Theorems · Theorem · order theory
Finset.sup_mem_sups
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SemilatticeSup α] {s t : Finset α} {a b : α},
a ∈ s → b ∈ t → a ⊔ b ∈ s ⊻ t- Defined in
- Mathlib.Data.Finset.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqSemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SemilatticeSupstatement and proof · cited by 785
- HasSups.supsstatement · cited by 103
- Finset.hasSupsstatement · cited by 61
- Finset.mem_image₂_of_memproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- Finset.union_mem_supsproof · cited by 1