Theorems · Theorem · order theory

Finset.add_sup

∀ {ι : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : LinearOrder M] [CanonicallyOrderedAdd M]
  [inst_3 : Sub M] [AddLeftReflectLE M] [OrderedSub M] {s : Finset ι} [inst_6 : OrderBot M],
  s.Nonempty → ∀ (f : ι → M) (a : M), a + s.sup f = s.sup fun i => a + f i

Defined in

Mathlib.Algebra.Order.Group.Finset

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidLinearOrderCanonicallyOrderedAddSubAddLeftReflectLEOrderedSubOrderBot