Theorems · Theorem · combinatorics

Multiset.fold_union_inter

∀ {α : Type u_1} (op : α → α → α) [hc : Std.Commutative op] [ha : Std.Associative op] [inst : DecidableEq α]
  (s₁ s₂ : Multiset α) (b₁ b₂ : α),
  op (Multiset.fold op b₁ (s₁ ∪ s₂)) (Multiset.fold op b₂ (s₁ ∩ s₂)) =
    op (Multiset.fold op b₁ s₁) (Multiset.fold op b₂ s₂)

Defined in: Mathlib.Data.Multiset.Fold
Cited by: 0 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Std.Commutative Std.Associative DecidableEq

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Multisetstatement and proof · cited by 2,627
Multiset.foldstatement and proof · cited by 38
Multiset.fold_addproof · cited by 9
Multiset.union_add_interproof · cited by 3

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