Theorems · Definition · order theory
Finset.hasSups
{α : Type u_2} → [DecidableEq α] → [SemilatticeSup α] → HasSups (Finset α)s ⊻ t is the finset of elements of the form a ⊔ b where a ∈ s, b ∈ t.
- Defined in
- Mathlib.Data.Finset.Sups
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 75 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- SemilatticeSupstatement and proof · cited by 785
- Finset.image₂proof · cited by 104
- HasSupsstatement · cited by 1
Cited by61
Results whose statement or proof uses this declaration.
- four_functions_theoremstatement · cited by 3
- Finset.coe_supsstatement · cited by 3
- Finset.univ_sups_univstatement · cited by 2
- Finset.sups_emptystatement · cited by 1
- Finset.disjSups_subset_supsstatement · cited by 1
- Finset.empty_supsstatement · cited by 1
- Finset.sups_singletonstatement · cited by 1
- Finset.sups_subsetstatement · cited by 1
- Finset.sups_subset_iffstatement · cited by 1
- Finset.truncatedInf_supsstatement · cited by 1
- Finset.truncatedInf_sups_of_notMemstatement · cited by 1
- Finset.le_card_diffs_mul_card_diffsproof · cited by 1