data.multiset.finset_ops
⟷
Mathlib.Data.Multiset.FinsetOps
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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This PR will split most of the lemmas in data.set.pairwise
which are independent of the data.set.lattice
. It makes a lot of files no longer depend on data.set.lattice
.
mathlib4 PR: https://github.com/leanprover-community/mathlib4/pull/1184
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
@@ -210,3 +210,7 @@ theorem ndinter_eq_zero_iff_disjoint {s t : multiset α} : ndinter s t = 0 ↔ d
by rw ← subset_zero; simp [subset_iff, disjoint]
end multiset
+
+-- Assert that we define `finset` without the material on the set lattice.
+-- Note that we cannot put this in `data.finset.basic` because we proved relevant lemmas there.
+assert_not_exists set.sInter
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -233,7 +233,7 @@ theorem ndunion_le_add (s t : Multiset α) : ndunion s t ≤ s + t :=
#print Multiset.ndunion_le /-
theorem ndunion_le {s t u : Multiset α} : ndunion s t ≤ u ↔ s ⊆ u ∧ t ≤ u :=
Multiset.induction_on s (by simp)
- (by simp (config := { contextual := true }) [ndinsert_le, and_comm', and_left_comm])
+ (by simp (config := { contextual := true }) [ndinsert_le, and_comm, and_left_comm])
#align multiset.ndunion_le Multiset.ndunion_le
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -144,10 +144,10 @@ theorem attach_ndinsert (a : α) (s : Multiset α) :
by
intro t ht
by_cases a ∈ s
- · rw [ndinsert_of_mem h] at ht
+ · rw [ndinsert_of_mem h] at ht
subst ht
rw [Eq, map_id, ndinsert_of_mem (mem_attach _ _)]
- · rw [ndinsert_of_not_mem h] at ht
+ · rw [ndinsert_of_not_mem h] at ht
subst ht
simp [attach_cons, h]
this _ rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
-import Mathbin.Data.Multiset.Dedup
+import Data.Multiset.Dedup
#align_import data.multiset.finset_ops from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -208,7 +208,7 @@ theorem cons_ndunion (s t : Multiset α) (a : α) : ndunion (a ::ₘ s) t = ndin
#print Multiset.mem_ndunion /-
@[simp]
theorem mem_ndunion {s t : Multiset α} {a : α} : a ∈ ndunion s t ↔ a ∈ s ∨ a ∈ t :=
- Quotient.induction_on₂ s t fun l₁ l₂ => List.mem_union
+ Quotient.induction_on₂ s t fun l₁ l₂ => List.mem_union_iff
#align multiset.mem_ndunion Multiset.mem_ndunion
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.multiset.finset_ops
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Multiset.Dedup
+#align_import data.multiset.finset_ops from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
+
/-!
# Preparations for defining operations on `finset`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -74,10 +74,12 @@ theorem mem_ndinsert {a b : α} {s : Multiset α} : a ∈ ndinsert b s ↔ a = b
#align multiset.mem_ndinsert Multiset.mem_ndinsert
-/
+#print Multiset.le_ndinsert_self /-
@[simp]
theorem le_ndinsert_self (a : α) (s : Multiset α) : s ≤ ndinsert a s :=
Quot.inductionOn s fun l => (sublist_insert _ _).Subperm
#align multiset.le_ndinsert_self Multiset.le_ndinsert_self
+-/
#print Multiset.mem_ndinsert_self /-
@[simp]
@@ -92,15 +94,19 @@ theorem mem_ndinsert_of_mem {a b : α} {s : Multiset α} (h : a ∈ s) : a ∈ n
#align multiset.mem_ndinsert_of_mem Multiset.mem_ndinsert_of_mem
-/
+#print Multiset.length_ndinsert_of_mem /-
@[simp]
theorem length_ndinsert_of_mem {a : α} {s : Multiset α} (h : a ∈ s) :
card (ndinsert a s) = card s := by simp [h]
#align multiset.length_ndinsert_of_mem Multiset.length_ndinsert_of_mem
+-/
+#print Multiset.length_ndinsert_of_not_mem /-
@[simp]
theorem length_ndinsert_of_not_mem {a : α} {s : Multiset α} (h : a ∉ s) :
card (ndinsert a s) = card s + 1 := by simp [h]
#align multiset.length_ndinsert_of_not_mem Multiset.length_ndinsert_of_not_mem
+-/
#print Multiset.dedup_cons /-
theorem dedup_cons {a : α} {s : Multiset α} : dedup (a ::ₘ s) = ndinsert a (dedup s) := by
@@ -114,6 +120,7 @@ theorem Nodup.ndinsert (a : α) : Nodup s → Nodup (ndinsert a s) :=
#align multiset.nodup.ndinsert Multiset.Nodup.ndinsert
-/
+#print Multiset.ndinsert_le /-
theorem ndinsert_le {a : α} {s t : Multiset α} : ndinsert a s ≤ t ↔ s ≤ t ∧ a ∈ t :=
⟨fun h => ⟨le_trans (le_ndinsert_self _ _) h, mem_of_le h (mem_ndinsert_self _ _)⟩, fun ⟨l, m⟩ =>
if h : a ∈ s then by simp [h, l]
@@ -122,7 +129,9 @@ theorem ndinsert_le {a : α} {s t : Multiset α} : ndinsert a s ≤ t ↔ s ≤
cons_erase m] <;>
exact l⟩
#align multiset.ndinsert_le Multiset.ndinsert_le
+-/
+#print Multiset.attach_ndinsert /-
theorem attach_ndinsert (a : α) (s : Multiset α) :
(s.ndinsert a).attach =
ndinsert ⟨a, mem_ndinsert_self a s⟩ (s.attach.map fun p => ⟨p.1, mem_ndinsert_of_mem p.2⟩) :=
@@ -146,6 +155,7 @@ theorem attach_ndinsert (a : α) (s : Multiset α) :
simp [attach_cons, h]
this _ rfl
#align multiset.attach_ndinsert Multiset.attach_ndinsert
+-/
#print Multiset.disjoint_ndinsert_left /-
@[simp]
@@ -205,9 +215,11 @@ theorem mem_ndunion {s t : Multiset α} {a : α} : a ∈ ndunion s t ↔ a ∈ s
#align multiset.mem_ndunion Multiset.mem_ndunion
-/
+#print Multiset.le_ndunion_right /-
theorem le_ndunion_right (s t : Multiset α) : t ≤ ndunion s t :=
Quotient.induction_on₂ s t fun l₁ l₂ => (suffix_union_right _ _).Sublist.Subperm
#align multiset.le_ndunion_right Multiset.le_ndunion_right
+-/
#print Multiset.subset_ndunion_right /-
theorem subset_ndunion_right (s t : Multiset α) : t ⊆ ndunion s t :=
@@ -215,14 +227,18 @@ theorem subset_ndunion_right (s t : Multiset α) : t ⊆ ndunion s t :=
#align multiset.subset_ndunion_right Multiset.subset_ndunion_right
-/
+#print Multiset.ndunion_le_add /-
theorem ndunion_le_add (s t : Multiset α) : ndunion s t ≤ s + t :=
Quotient.induction_on₂ s t fun l₁ l₂ => (union_sublist_append _ _).Subperm
#align multiset.ndunion_le_add Multiset.ndunion_le_add
+-/
+#print Multiset.ndunion_le /-
theorem ndunion_le {s t u : Multiset α} : ndunion s t ≤ u ↔ s ⊆ u ∧ t ≤ u :=
Multiset.induction_on s (by simp)
(by simp (config := { contextual := true }) [ndinsert_le, and_comm', and_left_comm])
#align multiset.ndunion_le Multiset.ndunion_le
+-/
#print Multiset.subset_ndunion_left /-
theorem subset_ndunion_left (s t : Multiset α) : s ⊆ ndunion s t := fun a h =>
@@ -230,13 +246,17 @@ theorem subset_ndunion_left (s t : Multiset α) : s ⊆ ndunion s t := fun a h =
#align multiset.subset_ndunion_left Multiset.subset_ndunion_left
-/
+#print Multiset.le_ndunion_left /-
theorem le_ndunion_left {s} (t : Multiset α) (d : Nodup s) : s ≤ ndunion s t :=
(le_iff_subset d).2 <| subset_ndunion_left _ _
#align multiset.le_ndunion_left Multiset.le_ndunion_left
+-/
+#print Multiset.ndunion_le_union /-
theorem ndunion_le_union (s t : Multiset α) : ndunion s t ≤ s ∪ t :=
ndunion_le.2 ⟨subset_of_le (le_union_left _ _), le_union_right _ _⟩
#align multiset.ndunion_le_union Multiset.ndunion_le_union
+-/
#print Multiset.Nodup.ndunion /-
theorem Nodup.ndunion (s : Multiset α) {t : Multiset α} : Nodup t → Nodup (ndunion s t) :=
@@ -312,13 +332,17 @@ theorem Nodup.ndinter {s : Multiset α} (t : Multiset α) : Nodup s → Nodup (n
#align multiset.nodup.ndinter Multiset.Nodup.ndinter
-/
+#print Multiset.le_ndinter /-
theorem le_ndinter {s t u : Multiset α} : s ≤ ndinter t u ↔ s ≤ t ∧ s ⊆ u := by
simp [ndinter, le_filter, subset_iff]
#align multiset.le_ndinter Multiset.le_ndinter
+-/
+#print Multiset.ndinter_le_left /-
theorem ndinter_le_left (s t : Multiset α) : ndinter s t ≤ s :=
(le_ndinter.1 le_rfl).1
#align multiset.ndinter_le_left Multiset.ndinter_le_left
+-/
#print Multiset.ndinter_subset_left /-
theorem ndinter_subset_left (s t : Multiset α) : ndinter s t ⊆ s :=
@@ -332,13 +356,17 @@ theorem ndinter_subset_right (s t : Multiset α) : ndinter s t ⊆ t :=
#align multiset.ndinter_subset_right Multiset.ndinter_subset_right
-/
+#print Multiset.ndinter_le_right /-
theorem ndinter_le_right {s} (t : Multiset α) (d : Nodup s) : ndinter s t ≤ t :=
(le_iff_subset <| d.ndinter _).2 <| ndinter_subset_right _ _
#align multiset.ndinter_le_right Multiset.ndinter_le_right
+-/
+#print Multiset.inter_le_ndinter /-
theorem inter_le_ndinter (s t : Multiset α) : s ∩ t ≤ ndinter s t :=
le_ndinter.2 ⟨inter_le_left _ _, subset_of_le <| inter_le_right _ _⟩
#align multiset.inter_le_ndinter Multiset.inter_le_ndinter
+-/
#print Multiset.ndinter_eq_inter /-
@[simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -138,10 +138,10 @@ theorem attach_ndinsert (a : α) (s : Multiset α) :
by
intro t ht
by_cases a ∈ s
- · rw [ndinsert_of_mem h] at ht
+ · rw [ndinsert_of_mem h] at ht
subst ht
rw [Eq, map_id, ndinsert_of_mem (mem_attach _ _)]
- · rw [ndinsert_of_not_mem h] at ht
+ · rw [ndinsert_of_not_mem h] at ht
subst ht
simp [attach_cons, h]
this _ rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -74,12 +74,6 @@ theorem mem_ndinsert {a b : α} {s : Multiset α} : a ∈ ndinsert b s ↔ a = b
#align multiset.mem_ndinsert Multiset.mem_ndinsert
-/
-/- warning: multiset.le_ndinsert_self -> Multiset.le_ndinsert_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align multiset.le_ndinsert_self Multiset.le_ndinsert_selfₓ'. -/
@[simp]
theorem le_ndinsert_self (a : α) (s : Multiset α) : s ≤ ndinsert a s :=
Quot.inductionOn s fun l => (sublist_insert _ _).Subperm
@@ -98,20 +92,11 @@ theorem mem_ndinsert_of_mem {a b : α} {s : Multiset α} (h : a ∈ s) : a ∈ n
#align multiset.mem_ndinsert_of_mem Multiset.mem_ndinsert_of_mem
-/
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-Case conversion may be inaccurate. Consider using '#align multiset.length_ndinsert_of_mem Multiset.length_ndinsert_of_memₓ'. -/
@[simp]
theorem length_ndinsert_of_mem {a : α} {s : Multiset α} (h : a ∈ s) :
card (ndinsert a s) = card s := by simp [h]
#align multiset.length_ndinsert_of_mem Multiset.length_ndinsert_of_mem
-/- warning: multiset.length_ndinsert_of_not_mem -> Multiset.length_ndinsert_of_not_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multiset.length_ndinsert_of_not_mem Multiset.length_ndinsert_of_not_memₓ'. -/
@[simp]
theorem length_ndinsert_of_not_mem {a : α} {s : Multiset α} (h : a ∉ s) :
card (ndinsert a s) = card s + 1 := by simp [h]
@@ -129,12 +114,6 @@ theorem Nodup.ndinsert (a : α) : Nodup s → Nodup (ndinsert a s) :=
#align multiset.nodup.ndinsert Multiset.Nodup.ndinsert
-/
-/- warning: multiset.ndinsert_le -> Multiset.ndinsert_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align multiset.ndinsert_le Multiset.ndinsert_leₓ'. -/
theorem ndinsert_le {a : α} {s t : Multiset α} : ndinsert a s ≤ t ↔ s ≤ t ∧ a ∈ t :=
⟨fun h => ⟨le_trans (le_ndinsert_self _ _) h, mem_of_le h (mem_ndinsert_self _ _)⟩, fun ⟨l, m⟩ =>
if h : a ∈ s then by simp [h, l]
@@ -144,12 +123,6 @@ theorem ndinsert_le {a : α} {s t : Multiset α} : ndinsert a s ≤ t ↔ s ≤
exact l⟩
#align multiset.ndinsert_le Multiset.ndinsert_le
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-Case conversion may be inaccurate. Consider using '#align multiset.attach_ndinsert Multiset.attach_ndinsertₓ'. -/
theorem attach_ndinsert (a : α) (s : Multiset α) :
(s.ndinsert a).attach =
ndinsert ⟨a, mem_ndinsert_self a s⟩ (s.attach.map fun p => ⟨p.1, mem_ndinsert_of_mem p.2⟩) :=
@@ -232,12 +205,6 @@ theorem mem_ndunion {s t : Multiset α} {a : α} : a ∈ ndunion s t ↔ a ∈ s
#align multiset.mem_ndunion Multiset.mem_ndunion
-/
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theorem le_ndunion_right (s t : Multiset α) : t ≤ ndunion s t :=
Quotient.induction_on₂ s t fun l₁ l₂ => (suffix_union_right _ _).Sublist.Subperm
#align multiset.le_ndunion_right Multiset.le_ndunion_right
@@ -248,22 +215,10 @@ theorem subset_ndunion_right (s t : Multiset α) : t ⊆ ndunion s t :=
#align multiset.subset_ndunion_right Multiset.subset_ndunion_right
-/
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theorem ndunion_le_add (s t : Multiset α) : ndunion s t ≤ s + t :=
Quotient.induction_on₂ s t fun l₁ l₂ => (union_sublist_append _ _).Subperm
#align multiset.ndunion_le_add Multiset.ndunion_le_add
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-Case conversion may be inaccurate. Consider using '#align multiset.ndunion_le Multiset.ndunion_leₓ'. -/
theorem ndunion_le {s t u : Multiset α} : ndunion s t ≤ u ↔ s ⊆ u ∧ t ≤ u :=
Multiset.induction_on s (by simp)
(by simp (config := { contextual := true }) [ndinsert_le, and_comm', and_left_comm])
@@ -275,22 +230,10 @@ theorem subset_ndunion_left (s t : Multiset α) : s ⊆ ndunion s t := fun a h =
#align multiset.subset_ndunion_left Multiset.subset_ndunion_left
-/
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theorem le_ndunion_left {s} (t : Multiset α) (d : Nodup s) : s ≤ ndunion s t :=
(le_iff_subset d).2 <| subset_ndunion_left _ _
#align multiset.le_ndunion_left Multiset.le_ndunion_left
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theorem ndunion_le_union (s t : Multiset α) : ndunion s t ≤ s ∪ t :=
ndunion_le.2 ⟨subset_of_le (le_union_left _ _), le_union_right _ _⟩
#align multiset.ndunion_le_union Multiset.ndunion_le_union
@@ -369,22 +312,10 @@ theorem Nodup.ndinter {s : Multiset α} (t : Multiset α) : Nodup s → Nodup (n
#align multiset.nodup.ndinter Multiset.Nodup.ndinter
-/
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-Case conversion may be inaccurate. Consider using '#align multiset.le_ndinter Multiset.le_ndinterₓ'. -/
theorem le_ndinter {s t u : Multiset α} : s ≤ ndinter t u ↔ s ≤ t ∧ s ⊆ u := by
simp [ndinter, le_filter, subset_iff]
#align multiset.le_ndinter Multiset.le_ndinter
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-Case conversion may be inaccurate. Consider using '#align multiset.ndinter_le_left Multiset.ndinter_le_leftₓ'. -/
theorem ndinter_le_left (s t : Multiset α) : ndinter s t ≤ s :=
(le_ndinter.1 le_rfl).1
#align multiset.ndinter_le_left Multiset.ndinter_le_left
@@ -401,22 +332,10 @@ theorem ndinter_subset_right (s t : Multiset α) : ndinter s t ⊆ t :=
#align multiset.ndinter_subset_right Multiset.ndinter_subset_right
-/
-/- warning: multiset.ndinter_le_right -> Multiset.ndinter_le_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align multiset.ndinter_le_right Multiset.ndinter_le_rightₓ'. -/
theorem ndinter_le_right {s} (t : Multiset α) (d : Nodup s) : ndinter s t ≤ t :=
(le_iff_subset <| d.ndinter _).2 <| ndinter_subset_right _ _
#align multiset.ndinter_le_right Multiset.ndinter_le_right
-/- warning: multiset.inter_le_ndinter -> Multiset.inter_le_ndinter is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align multiset.inter_le_ndinter Multiset.inter_le_ndinterₓ'. -/
theorem inter_le_ndinter (s t : Multiset α) : s ∩ t ≤ ndinter s t :=
le_ndinter.2 ⟨inter_le_left _ _, subset_of_le <| inter_le_right _ _⟩
#align multiset.inter_le_ndinter Multiset.inter_le_ndinter
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -110,10 +110,7 @@ theorem length_ndinsert_of_mem {a : α} {s : Multiset α} (h : a ∈ s) :
#align multiset.length_ndinsert_of_mem Multiset.length_ndinsert_of_mem
/- warning: multiset.length_ndinsert_of_not_mem -> Multiset.length_ndinsert_of_not_mem is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align multiset.length_ndinsert_of_not_mem Multiset.length_ndinsert_of_not_memₓ'. -/
@[simp]
theorem length_ndinsert_of_not_mem {a : α} {s : Multiset α} (h : a ∉ s) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -76,7 +76,7 @@ theorem mem_ndinsert {a b : α} {s : Multiset α} : a ∈ ndinsert b s ↔ a = b
/- warning: multiset.le_ndinsert_self -> Multiset.le_ndinsert_self is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (a : α) (s : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (a : α) (s : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (a : α) (s : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) s (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)
Case conversion may be inaccurate. Consider using '#align multiset.le_ndinsert_self Multiset.le_ndinsert_selfₓ'. -/
@@ -134,7 +134,7 @@ theorem Nodup.ndinsert (a : α) : Nodup s → Nodup (ndinsert a s) :=
