Theorems · Theorem · order theory

IsNonarchimedean.apply_sum_le_sup

∀ {R : Type u_1} [inst : LinearOrder R] {α : Type u_2} {β : Type u_3} [inst_1 : AddCommMonoid α] {f : α → R},
  IsNonarchimedean f →
    ∀ {s : Finset β} (hnonempty : s.Nonempty) {l : β → α}, f (∑ i ∈ s, l i) ≤ s.sup' hnonempty fun i => f (l i)

Ultrametric inequality with Finset.sum.

Defined in

Mathlib.Algebra.Order.Ring.IsNonarchimedean

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderAddCommMonoid