) m) (fun (a : Prod.{0, 0} Nat Nat) => Nat.decidableEq (Prod.fst.{0, 0} Nat Nat a) m) (Finset.Nat.antidiagonal n)) (ite.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.decidableLe m n) (Singleton.singleton.{0, 0} (Prod.{0, 0} Nat Nat) (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.hasSingleton.{0} (Prod.{0, 0} Nat Nat)) (Prod.mk.{0, 0} Nat Nat m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n m))) (EmptyCollection.emptyCollection.{0} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.hasEmptyc.{0} (Prod.{0, 0} Nat Nat))))
-but is expected to have type
-  forall (n : Nat) (m : Nat), Eq.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.filter.{0} (Prod.{0, 0} Nat Nat) (fun (x : Prod.{0, 0} Nat Nat) => Eq.{1} Nat (Prod.fst.{0, 0} Nat Nat x) m) (fun (a : Prod.{0, 0} Nat Nat) => instDecidableEqNat (Prod.fst.{0, 0} Nat Nat a) m) (Finset.Nat.antidiagonal n)) (ite.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (LE.le.{0} Nat instLENat m n) (Nat.decLe m n) (Singleton.singleton.{0, 0} (Prod.{0, 0} Nat Nat) (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.instSingletonFinset.{0} (Prod.{0, 0} Nat Nat)) (Prod.mk.{0, 0} Nat Nat m (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n m))) (EmptyCollection.emptyCollection.{0} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.instEmptyCollectionFinset.{0} (Prod.{0, 0} Nat Nat))))
-Case conversion may be inaccurate. Consider using '#align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonalₓ'. -/
 theorem filter_fst_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅ :=
   by
@@ -158,12 +152,6 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
     exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
 #align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonal
 
-/- warning: finset.nat.filter_snd_eq_antidiagonal -> Finset.Nat.filter_snd_eq_antidiagonal is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat) (m : Nat), Eq.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.filter.{0} (Prod.{0, 0} Nat Nat) (fun (x : Prod.{0, 0} Nat Nat) => Eq.{1} Nat (Prod.snd.{0, 0} Nat Nat x) m) (fun (a : Prod.{0, 0} Nat Nat) => Nat.decidableEq (Prod.snd.{0, 0} Nat Nat a) m) (Finset.Nat.antidiagonal n)) (ite.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (LE.le.{0} Nat Nat.hasLe m n) (Nat.decidableLe m n) (Singleton.singleton.{0, 0} (Prod.{0, 0} Nat Nat) (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.hasSingleton.{0} (Prod.{0, 0} Nat Nat)) (Prod.mk.{0, 0} Nat Nat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n m) m)) (EmptyCollection.emptyCollection.{0} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.hasEmptyc.{0} (Prod.{0, 0} Nat Nat))))
-but is expected to have type
-  forall (n : Nat) (m : Nat), Eq.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.filter.{0} (Prod.{0, 0} Nat Nat) (fun (x : Prod.{0, 0} Nat Nat) => Eq.{1} Nat (Prod.snd.{0, 0} Nat Nat x) m) (fun (a : Prod.{0, 0} Nat Nat) => instDecidableEqNat (Prod.snd.{0, 0} Nat Nat a) m) (Finset.Nat.antidiagonal n)) (ite.{1} (Finset.{0} (Prod.{0, 0} Nat Nat)) (LE.le.{0} Nat instLENat m n) (Nat.decLe m n) (Singleton.singleton.{0, 0} (Prod.{0, 0} Nat Nat) (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.instSingletonFinset.{0} (Prod.{0, 0} Nat Nat)) (Prod.mk.{0, 0} Nat Nat (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n m) m)) (EmptyCollection.emptyCollection.{0} (Finset.{0} (Prod.{0, 0} Nat Nat)) (Finset.instEmptyCollectionFinset.{0} (Prod.{0, 0} Nat Nat))))
-Case conversion may be inaccurate. Consider using '#align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonalₓ'. -/
 theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ :=
   by

cc70d914

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -100,9 +100,7 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
                 ⟨Nat.succ, Nat.succ_injective⟩)) <|
           by simp)
         (by simp) :=
-  by
-  simp_rw [antidiagonal_succ (n + 1), antidiagonal_succ', Finset.map_cons, map_map]
-  rfl
+  by simp_rw [antidiagonal_succ (n + 1), antidiagonal_succ', Finset.map_cons, map_map]; rfl
 #align finset.nat.antidiagonal_succ_succ' Finset.Nat.antidiagonal_succ_succ'
 -/
 
@@ -169,10 +167,7 @@ Case conversion may be inaccurate. Consider using '#align finset.nat.filter_snd_
 theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ :=
   by
-  have : (fun x : ℕ × ℕ => x.snd = m) ∘ Prod.swap = fun x : ℕ × ℕ => x.fst = m :=
-    by
-    ext
-    simp
+  have : (fun x : ℕ × ℕ => x.snd = m) ∘ Prod.swap = fun x : ℕ × ℕ => x.fst = m := by ext; simp
   rw [← map_swap_antidiagonal]
   simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
 #align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal

cc70d914

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

9003f287

chore: remove unnecessary cdots (#12417)

These · are scoping when there is a single active goal.

These were found using a modification of the linter at #12339.

5450e922

Diff

@@ -72,7 +72,7 @@ theorem antidiagonal_succ (n : ℕ) :
         (by simp) := by
   apply eq_of_veq
   rw [cons_val, map_val]
-  · apply Multiset.Nat.antidiagonal_succ
+  apply Multiset.Nat.antidiagonal_succ
 #align finset.nat.antidiagonal_succ Finset.Nat.antidiagonal_succ
 
 theorem antidiagonal_succ' (n : ℕ) :

9003f287

chore: Split Data.{Nat,Int}{.Order}.Basic in group vs ring instances (#11924)

Scatter the content of Data.Nat.Basic across:

Data.Nat.Defs for the lemmas having no dependencies
Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before pre_11924

After post_11924

47062a71

Diff

@@ -3,9 +3,10 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
+import Mathlib.Algebra.Order.Ring.CharZero
+import Mathlib.Data.Finset.Antidiagonal
 import Mathlib.Data.Finset.Card
 import Mathlib.Data.Multiset.NatAntidiagonal
-import Mathlib.Data.Finset.Antidiagonal
 
 #align_import data.finset.nat_antidiagonal from "leanprover-community/mathlib"@"9003f28797c0664a49e4179487267c494477d853"

9003f287

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -99,10 +99,10 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
 #align finset.nat.antidiagonal_succ_succ' Finset.Nat.antidiagonal_succ_succ'
 
 theorem antidiagonal.fst_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 < n + 1 :=
-  Nat.lt_succ_of_le $ antidiagonal.fst_le hlk
+  Nat.lt_succ_of_le <| antidiagonal.fst_le hlk
 
 theorem antidiagonal.snd_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 < n + 1 :=
-  Nat.lt_succ_of_le $ antidiagonal.snd_le hlk
+  Nat.lt_succ_of_le <| antidiagonal.snd_le hlk
 
 @[simp] lemma antidiagonal_filter_snd_le_of_le {n k : ℕ} (h : k ≤ n) :
     (antidiagonal n).filter (fun a ↦ a.snd ≤ k) = (antidiagonal k).map

9003f287

feat: Antidiagonal lemmas (#9224)

From LeanAPAP

503aade4

Diff

@@ -35,6 +35,23 @@ instance instHasAntidiagonal : HasAntidiagonal ℕ where
   mem_antidiagonal {n} {xy} := by
     rw [mem_def, Multiset.Nat.mem_antidiagonal]
 
+lemma antidiagonal_eq_map (n : ℕ) :
+    antidiagonal n = (range (n + 1)).map ⟨fun i ↦ (i, n - i), fun _ _ h ↦ (Prod.ext_iff.1 h).1⟩ :=
+  rfl
+
+lemma antidiagonal_eq_map' (n : ℕ) :
+    antidiagonal n =
+      (range (n + 1)).map ⟨fun i ↦ (n - i, i), fun _ _ h ↦ (Prod.ext_iff.1 h).2⟩ := by
+  rw [← map_swap_antidiagonal, antidiagonal_eq_map, map_map]; rfl
+
+lemma antidiagonal_eq_image (n : ℕ) :
+    antidiagonal n = (range (n + 1)).image fun i ↦ (i, n - i) := by
+  simp only [antidiagonal_eq_map, map_eq_image, Function.Embedding.coeFn_mk]
+
+lemma antidiagonal_eq_image' (n : ℕ) :
+    antidiagonal n = (range (n + 1)).image fun i ↦ (n - i, i) := by
+  simp only [antidiagonal_eq_map', map_eq_image, Function.Embedding.coeFn_mk]
+
 /-- The cardinality of the antidiagonal of `n` is `n + 1`. -/
 @[simp]
 theorem card_antidiagonal (n : ℕ) : (antidiagonal n).card = n + 1 := by simp [antidiagonal]

9003f287

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

@@ -5,6 +5,7 @@ Authors: Johan Commelin
 -/
 import Mathlib.Data.Finset.Card
 import Mathlib.Data.Multiset.NatAntidiagonal
+import Mathlib.Data.Finset.Antidiagonal
 
 #align_import data.finset.nat_antidiagonal from "leanprover-community/mathlib"@"9003f28797c0664a49e4179487267c494477d853"
 
@@ -17,7 +18,8 @@ generally for sums going from `0` to `n`.
 
 ## Notes
 
-This refines files `Data.List.NatAntidiagonal` and `Data.Multiset.NatAntidiagonal`.
+This refines files `Data.List.NatAntidiagonal` and `Data.Multiset.NatAntidiagonal`, providing an
+instance enabling `Finset.antidiagonal` on `Nat`.
 -/
 
 open Function
@@ -28,15 +30,10 @@ namespace Nat
 
 /-- The antidiagonal of a natural number `n` is
     the finset of pairs `(i, j)` such that `i + j = n`. -/
-def antidiagonal (n : ℕ) : Finset (ℕ × ℕ) :=
-  ⟨Multiset.Nat.antidiagonal n, Multiset.Nat.nodup_antidiagonal n⟩
-#align finset.nat.antidiagonal Finset.Nat.antidiagonal
-
-/-- A pair (i, j) is contained in the antidiagonal of `n` if and only if `i + j = n`. -/
-@[simp]
-theorem mem_antidiagonal {n : ℕ} {x : ℕ × ℕ} : x ∈ antidiagonal n ↔ x.1 + x.2 = n := by
-  rw [antidiagonal, mem_def, Multiset.Nat.mem_antidiagonal]
-#align finset.nat.mem_antidiagonal Finset.Nat.mem_antidiagonal
+instance instHasAntidiagonal : HasAntidiagonal ℕ where
+  antidiagonal n := ⟨Multiset.Nat.antidiagonal n, Multiset.Nat.nodup_antidiagonal n⟩
+  mem_antidiagonal {n} {xy} := by
+    rw [mem_def, Multiset.Nat.mem_antidiagonal]
 
 /-- The cardinality of the antidiagonal of `n` is `n + 1`. -/
 @[simp]
@@ -44,7 +41,8 @@ theorem card_antidiagonal (n : ℕ) : (antidiagonal n).card = n + 1 := by simp [
 #align finset.nat.card_antidiagonal Finset.Nat.card_antidiagonal
 
 /-- The antidiagonal of `0` is the list `[(0, 0)]` -/
-@[simp]
+-- nolint as this is for dsimp
+@[simp, nolint simpNF]
 theorem antidiagonal_zero : antidiagonal 0 = {(0, 0)} := rfl
 #align finset.nat.antidiagonal_zero Finset.Nat.antidiagonal_zero
 
@@ -83,66 +81,12 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
   rfl
 #align finset.nat.antidiagonal_succ_succ' Finset.Nat.antidiagonal_succ_succ'
 
-/-- See also `Finset.map.map_prodComm_antidiagonal`. -/
-@[simp] theorem map_swap_antidiagonal {n : ℕ} :
-    (antidiagonal n).map ⟨Prod.swap, Prod.swap_injective⟩ = antidiagonal n :=
-  eq_of_veq <| by simp [antidiagonal, Multiset.Nat.map_swap_antidiagonal]
-#align finset.nat.map_swap_antidiagonal Finset.Nat.map_swap_antidiagonal
-
-@[simp] theorem map_prodComm_antidiagonal {n : ℕ} :
-    (antidiagonal n).map (Equiv.prodComm ℕ ℕ) = antidiagonal n :=
-  map_swap_antidiagonal
-
-/-- A point in the antidiagonal is determined by its first co-ordinate. -/
-theorem antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal n)
-    (hq : q ∈ antidiagonal n) : p = q ↔ p.fst = q.fst := by
-  refine' ⟨congr_arg Prod.fst, fun h ↦ Prod.ext h ((add_right_inj q.fst).mp _)⟩
-  rw [mem_antidiagonal] at hp hq
-  rw [hq, ← h, hp]
-#align finset.nat.antidiagonal_congr Finset.Nat.antidiagonal_congr
-
-/-- A point in the antidiagonal is determined by its first co-ordinate (subtype version of
-`antidiagonal_congr`). This lemma is used by the `ext` tactic. -/
-@[ext] theorem antidiagonal_subtype_ext {n : ℕ} {p q : antidiagonal n} (h : p.val.1 = q.val.1) :
-    p = q := Subtype.ext ((antidiagonal_congr p.prop q.prop).mpr h)
-
-theorem antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 ≤ n := by
-  rw [le_iff_exists_add]
-  use kl.2
-  rwa [mem_antidiagonal, eq_comm] at hlk
-#align finset.nat.antidiagonal.fst_le Finset.Nat.antidiagonal.fst_le
-
 theorem antidiagonal.fst_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 < n + 1 :=
   Nat.lt_succ_of_le $ antidiagonal.fst_le hlk
 
-theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 ≤ n := by
-  rw [le_iff_exists_add]
-  use kl.1
-  rwa [mem_antidiagonal, eq_comm, add_comm] at hlk
-#align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
-
 theorem antidiagonal.snd_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 < n + 1 :=
   Nat.lt_succ_of_le $ antidiagonal.snd_le hlk
 
-theorem filter_fst_eq_antidiagonal (n m : ℕ) :
-    filter (fun x : ℕ × ℕ ↦ x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅ := by
-  ext ⟨x, y⟩
-  simp only [mem_filter, Nat.mem_antidiagonal]
-  split_ifs with h
-  · simp (config := { contextual := true }) [and_comm, eq_tsub_iff_add_eq_of_le h, add_comm]
-  · rw [not_le] at h
-    simp only [not_mem_empty, iff_false_iff, not_and, decide_eq_true_eq]
-    exact fun hn => ne_of_lt (lt_of_le_of_lt (le_self_add.trans hn.le) h)
-#align finset.nat.filter_fst_eq_antidiagonal Finset.Nat.filter_fst_eq_antidiagonal
-
-theorem filter_snd_eq_antidiagonal (n m : ℕ) :
-    filter (fun x : ℕ × ℕ ↦ x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ := by
-  have : (fun x : ℕ × ℕ ↦ (x.snd = m)) ∘ Prod.swap = fun x : ℕ × ℕ ↦ x.fst = m := by
-    ext; simp
-  rw [← map_swap_antidiagonal, filter_map]
-  simp [this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
-#align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal
-
 @[simp] lemma antidiagonal_filter_snd_le_of_le {n k : ℕ} (h : k ≤ n) :
     (antidiagonal n).filter (fun a ↦ a.snd ≤ k) = (antidiagonal k).map
       (Embedding.prodMap ⟨_, add_left_injective (n - k)⟩ (Embedding.refl ℕ)) := by
@@ -192,26 +136,6 @@ theorem filter_snd_eq_antidiagonal (n m : ℕ) :
   ext ⟨i, j⟩
   simpa using aux₂ i j
 
-section EquivProd
-
-/-- The disjoint union of antidiagonals `Σ (n : ℕ), antidiagonal n` is equivalent to the product
-    `ℕ × ℕ`. This is such an equivalence, obtained by mapping `(n, (k, l))` to `(k, l)`. -/
-@[simps]
-def sigmaAntidiagonalEquivProd : (Σn : ℕ, antidiagonal n) ≃ ℕ × ℕ where
-  toFun x := x.2
-  invFun x := ⟨x.1 + x.2, x, mem_antidiagonal.mpr rfl⟩
-  left_inv := by
-    rintro ⟨n, ⟨k, l⟩, h⟩
-    rw [mem_antidiagonal] at h
-    exact Sigma.subtype_ext h rfl
-  right_inv x := rfl
-#align finset.nat.sigma_antidiagonal_equiv_prod Finset.Nat.sigmaAntidiagonalEquivProd
-#align finset.nat.sigma_antidiagonal_equiv_prod_symm_apply_fst Finset.Nat.sigmaAntidiagonalEquivProd_symm_apply_fst
-#align finset.nat.sigma_antidiagonal_equiv_prod_symm_apply_snd_coe Finset.Nat.sigmaAntidiagonalEquivProd_symm_apply_snd_coe
-#align finset.nat.sigma_antidiagonal_equiv_prod_apply Finset.Nat.sigmaAntidiagonalEquivProd_apply
-
-end EquivProd
-
 /-- The set `antidiagonal n` is equivalent to `Fin (n+1)`, via the first projection. --/
 @[simps]
 def antidiagonalEquivFin (n : ℕ) : antidiagonal n ≃ Fin (n + 1) where

9003f287

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

bdc47f68

Diff

@@ -147,8 +147,7 @@ theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     (antidiagonal n).filter (fun a ↦ a.snd ≤ k) = (antidiagonal k).map
       (Embedding.prodMap ⟨_, add_left_injective (n - k)⟩ (Embedding.refl ℕ)) := by
   ext ⟨i, j⟩
-  suffices : i + j = n ∧ j ≤ k ↔ ∃ a, a + j = k ∧ a + (n - k) = i
-  · simpa
+  suffices i + j = n ∧ j ≤ k ↔ ∃ a, a + j = k ∧ a + (n - k) = i by simpa
   refine' ⟨fun hi ↦ ⟨k - j, tsub_add_cancel_of_le hi.2, _⟩, _⟩
   · rw [add_comm, tsub_add_eq_add_tsub h, ← hi.1, add_assoc, Nat.add_sub_of_le hi.2,
       add_tsub_cancel_right]
@@ -173,8 +172,7 @@ theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     (antidiagonal n).filter (fun a ↦ k ≤ a.fst) = (antidiagonal (n - k)).map
       (Embedding.prodMap ⟨_, add_left_injective k⟩ (Embedding.refl ℕ)) := by
   ext ⟨i, j⟩
-  suffices : i + j = n ∧ k ≤ i ↔ ∃ a, a + j = n - k ∧ a + k = i
-  · simpa
+  suffices i + j = n ∧ k ≤ i ↔ ∃ a, a + j = n - k ∧ a + k = i by simpa
   refine' ⟨fun hi ↦ ⟨i - k, _, tsub_add_cancel_of_le hi.2⟩, _⟩
   · rw [← Nat.sub_add_comm hi.2, hi.1]
   · rintro ⟨l, hl, rfl⟩

9003f287

chore(Data/Finset/NatAntidiagonal): naming of antidiagonalEquivFin (#6784)

and add simps, as pointed out by @eric-wieser in https://github.com/leanprover-community/mathlib4/pull/6766#pullrequestreview-1595354618

7e9ae5f4

Diff

@@ -215,7 +215,8 @@ def sigmaAntidiagonalEquivProd : (Σn : ℕ, antidiagonal n) ≃ ℕ × ℕ wher
 end EquivProd
 
 /-- The set `antidiagonal n` is equivalent to `Fin (n+1)`, via the first projection. --/
-def antidiagonal_equiv_fin (n : ℕ) : antidiagonal n ≃ Fin (n + 1) where
+@[simps]
+def antidiagonalEquivFin (n : ℕ) : antidiagonal n ≃ Fin (n + 1) where
   toFun := fun ⟨⟨i, j⟩, h⟩ ↦ ⟨i, antidiagonal.fst_lt h⟩
   invFun := fun ⟨i, h⟩ ↦ ⟨⟨i, n - i⟩, by
     rw [mem_antidiagonal, add_comm, tsub_add_cancel_iff_le]

9003f287

feat: Data.Finset.NatAntidiagonal.antidiagonal_equiv_fin (#6766)

a57b2c25

Diff

@@ -101,18 +101,29 @@ theorem antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal
   rw [hq, ← h, hp]
 #align finset.nat.antidiagonal_congr Finset.Nat.antidiagonal_congr
 
+/-- A point in the antidiagonal is determined by its first co-ordinate (subtype version of
+`antidiagonal_congr`). This lemma is used by the `ext` tactic. -/
+@[ext] theorem antidiagonal_subtype_ext {n : ℕ} {p q : antidiagonal n} (h : p.val.1 = q.val.1) :
+    p = q := Subtype.ext ((antidiagonal_congr p.prop q.prop).mpr h)
+
 theorem antidiagonal.fst_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 ≤ n := by
   rw [le_iff_exists_add]
   use kl.2
   rwa [mem_antidiagonal, eq_comm] at hlk
 #align finset.nat.antidiagonal.fst_le Finset.Nat.antidiagonal.fst_le
 
+theorem antidiagonal.fst_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.1 < n + 1 :=
+  Nat.lt_succ_of_le $ antidiagonal.fst_le hlk
+
 theorem antidiagonal.snd_le {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 ≤ n := by
   rw [le_iff_exists_add]
   use kl.1
   rwa [mem_antidiagonal, eq_comm, add_comm] at hlk
 #align finset.nat.antidiagonal.snd_le Finset.Nat.antidiagonal.snd_le
 
+theorem antidiagonal.snd_lt {n : ℕ} {kl : ℕ × ℕ} (hlk : kl ∈ antidiagonal n) : kl.2 < n + 1 :=
+  Nat.lt_succ_of_le $ antidiagonal.snd_le hlk
+
 theorem filter_fst_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ ↦ x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅ := by
   ext ⟨x, y⟩
@@ -203,6 +214,15 @@ def sigmaAntidiagonalEquivProd : (Σn : ℕ, antidiagonal n) ≃ ℕ × ℕ wher
 
 end EquivProd
 
+/-- The set `antidiagonal n` is equivalent to `Fin (n+1)`, via the first projection. --/
+def antidiagonal_equiv_fin (n : ℕ) : antidiagonal n ≃ Fin (n + 1) where
+  toFun := fun ⟨⟨i, j⟩, h⟩ ↦ ⟨i, antidiagonal.fst_lt h⟩
+  invFun := fun ⟨i, h⟩ ↦ ⟨⟨i, n - i⟩, by
+    rw [mem_antidiagonal, add_comm, tsub_add_cancel_iff_le]
+    exact Nat.le_of_lt_succ h⟩
+  left_inv := by rintro ⟨⟨i, j⟩, h⟩; ext; rfl
+  right_inv x := rfl
+
 end Nat
 
 end Finset

9003f287

feat: lemmas about parity and Nat.antidiagonal (#6540)

704efa4d

Diff

@@ -20,6 +20,7 @@ generally for sums going from `0` to `n`.
 This refines files `Data.List.NatAntidiagonal` and `Data.Multiset.NatAntidiagonal`.
 -/
 
+open Function
 
 namespace Finset
 
@@ -51,7 +52,7 @@ theorem antidiagonal_succ (n : ℕ) :
     antidiagonal (n + 1) =
       cons (0, n + 1)
         ((antidiagonal n).map
-          (Function.Embedding.prodMap ⟨Nat.succ, Nat.succ_injective⟩ (Function.Embedding.refl _)))
+          (Embedding.prodMap ⟨Nat.succ, Nat.succ_injective⟩ (Embedding.refl _)))
         (by simp) := by
   apply eq_of_veq
   rw [cons_val, map_val]
@@ -62,7 +63,7 @@ theorem antidiagonal_succ' (n : ℕ) :
     antidiagonal (n + 1) =
       cons (n + 1, 0)
         ((antidiagonal n).map
-          (Function.Embedding.prodMap (Function.Embedding.refl _) ⟨Nat.succ, Nat.succ_injective⟩))
+          (Embedding.prodMap (Embedding.refl _) ⟨Nat.succ, Nat.succ_injective⟩))
         (by simp) := by
   apply eq_of_veq
   rw [cons_val, map_val]
@@ -74,7 +75,7 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
       cons (0, n + 2)
         (cons (n + 2, 0)
             ((antidiagonal n).map
-              (Function.Embedding.prodMap ⟨Nat.succ, Nat.succ_injective⟩
+              (Embedding.prodMap ⟨Nat.succ, Nat.succ_injective⟩
                 ⟨Nat.succ, Nat.succ_injective⟩)) <|
           by simp)
         (by simp) := by
@@ -82,11 +83,16 @@ theorem antidiagonal_succ_succ' {n : ℕ} :
   rfl
 #align finset.nat.antidiagonal_succ_succ' Finset.Nat.antidiagonal_succ_succ'
 
-theorem map_swap_antidiagonal {n : ℕ} :
+/-- See also `Finset.map.map_prodComm_antidiagonal`. -/
+@[simp] theorem map_swap_antidiagonal {n : ℕ} :
     (antidiagonal n).map ⟨Prod.swap, Prod.swap_injective⟩ = antidiagonal n :=
   eq_of_veq <| by simp [antidiagonal, Multiset.Nat.map_swap_antidiagonal]
 #align finset.nat.map_swap_antidiagonal Finset.Nat.map_swap_antidiagonal
 
