Theorems · Theorem · combinatorics
Set.mem_sups
∀ {α : Type u_2} [inst : SemilatticeSup α] {s t : Set α} {c : α}, c ∈ s ⊻ t ↔ ∃ a ∈ s, ∃ b ∈ t, a ⊔ b = c- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SemilatticeSupstatement and proof · cited by 785
- HasSups.supsstatement · cited by 103
- Set.hasSupsstatement · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- Set.subset_sups_selfproof · cited by 1