Mathlib Map

Theorems · Theorem · order theory

Finset.sups_singleton

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SemilatticeSup α] {s : Finset α} {b : α},
  s ⊻ {b} = Finset.image (fun x => x ⊔ b) s
Defined in
Mathlib.Data.Finset.Sups
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqSemilatticeSup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.four_functions_theorem · cited by 0Finset.four_functions_the…Finset · cited by 13712FinsetFinset.image · cited by 910Finset.imageSemilatticeSup · cited by 785SemilatticeSupHasSups.sups · cited by 103HasSups.supsFinset.hasSups · cited by 61Finset.hasSupsFinset.image₂_singleton_right · cited by 17Finset.image₂_singleton_r…Finset.sups_singletonCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.