Theorems · Theorem · combinatorics

Finset.fold_op_rel_iff_and

∀ {α : Type u_1} {β : Type u_2} {op : β → β → β} [hc : Std.Commutative op] [ha : Std.Associative op] {f : α → β} {b : β}
  {s : Finset α} {r : β → β → Prop},
  (∀ {x y z : β}, r x (op y z) ↔ r x y ∧ r x z) → ∀ {c : β}, r c (Finset.fold op b f s) ↔ r c b ∧ ∀ x ∈ s, r c (f x)

Defined in

Mathlib.Data.Finset.Fold

Cited by

5 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Std.CommutativeStd.Associative