Theorems · Theorem · order theory

ArchimedeanClass.mk_sum

∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {ι : Type u_2}
  [inst_3 : LinearOrder ι] {s : Finset ι} (hnonempty : s.Nonempty) {a : ι → M},
  StrictMonoOn (ArchimedeanClass.mk ∘ a) ↑s →
    ArchimedeanClass.mk (∑ i ∈ s, a i) = ArchimedeanClass.mk (a (s.min' hnonempty))

The sum over a set of an elements in distinct classes is in the lowest class.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

2 results in Mathlib

Foundations

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

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidLinearOrder