data.finset.sum
⟷
Mathlib.Data.Finset.Sum
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 proves locally_finite_order (α ⊕ₗ β)
where α
and β
are locally finite themselves.
@@ -54,6 +54,8 @@ multiset.mem_disj_sum
@[simp] lemma inl_mem_disj_sum : inl a ∈ s.disj_sum t ↔ a ∈ s := inl_mem_disj_sum
@[simp] lemma inr_mem_disj_sum : inr b ∈ s.disj_sum t ↔ b ∈ t := inr_mem_disj_sum
+@[simp] lemma disj_sum_eq_empty : s.disj_sum t = ∅ ↔ s = ∅ ∧ t = ∅ := by simp [ext_iff]
+
lemma disj_sum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disj_sum t₁ ⊆ s₂.disj_sum t₂ :=
val_le_iff.1 $ disj_sum_mono (val_le_iff.2 hs) (val_le_iff.2 ht)
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -101,9 +101,11 @@ theorem inr_mem_disjSum : inr b ∈ s.disjSum t ↔ b ∈ t :=
#align finset.inr_mem_disj_sum Finset.inr_mem_disjSum
-/
+#print Finset.disjSum_eq_empty /-
@[simp]
theorem disjSum_eq_empty : s.disjSum t = ∅ ↔ s = ∅ ∧ t = ∅ := by simp [ext_iff]
#align finset.disj_sum_eq_empty Finset.disjSum_eq_empty
+-/
#print Finset.disjSum_mono /-
theorem disjSum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disjSum t₁ ⊆ s₂.disjSum t₂ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
-import Mathbin.Data.Multiset.Sum
-import Mathbin.Data.Finset.Card
+import Data.Multiset.Sum
+import Data.Finset.Card
#align_import data.finset.sum from "leanprover-community/mathlib"@"48a058d7e39a80ed56858505719a0b2197900999"
mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999
@@ -6,7 +6,7 @@ Authors: Yaël Dillies
import Mathbin.Data.Multiset.Sum
import Mathbin.Data.Finset.Card
-#align_import data.finset.sum from "leanprover-community/mathlib"@"e04043d6bf7264a3c84bc69711dc354958ca4516"
+#align_import data.finset.sum from "leanprover-community/mathlib"@"48a058d7e39a80ed56858505719a0b2197900999"
/-!
# Disjoint sum of finsets
@@ -101,6 +101,10 @@ theorem inr_mem_disjSum : inr b ∈ s.disjSum t ↔ b ∈ t :=
#align finset.inr_mem_disj_sum Finset.inr_mem_disjSum
-/
+@[simp]
+theorem disjSum_eq_empty : s.disjSum t = ∅ ↔ s = ∅ ∧ t = ∅ := by simp [ext_iff]
+#align finset.disj_sum_eq_empty Finset.disjSum_eq_empty
+
#print Finset.disjSum_mono /-
theorem disjSum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disjSum t₁ ⊆ s₂.disjSum t₂ :=
val_le_iff.1 <| disjSum_mono (val_le_iff.2 hs) (val_le_iff.2 ht)
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module data.finset.sum
-! leanprover-community/mathlib commit e04043d6bf7264a3c84bc69711dc354958ca4516
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Multiset.Sum
import Mathbin.Data.Finset.Card
+#align_import data.finset.sum from "leanprover-community/mathlib"@"e04043d6bf7264a3c84bc69711dc354958ca4516"
+
/-!
# Disjoint sum of finsets
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -39,42 +39,56 @@ def disjSum : Finset (Sum α β) :=
#align finset.disj_sum Finset.disjSum
-/
+#print Finset.val_disjSum /-
@[simp]
theorem val_disjSum : (s.disjSum t).1 = s.1.disjSum t.1 :=
rfl
#align finset.val_disj_sum Finset.val_disjSum
+-/
+#print Finset.empty_disjSum /-
@[simp]
theorem empty_disjSum : (∅ : Finset α).disjSum t = t.map Embedding.inr :=
val_inj.1 <| Multiset.zero_disjSum _
#align finset.empty_disj_sum Finset.empty_disjSum
+-/
+#print Finset.disjSum_empty /-
@[simp]
theorem disjSum_empty : s.disjSum (∅ : Finset β) = s.map Embedding.inl :=
val_inj.1 <| Multiset.disjSum_zero _
#align finset.disj_sum_empty Finset.disjSum_empty
+-/
+#print Finset.card_disjSum /-
@[simp]
theorem card_disjSum : (s.disjSum t).card = s.card + t.card :=
Multiset.card_disjSum _ _
#align finset.card_disj_sum Finset.card_disjSum
+-/
+#print Finset.disjoint_map_inl_map_inr /-
theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) := by
simp_rw [disjoint_left, mem_map]; rintro x ⟨a, _, rfl⟩ ⟨b, _, ⟨⟩⟩
#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inr
+-/
+#print Finset.map_inl_disjUnion_map_inr /-
@[simp]
theorem map_inl_disjUnion_map_inr :
(s.map Embedding.inl).disjUnion (t.map Embedding.inr) (disjoint_map_inl_map_inr _ _) =
s.disjSum t :=
rfl
#align finset.map_inl_disj_union_map_inr Finset.map_inl_disjUnion_map_inr
+-/
variable {s t} {s₁ s₂ : Finset α} {t₁ t₂ : Finset β} {a : α} {b : β} {x : Sum α β}
+#print Finset.mem_disjSum /-
theorem mem_disjSum : x ∈ s.disjSum t ↔ (∃ a, a ∈ s ∧ inl a = x) ∨ ∃ b, b ∈ t ∧ inr b = x :=
Multiset.mem_disjSum
#align finset.mem_disj_sum Finset.mem_disjSum
+-/
#print Finset.inl_mem_disjSum /-
@[simp]
@@ -90,9 +104,11 @@ theorem inr_mem_disjSum : inr b ∈ s.disjSum t ↔ b ∈ t :=
#align finset.inr_mem_disj_sum Finset.inr_mem_disjSum
-/
+#print Finset.disjSum_mono /-
theorem disjSum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disjSum t₁ ⊆ s₂.disjSum t₂ :=
val_le_iff.1 <| disjSum_mono (val_le_iff.2 hs) (val_le_iff.2 ht)
#align finset.disj_sum_mono Finset.disjSum_mono
+-/
#print Finset.disjSum_mono_left /-
theorem disjSum_mono_left (t : Finset β) : Monotone fun s : Finset α => s.disjSum t :=
@@ -100,19 +116,25 @@ theorem disjSum_mono_left (t : Finset β) : Monotone fun s : Finset α => s.disj
#align finset.disj_sum_mono_left Finset.disjSum_mono_left
-/
+#print Finset.disjSum_mono_right /-
theorem disjSum_mono_right (s : Finset α) : Monotone (s.disjSum : Finset β → Finset (Sum α β)) :=
fun t₁ t₂ => disjSum_mono Subset.rfl
#align finset.disj_sum_mono_right Finset.disjSum_mono_right
+-/
+#print Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset /-
theorem disjSum_ssubset_disjSum_of_ssubset_of_subset (hs : s₁ ⊂ s₂) (ht : t₁ ⊆ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_lt_of_le (val_lt_iff.2 hs) (val_le_iff.2 ht)
#align finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset
+-/
+#print Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset /-
theorem disjSum_ssubset_disjSum_of_subset_of_ssubset (hs : s₁ ⊆ s₂) (ht : t₁ ⊂ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_le_of_lt (val_le_iff.2 hs) (val_lt_iff.2 ht)
#align finset.disj_sum_ssubset_disj_sum_of_subset_of_ssubset Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset
+-/
#print Finset.disjSum_strictMono_left /-
theorem disjSum_strictMono_left (t : Finset β) : StrictMono fun s : Finset α => s.disjSum t :=
@@ -120,10 +142,12 @@ theorem disjSum_strictMono_left (t : Finset β) : StrictMono fun s : Finset α =
#align finset.disj_sum_strict_mono_left Finset.disjSum_strictMono_left
-/
+#print Finset.disj_sum_strictMono_right /-
theorem disj_sum_strictMono_right (s : Finset α) :
StrictMono (s.disjSum : Finset β → Finset (Sum α β)) := fun s₁ s₂ =>
disjSum_ssubset_disjSum_of_subset_of_ssubset Subset.rfl
#align finset.disj_sum_strict_mono_right Finset.disj_sum_strictMono_right
+-/
end Finset
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -39,66 +39,30 @@ def disjSum : Finset (Sum α β) :=
#align finset.disj_sum Finset.disjSum
-/
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@[simp]
theorem val_disjSum : (s.disjSum t).1 = s.1.disjSum t.1 :=
rfl
#align finset.val_disj_sum Finset.val_disjSum
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@[simp]
theorem empty_disjSum : (∅ : Finset α).disjSum t = t.map Embedding.inr :=
val_inj.1 <| Multiset.zero_disjSum _
#align finset.empty_disj_sum Finset.empty_disjSum
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@[simp]
theorem disjSum_empty : s.disjSum (∅ : Finset β) = s.map Embedding.inl :=
val_inj.1 <| Multiset.disjSum_zero _
#align finset.disj_sum_empty Finset.disjSum_empty
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@[simp]
theorem card_disjSum : (s.disjSum t).card = s.card + t.card :=
Multiset.card_disjSum _ _
#align finset.card_disj_sum Finset.card_disjSum
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theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) := by
simp_rw [disjoint_left, mem_map]; rintro x ⟨a, _, rfl⟩ ⟨b, _, ⟨⟩⟩
#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inr
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@[simp]
theorem map_inl_disjUnion_map_inr :
(s.map Embedding.inl).disjUnion (t.map Embedding.inr) (disjoint_map_inl_map_inr _ _) =
@@ -108,12 +72,6 @@ theorem map_inl_disjUnion_map_inr :
variable {s t} {s₁ s₂ : Finset α} {t₁ t₂ : Finset β} {a : α} {b : β} {x : Sum α β}
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theorem mem_disjSum : x ∈ s.disjSum t ↔ (∃ a, a ∈ s ∧ inl a = x) ∨ ∃ b, b ∈ t ∧ inr b = x :=
Multiset.mem_disjSum
#align finset.mem_disj_sum Finset.mem_disjSum
@@ -132,12 +90,6 @@ theorem inr_mem_disjSum : inr b ∈ s.disjSum t ↔ b ∈ t :=
#align finset.inr_mem_disj_sum Finset.inr_mem_disjSum
-/
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theorem disjSum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disjSum t₁ ⊆ s₂.disjSum t₂ :=
val_le_iff.1 <| disjSum_mono (val_le_iff.2 hs) (val_le_iff.2 ht)
#align finset.disj_sum_mono Finset.disjSum_mono
@@ -148,33 +100,15 @@ theorem disjSum_mono_left (t : Finset β) : Monotone fun s : Finset α => s.disj
#align finset.disj_sum_mono_left Finset.disjSum_mono_left
-/
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theorem disjSum_mono_right (s : Finset α) : Monotone (s.disjSum : Finset β → Finset (Sum α β)) :=
fun t₁ t₂ => disjSum_mono Subset.rfl
#align finset.disj_sum_mono_right Finset.disjSum_mono_right
-/- warning: finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset -> Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {s₁ : Finset.{u1} α} {s₂ : Finset.{u1} α} {t₁ : Finset.{u2} β} {t₂ : Finset.{u2} β}, (HasSSubset.SSubset.{u1} (Finset.{u1} α) (Finset.hasSsubset.{u1} α) s₁ s₂) -> (HasSubset.Subset.{u2} (Finset.{u2} β) (Finset.hasSubset.{u2} β) t₁ t₂) -> (HasSSubset.SSubset.{max u1 u2} (Finset.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.hasSsubset.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.disjSum.{u1, u2} α β s₁ t₁) (Finset.disjSum.{u1, u2} α β s₂ t₂))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {s₁ : Finset.{u2} α} {s₂ : Finset.{u2} α} {t₁ : Finset.{u1} β} {t₂ : Finset.{u1} β}, (HasSSubset.SSubset.{u2} (Finset.{u2} α) (Finset.instHasSSubsetFinset.{u2} α) s₁ s₂) -> (HasSubset.Subset.{u1} (Finset.{u1} β) (Finset.instHasSubsetFinset.{u1} β) t₁ t₂) -> (HasSSubset.SSubset.{max u2 u1} (Finset.{max u1 u2} (Sum.{u2, u1} α β)) (Finset.instHasSSubsetFinset.{max u2 u1} (Sum.{u2, u1} α β)) (Finset.disjSum.{u2, u1} α β s₁ t₁) (Finset.disjSum.{u2, u1} α β s₂ t₂))
-Case conversion may be inaccurate. Consider using '#align finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset Finset.disjSum_ssubset_disjSum_of_ssubset_of_subsetₓ'. -/
theorem disjSum_ssubset_disjSum_of_ssubset_of_subset (hs : s₁ ⊂ s₂) (ht : t₁ ⊆ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_lt_of_le (val_lt_iff.2 hs) (val_le_iff.2 ht)
#align finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset
-/- warning: finset.disj_sum_ssubset_disj_sum_of_subset_of_ssubset -> Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {s₁ : Finset.{u1} α} {s₂ : Finset.{u1} α} {t₁ : Finset.{u2} β} {t₂ : Finset.{u2} β}, (HasSubset.Subset.{u1} (Finset.{u1} α) (Finset.hasSubset.{u1} α) s₁ s₂) -> (HasSSubset.SSubset.{u2} (Finset.{u2} β) (Finset.hasSsubset.{u2} β) t₁ t₂) -> (HasSSubset.SSubset.{max u1 u2} (Finset.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.hasSsubset.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.disjSum.{u1, u2} α β s₁ t₁) (Finset.disjSum.{u1, u2} α β s₂ t₂))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {s₁ : Finset.{u2} α} {s₂ : Finset.{u2} α} {t₁ : Finset.{u1} β} {t₂ : Finset.{u1} β}, (HasSubset.Subset.{u2} (Finset.{u2} α) (Finset.instHasSubsetFinset.{u2} α) s₁ s₂) -> (HasSSubset.SSubset.{u1} (Finset.{u1} β) (Finset.instHasSSubsetFinset.{u1} β) t₁ t₂) -> (HasSSubset.SSubset.{max u2 u1} (Finset.{max u1 u2} (Sum.{u2, u1} α β)) (Finset.instHasSSubsetFinset.{max u2 u1} (Sum.{u2, u1} α β)) (Finset.disjSum.{u2, u1} α β s₁ t₁) (Finset.disjSum.{u2, u1} α β s₂ t₂))
-Case conversion may be inaccurate. Consider using '#align finset.disj_sum_ssubset_disj_sum_of_subset_of_ssubset Finset.disjSum_ssubset_disjSum_of_subset_of_ssubsetₓ'. -/
theorem disjSum_ssubset_disjSum_of_subset_of_ssubset (hs : s₁ ⊆ s₂) (ht : t₁ ⊂ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_le_of_lt (val_le_iff.2 hs) (val_lt_iff.2 ht)
@@ -186,12 +120,6 @@ theorem disjSum_strictMono_left (t : Finset β) : StrictMono fun s : Finset α =
#align finset.disj_sum_strict_mono_left Finset.disjSum_strictMono_left
-/
-/- warning: finset.disj_sum_strict_mono_right -> Finset.disj_sum_strictMono_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} (s : Finset.{u1} α), StrictMono.{u2, max u1 u2} (Finset.{u2} β) (Finset.{max u1 u2} (Sum.{u1, u2} α β)) (PartialOrder.toPreorder.{u2} (Finset.{u2} β) (Finset.partialOrder.{u2} β)) (PartialOrder.toPreorder.{max u1 u2} (Finset.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.partialOrder.{max u1 u2} (Sum.{u1, u2} α β))) (Finset.disjSum.{u1, u2} α β s)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} (s : Finset.{u2} α), StrictMono.{u1, max u2 u1} (Finset.{u1} β) (Finset.{max u1 u2} (Sum.{u2, u1} α β)) (PartialOrder.toPreorder.{u1} (Finset.{u1} β) (Finset.partialOrder.{u1} β)) (PartialOrder.toPreorder.{max u2 u1} (Finset.{max u1 u2} (Sum.{u2, u1} α β)) (Finset.partialOrder.{max u2 u1} (Sum.{u2, u1} α β))) (Finset.disjSum.{u2, u1} α β s)
-Case conversion may be inaccurate. Consider using '#align finset.disj_sum_strict_mono_right Finset.disj_sum_strictMono_rightₓ'. -/
theorem disj_sum_strictMono_right (s : Finset α) :
StrictMono (s.disjSum : Finset β → Finset (Sum α β)) := fun s₁ s₂ =>
disjSum_ssubset_disjSum_of_subset_of_ssubset Subset.rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -89,10 +89,8 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} (s : Finset.{u1} α) (t : Finset.{u2} β), Disjoint.{max u2 u1} (Finset.{max u2 u1} (Sum.{u1, u2} α β)) (Finset.partialOrder.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{max u1 u2} (Sum.{u1, u2} α β)) (Finset.map.{u1, max u2 u1} α (Sum.{u1, u2} α β) (Function.Embedding.inl.{u1, u2} α β) s) (Finset.map.{u2, max u1 u2} β (Sum.{u1, u2} α β) (Function.Embedding.inr.{u1, u2} α β) t)
Case conversion may be inaccurate. Consider using '#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inrₓ'. -/
-theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) :=
- by
- simp_rw [disjoint_left, mem_map]
- rintro x ⟨a, _, rfl⟩ ⟨b, _, ⟨⟩⟩
+theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) := by
+ simp_rw [disjoint_left, mem_map]; rintro x ⟨a, _, rfl⟩ ⟨b, _, ⟨⟩⟩
#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inr
/- warning: finset.map_inl_disj_union_map_inr -> Finset.map_inl_disjUnion_map_inr is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Forward-ports https://github.com/leanprover-community/mathlib/pull/11352
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -6,7 +6,7 @@ Authors: Yaël Dillies
import Mathlib.Data.Multiset.Sum
import Mathlib.Data.Finset.Card
-#align_import data.finset.sum from "leanprover-community/mathlib"@"9003f28797c0664a49e4179487267c494477d853"
+#align_import data.finset.sum from "leanprover-community/mathlib"@"48a058d7e39a80ed56858505719a0b2197900999"
/-!
# Disjoint sum of finsets
@@ -79,6 +79,10 @@ theorem inr_mem_disjSum : inr b ∈ s.disjSum t ↔ b ∈ t :=
Multiset.inr_mem_disjSum
#align finset.inr_mem_disj_sum Finset.inr_mem_disjSum
+@[simp]
+theorem disjSum_eq_empty : s.disjSum t = ∅ ↔ s = ∅ ∧ t = ∅ := by simp [ext_iff]
+#align finset.disj_sum_eq_empty Finset.disjSum_eq_empty
+
theorem disjSum_mono (hs : s₁ ⊆ s₂) (ht : t₁ ⊆ t₂) : s₁.disjSum t₁ ⊆ s₂.disjSum t₂ :=
val_le_iff.1 <| Multiset.disjSum_mono (val_le_iff.2 hs) (val_le_iff.2 ht)
#align finset.disj_sum_mono Finset.disjSum_mono
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -24,7 +24,7 @@ open Function Multiset Sum
namespace Finset
-variable {α β : Type _} (s : Finset α) (t : Finset β)
+variable {α β : Type*} (s : Finset α) (t : Finset β)
/-- Disjoint sum of finsets. -/
def disjSum : Finset (Sum α β) :=
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module data.finset.sum
-! 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.Multiset.Sum
import Mathlib.Data.Finset.Card
+#align_import data.finset.sum from "leanprover-community/mathlib"@"9003f28797c0664a49e4179487267c494477d853"
+
/-!
# Disjoint sum of finsets
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".
@@ -54,8 +54,7 @@ theorem card_disjSum : (s.disjSum t).card = s.card + t.card :=
Multiset.card_disjSum _ _
#align finset.card_disj_sum Finset.card_disjSum
-theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) :=
- by
+theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embedding.inr) := by
simp_rw [disjoint_left, mem_map]
rintro x ⟨a, _, rfl⟩ ⟨b, _, ⟨⟩⟩
#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inr
@@ -98,16 +98,12 @@ theorem disjSum_mono_right (s : Finset α) : Monotone (s.disjSum : Finset β →
theorem disjSum_ssubset_disjSum_of_ssubset_of_subset (hs : s₁ ⊂ s₂) (ht : t₁ ⊆ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_lt_of_le (val_lt_iff.2 hs) (val_le_iff.2 ht)
-#align
- finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset
- Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset
+#align finset.disj_sum_ssubset_disj_sum_of_ssubset_of_subset Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset
theorem disjSum_ssubset_disjSum_of_subset_of_ssubset (hs : s₁ ⊆ s₂) (ht : t₁ ⊂ t₂) :
s₁.disjSum t₁ ⊂ s₂.disjSum t₂ :=
val_lt_iff.1 <| disjSum_lt_disjSum_of_le_of_lt (val_le_iff.2 hs) (val_lt_iff.2 ht)
-#align
- finset.disj_sum_ssubset_disj_sum_of_subset_of_ssubset
- Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset
+#align finset.disj_sum_ssubset_disj_sum_of_subset_of_ssubset Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset
theorem disjSum_strictMono_left (t : Finset β) : StrictMono fun s : Finset α => s.disjSum t :=
fun _ _ hs => disjSum_ssubset_disjSum_of_ssubset_of_subset hs Subset.rfl
@@ -61,11 +61,11 @@ theorem disjoint_map_inl_map_inr : Disjoint (s.map Embedding.inl) (t.map Embeddi
#align finset.disjoint_map_inl_map_inr Finset.disjoint_map_inl_map_inr
@[simp]
-theorem map_inl_disj_union_map_inr :
+theorem map_inl_disjUnion_map_inr :
(s.map Embedding.inl).disjUnion (t.map Embedding.inr) (disjoint_map_inl_map_inr _ _) =
s.disjSum t :=
rfl
-#align finset.map_inl_disj_union_map_inr Finset.map_inl_disj_union_map_inr
+#align finset.map_inl_disj_union_map_inr Finset.map_inl_disjUnion_map_inr
variable {s t} {s₁ s₂ : Finset α} {t₁ t₂ : Finset β} {a : α} {b : β} {x : Sum α β}
The unported dependencies are