+@[simp] theorem map_prodComm_antidiagonal {n : ℕ} :
+    (antidiagonal n).map (Equiv.prodComm ℕ ℕ) = antidiagonal n :=
+  map_swap_antidiagonal
+
 /-- A point in the antidiagonal is determined by its first co-ordinate. -/
 theorem antidiagonal_congr {n : ℕ} {p q : ℕ × ℕ} (hp : p ∈ antidiagonal n)
     (hq : q ∈ antidiagonal n) : p = q ↔ p.fst = q.fst := by
@@ -122,10 +128,61 @@ theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ ↦ x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ := by
   have : (fun x : ℕ × ℕ ↦ (x.snd = m)) ∘ Prod.swap = fun x : ℕ × ℕ ↦ x.fst = m := by
     ext; simp
-  rw [← map_swap_antidiagonal]
-  simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
+  rw [← map_swap_antidiagonal, filter_map]
+  simp [this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
 #align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal
 
+@[simp] lemma antidiagonal_filter_snd_le_of_le {n k : ℕ} (h : k ≤ n) :
+    (antidiagonal n).filter (fun a ↦ a.snd ≤ k) = (antidiagonal k).map
+      (Embedding.prodMap ⟨_, add_left_injective (n - k)⟩ (Embedding.refl ℕ)) := by
+  ext ⟨i, j⟩
+  suffices : i + j = n ∧ j ≤ k ↔ ∃ a, a + j = k ∧ a + (n - k) = i
+  · simpa
+  refine' ⟨fun hi ↦ ⟨k - j, tsub_add_cancel_of_le hi.2, _⟩, _⟩
+  · rw [add_comm, tsub_add_eq_add_tsub h, ← hi.1, add_assoc, Nat.add_sub_of_le hi.2,
+      add_tsub_cancel_right]
+  · rintro ⟨l, hl, rfl⟩
+    refine' ⟨_, hl ▸ Nat.le_add_left j l⟩
+    rw [add_assoc, add_comm, add_assoc, add_comm j l, hl]
+    exact Nat.sub_add_cancel h
+
+@[simp] lemma antidiagonal_filter_fst_le_of_le {n k : ℕ} (h : k ≤ n) :
+    (antidiagonal n).filter (fun a ↦ a.fst ≤ k) = (antidiagonal k).map
+      (Embedding.prodMap (Embedding.refl ℕ) ⟨_, add_left_injective (n - k)⟩) := by
+  have aux₁ : fun a ↦ a.fst ≤ k = (fun a ↦ a.snd ≤ k) ∘ (Equiv.prodComm ℕ ℕ).symm := rfl
+  have aux₂ : ∀ i j, (∃ a b, a + b = k ∧ b = i ∧ a + (n - k) = j) ↔
+                      ∃ a b, a + b = k ∧ a = i ∧ b + (n - k) = j :=
+    fun i j ↦ by rw [exists_comm]; exact exists₂_congr (fun a b ↦ by rw [add_comm])
+  rw [← map_prodComm_antidiagonal]
+  simp_rw [aux₁, ← map_filter, antidiagonal_filter_snd_le_of_le h, map_map]
+  ext ⟨i, j⟩
+  simpa using aux₂ i j
+
+@[simp] lemma antidiagonal_filter_le_fst_of_le {n k : ℕ} (h : k ≤ n) :
+    (antidiagonal n).filter (fun a ↦ k ≤ a.fst) = (antidiagonal (n - k)).map
+      (Embedding.prodMap ⟨_, add_left_injective k⟩ (Embedding.refl ℕ)) := by
+  ext ⟨i, j⟩
+  suffices : i + j = n ∧ k ≤ i ↔ ∃ a, a + j = n - k ∧ a + k = i
+  · simpa
+  refine' ⟨fun hi ↦ ⟨i - k, _, tsub_add_cancel_of_le hi.2⟩, _⟩
+  · rw [← Nat.sub_add_comm hi.2, hi.1]
+  · rintro ⟨l, hl, rfl⟩
+    refine' ⟨_, Nat.le_add_left k l⟩
+    rw [add_right_comm, hl]
+    exact tsub_add_cancel_of_le h
+
+@[simp] lemma antidiagonal_filter_le_snd_of_le {n k : ℕ} (h : k ≤ n) :
+    (antidiagonal n).filter (fun a ↦ k ≤ a.snd) = (antidiagonal (n - k)).map
+      (Embedding.prodMap (Embedding.refl ℕ) ⟨_, add_left_injective k⟩) := by
+  have aux₁ : fun a ↦ k ≤ a.snd = (fun a ↦ k ≤ a.fst) ∘ (Equiv.prodComm ℕ ℕ).symm := rfl
+  have aux₂ : ∀ i j, (∃ a b, a + b = n - k ∧ b = i ∧ a + k = j) ↔
+                      ∃ a b, a + b = n - k ∧ a = i ∧ b + k = j :=
+    fun i j ↦ by rw [exists_comm]; exact exists₂_congr (fun a b ↦ by rw [add_comm])
+  rw [← map_prodComm_antidiagonal]
+  simp_rw [aux₁, ← map_filter, antidiagonal_filter_le_fst_of_le h, map_map]
+  ext ⟨i, j⟩
+  simpa using aux₂ i j
+
 section EquivProd
 
 /-- The disjoint union of antidiagonals `Σ (n : ℕ), antidiagonal n` is equivalent to the product

9003f287

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) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.finset.nat_antidiagonal
-! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Finset.Card
 import Mathlib.Data.Multiset.NatAntidiagonal
 
+#align_import data.finset.nat_antidiagonal from "leanprover-community/mathlib"@"9003f28797c0664a49e4179487267c494477d853"
+
 /-!
 # Antidiagonals in ℕ × ℕ as finsets

9003f287

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

@@ -124,7 +124,7 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
 theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ ↦ x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ := by
   have : (fun x : ℕ × ℕ ↦ (x.snd = m)) ∘ Prod.swap = fun x : ℕ × ℕ ↦ x.fst = m := by
-    ext ; simp
+    ext; simp
   rw [← map_swap_antidiagonal]
   simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]
 #align finset.nat.filter_snd_eq_antidiagonal Finset.Nat.filter_snd_eq_antidiagonal

9003f287

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -143,6 +143,9 @@ def sigmaAntidiagonalEquivProd : (Σn : ℕ, antidiagonal n) ≃ ℕ × ℕ wher
     exact Sigma.subtype_ext h rfl
   right_inv x := rfl
 #align finset.nat.sigma_antidiagonal_equiv_prod Finset.Nat.sigmaAntidiagonalEquivProd
+#align finset.nat.sigma_antidiagonal_equiv_prod_symm_apply_fst Finset.Nat.sigmaAntidiagonalEquivProd_symm_apply_fst
+#align finset.nat.sigma_antidiagonal_equiv_prod_symm_apply_snd_coe Finset.Nat.sigmaAntidiagonalEquivProd_symm_apply_snd_coe
+#align finset.nat.sigma_antidiagonal_equiv_prod_apply Finset.Nat.sigmaAntidiagonalEquivProd_apply
 
 end EquivProd

9003f287

chore: revert Multiset and Finset API to use Prop instead of Bool (#1652)

Co-authored-by: Reid Barton <rwbarton@gmail.com>

bc61efff

Diff

@@ -123,7 +123,7 @@ theorem filter_fst_eq_antidiagonal (n m : ℕ) :
 
 theorem filter_snd_eq_antidiagonal (n m : ℕ) :
     filter (fun x : ℕ × ℕ ↦ x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅ := by
-  have : (fun x : ℕ × ℕ ↦ (x.snd = m : Bool)) ∘ Prod.swap = fun x : ℕ × ℕ ↦ x.fst = m := by
+  have : (fun x : ℕ × ℕ ↦ (x.snd = m)) ∘ Prod.swap = fun x : ℕ × ℕ ↦ x.fst = m := by
     ext ; simp
   rw [← map_swap_antidiagonal]
   simp [filter_map, this, filter_fst_eq_antidiagonal, apply_ite (Finset.map _)]

9003f287

feat port : Data.Finset.NatAntidiagonal (#1598)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

76df73b5

`data.finset.nat_antidiagonal` ⟷ `Mathlib.Data.Finset.NatAntidiagonal`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 2 + 156

data.finset.nat_antidiagonal ⟷ Mathlib.Data.Finset.NatAntidiagonal

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 2 + 156

`data.finset.nat_antidiagonal` ⟷ `Mathlib.Data.Finset.NatAntidiagonal`