Theorems · Theorem · order theory
sSupIndep_pair
∀ {α : Type u_1} [inst : CompleteLattice α] {a b : α}, a ≠ b → (sSupIndep {a, b} ↔ Disjoint a b)- Defined in
- Mathlib.Order.SupIndep
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderproof · cited by 6,410
- Disjointstatement and proof · cited by 2,201
- OrderBotproof · cited by 1,055
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Set.mem_singletonproof · cited by 183
- Disjoint.symmproof · cited by 125
- Set.mem_insertproof · cited by 109
- Set.mem_insert_of_memproof · cited by 50
- sSupIndepstatement and proof · cited by 39
- Set.sdiff_singleton_eq_selfproof · cited by 38
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