/- warning: multiset.ndinsert_le -> Multiset.ndinsert_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α} {t : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s) t) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s t) (Membership.Mem.{u1, u1} α (Multiset.{u1} α) (Multiset.hasMem.{u1} α) a t))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α} {t : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s) t) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s t) (Membership.Mem.{u1, u1} α (Multiset.{u1} α) (Multiset.hasMem.{u1} α) a t))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α} {t : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s) t) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) s t) (Membership.mem.{u1, u1} α (Multiset.{u1} α) (Multiset.instMembershipMultiset.{u1} α) a t))
Case conversion may be inaccurate. Consider using '#align multiset.ndinsert_le Multiset.ndinsert_leₓ'. -/
@@ -237,7 +237,7 @@ theorem mem_ndunion {s t : Multiset α} {a : α} : a ∈ ndunion s t ↔ a ∈ s
/- warning: multiset.le_ndunion_right -> Multiset.le_ndunion_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) t (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) t (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) t (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
Case conversion may be inaccurate. Consider using '#align multiset.le_ndunion_right Multiset.le_ndunion_rightₓ'. -/
@@ -253,7 +253,7 @@ theorem subset_ndunion_right (s t : Multiset α) : t ⊆ ndunion s t :=
/- warning: multiset.ndunion_le_add -> Multiset.ndunion_le_add is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (HAdd.hAdd.{u1, u1, u1} (Multiset.{u1} α) (Multiset.{u1} α) (Multiset.{u1} α) (instHAdd.{u1} (Multiset.{u1} α) (Multiset.hasAdd.{u1} α)) s t)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (HAdd.hAdd.{u1, u1, u1} (Multiset.{u1} α) (Multiset.{u1} α) (Multiset.{u1} α) (instHAdd.{u1} (Multiset.{u1} α) (Multiset.hasAdd.{u1} α)) s t)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (HAdd.hAdd.{u1, u1, u1} (Multiset.{u1} α) (Multiset.{u1} α) (Multiset.{u1} α) (instHAdd.{u1} (Multiset.{u1} α) (Multiset.instAddMultiset.{u1} α)) s t)
Case conversion may be inaccurate. Consider using '#align multiset.ndunion_le_add Multiset.ndunion_le_addₓ'. -/
@@ -263,7 +263,7 @@ theorem ndunion_le_add (s t : Multiset α) : ndunion s t ≤ s + t :=
/- warning: multiset.ndunion_le -> Multiset.ndunion_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) u) (And (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.hasSubset.{u1} α) s u) (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) t u))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) u) (And (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.hasSubset.{u1} α) s u) (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) t u))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) u) (And (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.instHasSubsetMultiset.{u1} α) s u) (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) t u))
Case conversion may be inaccurate. Consider using '#align multiset.ndunion_le Multiset.ndunion_leₓ'. -/
@@ -280,7 +280,7 @@ theorem subset_ndunion_left (s t : Multiset α) : s ⊆ ndunion s t := fun a h =
/- warning: multiset.le_ndunion_left -> Multiset.le_ndunion_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) s (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t))
Case conversion may be inaccurate. Consider using '#align multiset.le_ndunion_left Multiset.le_ndunion_leftₓ'. -/
@@ -290,7 +290,7 @@ theorem le_ndunion_left {s} (t : Multiset α) (d : Nodup s) : s ≤ ndunion s t
/- warning: multiset.ndunion_le_union -> Multiset.ndunion_le_union is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (Union.union.{u1} (Multiset.{u1} α) (Multiset.hasUnion.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (Union.union.{u1} (Multiset.{u1} α) (Multiset.hasUnion.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndunion.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) (Union.union.{u1} (Multiset.{u1} α) (Multiset.instUnionMultiset.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t)
Case conversion may be inaccurate. Consider using '#align multiset.ndunion_le_union Multiset.ndunion_le_unionₓ'. -/
@@ -374,7 +374,7 @@ theorem Nodup.ndinter {s : Multiset α} (t : Multiset α) : Nodup s → Nodup (n
/- warning: multiset.le_ndinter -> Multiset.le_ndinter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) t u)) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s t) (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.hasSubset.{u1} α) s u))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) t u)) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) s t) (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.hasSubset.{u1} α) s u))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} {t : Multiset.{u1} α} {u : Multiset.{u1} α}, Iff (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) s (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) t u)) (And (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) s t) (HasSubset.Subset.{u1} (Multiset.{u1} α) (Multiset.instHasSubsetMultiset.{u1} α) s u))
Case conversion may be inaccurate. Consider using '#align multiset.le_ndinter Multiset.le_ndinterₓ'. -/
@@ -384,7 +384,7 @@ theorem le_ndinter {s t u : Multiset α} : s ≤ ndinter t u ↔ s ≤ t ∧ s
/- warning: multiset.ndinter_le_left -> Multiset.ndinter_le_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) s
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) s
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) s
Case conversion may be inaccurate. Consider using '#align multiset.ndinter_le_left Multiset.ndinter_le_leftₓ'. -/
@@ -406,7 +406,7 @@ theorem ndinter_subset_right (s t : Multiset α) : ndinter s t ⊆ t :=
/- warning: multiset.ndinter_le_right -> Multiset.ndinter_le_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) t)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) t)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {s : Multiset.{u1} α} (t : Multiset.{u1} α), (Multiset.Nodup.{u1} α s) -> (LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t) t)
Case conversion may be inaccurate. Consider using '#align multiset.ndinter_le_right Multiset.ndinter_le_rightₓ'. -/
@@ -416,7 +416,7 @@ theorem ndinter_le_right {s} (t : Multiset α) (d : Nodup s) : ndinter s t ≤ t
/- warning: multiset.inter_le_ndinter -> Multiset.inter_le_ndinter is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Inter.inter.{u1} (Multiset.{u1} α) (Multiset.hasInter.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toHasLe.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.partialOrder.{u1} α))) (Inter.inter.{u1} (Multiset.{u1} α) (Multiset.hasInter.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] (s : Multiset.{u1} α) (t : Multiset.{u1} α), LE.le.{u1} (Multiset.{u1} α) (Preorder.toLE.{u1} (Multiset.{u1} α) (PartialOrder.toPreorder.{u1} (Multiset.{u1} α) (Multiset.instPartialOrderMultiset.{u1} α))) (Inter.inter.{u1} (Multiset.{u1} α) (Multiset.instInterMultiset.{u1} α (fun (a : α) (b : α) => _inst_1 a b)) s t) (Multiset.ndinter.{u1} α (fun (a : α) (b : α) => _inst_1 a b) s t)
Case conversion may be inaccurate. Consider using '#align multiset.inter_le_ndinter Multiset.inter_le_ndinterₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -441,5 +441,5 @@ end Multiset
-- Assert that we define `finset` without the material on the set lattice.
-- Note that we cannot put this in `data.finset.basic` because we proved relevant lemmas there.
-assert_not_exists Set.interₛ
+assert_not_exists Set.sInter
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
! This file was ported from Lean 3 source module data.multiset.finset_ops
-! leanprover-community/mathlib commit f2f413b9d4be3a02840d0663dace76e8fe3da053
+! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -439,3 +439,7 @@ theorem ndinter_eq_zero_iff_disjoint {s t : Multiset α} : ndinter s t = 0 ↔ D
end Multiset
+-- Assert that we define `finset` without the material on the set lattice.
+-- Note that we cannot put this in `data.finset.basic` because we proved relevant lemmas there.
+assert_not_exists Set.interₛ
+
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -102,7 +102,7 @@ theorem mem_ndinsert_of_mem {a b : α} {s : Multiset α} (h : a ∈ s) : a ∈ n
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Membership.Mem.{u1, u1} α (Multiset.{u1} α) (Multiset.hasMem.{u1} α) a s) -> (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} α) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} α) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} α) s))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Membership.mem.{u1, u1} α (Multiset.{u1} α) (Multiset.instMembershipMultiset.{u1} α) a s) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) s))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Membership.mem.{u1, u1} α (Multiset.{u1} α) (Multiset.instMembershipMultiset.{u1} α) a s) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) s))
Case conversion may be inaccurate. Consider using '#align multiset.length_ndinsert_of_mem Multiset.length_ndinsert_of_memₓ'. -/
@[simp]
theorem length_ndinsert_of_mem {a : α} {s : Multiset α} (h : a ∈ s) :
@@ -113,7 +113,7 @@ theorem length_ndinsert_of_mem {a : α} {s : Multiset α} (h : a ∈ s) :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Not (Membership.Mem.{u1, u1} α (Multiset.{u1} α) (Multiset.hasMem.{u1} α) a s)) -> (Eq.{1} Nat (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} α) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u1} α) -> Nat) (AddMonoidHom.hasCoeToFun.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.orderedCancelAddCommMonoid.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u1} α) s) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Not (Membership.mem.{u1, u1} α (Multiset.{u1} α) (Multiset.instMembershipMultiset.{u1} α) a s)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) s) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) 1 (instOfNatNat 1))))
+ forall {α : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} α] {a : α} {s : Multiset.{u1} α}, (Not (Membership.mem.{u1, u1} α (Multiset.{u1} α) (Multiset.instMembershipMultiset.{u1} α) a s)) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) s) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) s) instAddNat) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) (fun (_x : Multiset.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} α) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} α) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} α) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} α) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} α) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} α) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} α)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} α) s) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} α) => Nat) (Multiset.ndinsert.{u1} α (fun (a : α) (b : α) => _inst_1 a b) a s)) 1 (instOfNatNat 1))))
Case conversion may be inaccurate. Consider using '#align multiset.length_ndinsert_of_not_mem Multiset.length_ndinsert_of_not_memₓ'. -/
@[simp]
theorem length_ndinsert_of_not_mem {a : α} {s : Multiset α} (h : a ∉ s) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -217,8 +217,10 @@ def ndinter (s t : Multiset α) : Multiset α :=
#align multiset.ndinter Multiset.ndinter
@[simp]
-theorem coe_ndinter (l₁ l₂ : List α) : @ndinter α _ l₁ l₂ = (l₁ ∩ l₂ : List α) :=
- rfl
+theorem coe_ndinter (l₁ l₂ : List α) : @ndinter α _ l₁ l₂ = (l₁ ∩ l₂ : List α) := by
+ simp only [ndinter, mem_coe, filter_coe, coe_eq_coe, ← elem_eq_mem]
+ apply Perm.refl
+
#align multiset.coe_ndinter Multiset.coe_ndinter
@[simp, nolint simpNF] -- Porting note (#10675): dsimp can not prove this
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -61,7 +61,7 @@ theorem le_ndinsert_self (a : α) (s : Multiset α) : s ≤ ndinsert a s :=
Quot.inductionOn s fun _ => (sublist_insert _ _).subperm
#align multiset.le_ndinsert_self Multiset.le_ndinsert_self
---Porting note: removing @[simp], simp can prove it
+-- Porting note: removing @[simp], simp can prove it
theorem mem_ndinsert_self (a : α) (s : Multiset α) : a ∈ ndinsert a s :=
mem_ndinsert.2 (Or.inl rfl)
#align multiset.mem_ndinsert_self Multiset.mem_ndinsert_self
@@ -146,7 +146,7 @@ theorem coe_ndunion (l₁ l₂ : List α) : @ndunion α _ l₁ l₂ = (l₁ ∪
rfl
#align multiset.coe_ndunion Multiset.coe_ndunion
---Porting note: removing @[simp], simp can prove it
+-- Porting note: removing @[simp], simp can prove it
theorem zero_ndunion (s : Multiset α) : ndunion 0 s = s :=
Quot.inductionOn s fun _ => rfl
#align multiset.zero_ndunion Multiset.zero_ndunion
@@ -36,7 +36,7 @@ theorem coe_ndinsert (a : α) (l : List α) : ndinsert a l = (insert a l : List
rfl
#align multiset.coe_ndinsert Multiset.coe_ndinsert
-@[simp, nolint simpNF] -- Porting note: dsimp can not prove this
+@[simp, nolint simpNF] -- Porting note (#10675): dsimp can not prove this
theorem ndinsert_zero (a : α) : ndinsert a 0 = {a} :=
rfl
#align multiset.ndinsert_zero Multiset.ndinsert_zero
@@ -221,7 +221,7 @@ theorem coe_ndinter (l₁ l₂ : List α) : @ndinter α _ l₁ l₂ = (l₁ ∩
rfl
#align multiset.coe_ndinter Multiset.coe_ndinter
-@[simp, nolint simpNF] -- Porting note: dsimp can not prove this
+@[simp, nolint simpNF] -- Porting note (#10675): dsimp can not prove this
theorem zero_ndinter (s : Multiset α) : ndinter 0 s = 0 :=
rfl
#align multiset.zero_ndinter Multiset.zero_ndinter
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -19,7 +19,7 @@ namespace Multiset
open List
-variable {α : Type _} [DecidableEq α] {s : Multiset α}
+variable {α : Type*} [DecidableEq α] {s : Multiset α}
/-! ### finset insert -/
Notably there is now a l1 ∪ l2
notation for List.union
.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Bulhwi Cha <chabulhwi@semmalgil.com>
@@ -158,7 +158,7 @@ theorem cons_ndunion (s t : Multiset α) (a : α) : ndunion (a ::ₘ s) t = ndin
@[simp]
theorem mem_ndunion {s t : Multiset α} {a : α} : a ∈ ndunion s t ↔ a ∈ s ∨ a ∈ t :=
- Quot.induction_on₂ s t fun _ _ => List.mem_union
+ Quot.induction_on₂ s t fun _ _ => List.mem_union_iff
#align multiset.mem_ndunion Multiset.mem_ndunion
theorem le_ndunion_right (s t : Multiset α) : t ≤ ndunion s t :=
@@ -2,14 +2,11 @@
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.multiset.finset_ops
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Multiset.Dedup
+#align_import data.multiset.finset_ops from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
+
/-!
# Preparations for defining operations on `Finset`.
@@ -284,7 +284,6 @@ theorem ndinter_eq_zero_iff_disjoint {s t : Multiset α} : ndinter s t = 0 ↔ D
end Multiset
--- Porting note: `assert_not_exists` has not been ported yet.
--- -- Assert that we define `finset` without the material on the set lattice.
--- -- Note that we cannot put this in `data.finset.basic` because we proved relevant lemmas there.
--- assert_not_exists set.sInter
+-- Assert that we define `Finset` without the material on the set lattice.
+-- Note that we cannot put this in `Data.Finset.Basic` because we proved relevant lemmas there.
+assert_not_exists Set.sInter
by
s! (#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 by
s".
@@ -107,12 +107,8 @@ theorem attach_ndinsert (a : α) (s : Multiset α) :
∀ h : ∀ p : { x // x ∈ s }, p.1 ∈ s,
(fun p : { x // x ∈ s } => ⟨p.val, h p⟩ : { x // x ∈ s } → { x // x ∈ s }) = id :=
fun h => funext fun p => Subtype.eq rfl
- have :
- ∀ (t) (eq : s.ndinsert a = t),
- t.attach =
- ndinsert ⟨a, eq ▸ mem_ndinsert_self a s⟩
- (s.attach.map fun p => ⟨p.1, eq ▸ mem_ndinsert_of_mem p.2⟩) :=
- by
+ have : ∀ (t) (eq : s.ndinsert a = t), t.attach = ndinsert ⟨a, eq ▸ mem_ndinsert_self a s⟩
+ (s.attach.map fun p => ⟨p.1, eq ▸ mem_ndinsert_of_mem p.2⟩) := by
intro t ht
by_cases h : a ∈ s
· rw [ndinsert_of_mem h] at ht
data.set.pairwise
(#3117)
Match https://github.com/leanprover-community/mathlib/pull/17880
The new import of Mathlib.Data.Set.Lattice
in Mathlib.Data.Finset.Basic
was implied transitively from tactic imports present in Lean 3.
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
! This file was ported from Lean 3 source module data.multiset.finset_ops
-! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
+! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -287,3 +287,8 @@ theorem ndinter_eq_zero_iff_disjoint {s t : Multiset α} : ndinter s t = 0 ↔ D
#align multiset.ndinter_eq_zero_iff_disjoint Multiset.ndinter_eq_zero_iff_disjoint
end Multiset
+
+-- Porting note: `assert_not_exists` has not been ported yet.
+-- -- Assert that we define `finset` without the material on the set lattice.
+-- -- Note that we cannot put this in `data.finset.basic` because we proved relevant lemmas there.
+-- assert_not_exists set.sInter
@@ -84,7 +84,7 @@ theorem length_ndinsert_of_not_mem {a : α} {s : Multiset α} (h : a ∉ s) :
#align multiset.length_ndinsert_of_not_mem Multiset.length_ndinsert_of_not_mem
theorem dedup_cons {a : α} {s : Multiset α} : dedup (a ::ₘ s) = ndinsert a (dedup s) := by
- by_cases a ∈ s <;> simp [h]
+ by_cases h : a ∈ s <;> simp [h]
#align multiset.dedup_cons Multiset.dedup_cons
theorem Nodup.ndinsert (a : α) : Nodup s → Nodup (ndinsert a s) :=
@@ -114,7 +114,7 @@ theorem attach_ndinsert (a : α) (s : Multiset α) :
(s.attach.map fun p => ⟨p.1, eq ▸ mem_ndinsert_of_mem p.2⟩) :=
by
intro t ht
- by_cases a ∈ s
+ by_cases h : a ∈ s
· rw [ndinsert_of_mem h] at ht
subst ht
rw [eq, map_id, ndinsert_of_mem (mem_attach _ _)]
@@ -217,7 +217,7 @@ theorem dedup_add (s t : Multiset α) : dedup (s + t) = ndunion s (dedup t) :=
/-- `ndinter s t` is the lift of the list `∩` operation. This operation
does not respect multiplicities, unlike `s ∩ t`, but it is suitable as
- an intersection operation on `finset`. (`s ∩ t` would also work as a union operation
+ an intersection operation on `Finset`. (`s ∩ t` would also work as a union operation
on finset, but this is more efficient.) -/
def ndinter (s t : Multiset α) : Multiset α :=
filter (· ∈ t) s
The unported dependencies are