Theorems · Theorem · order theory

IsNonarchimedean.apply_sum_eq_of_lt

∀ {R : Type u_1} [inst : LinearOrder R] {α : Type u_2} {β : Type u_3} [inst_1 : AddCommGroup α] {f : α → R},
  IsNonarchimedean f →
    (∀ (a : α), f a = f (-a)) →
      ∀ {s : Finset β} {l : β → α} {k : β}, k ∈ s → (∀ j ∈ s, j ≠ k → f (l j) < f (l k)) → f (∑ i ∈ s, l i) = f (l k)

Defined in

Mathlib.Algebra.Order.Ring.IsNonarchimedean

Cited by

1 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderAddCommGroup