Theorems · Theorem · order theory
Finset.supIndep_pair
∀ {α : Type u_1} {ι : Type u_3} [inst : Lattice α] [inst_1 : OrderBot α] {f : ι → α} [inst_2 : DecidableEq ι] {i j : ι},
i ≠ j → ({i, j}.SupIndep f ↔ Disjoint (f i) (f j))- Defined in
- Mathlib.Order.SupIndep
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LatticeOrderBotDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Disjointstatement and proof · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- Latticestatement and proof · cited by 916
- Finset.supproof · cited by 530
- Finset.eraseproof · cited by 455
- Finset.SupIndepstatement · cited by 52
- Finset.sup_singletonproof · cited by 42
- Finset.erase_eq_of_notMemproof · cited by 30
- Finset.erase_insert_eq_eraseproof · cited by 8
- Finset.pair_commproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- iSupIndep_iff_supIndepproof · cited by 2
- Finset.supIndep_univ_boolproof · cited by 0
- Finset.supIndep_univ_fin_twoproof · cited by 0