Theorems · Theorem · order theory
sup_eq_inf
∀ {α : Type u} [inst : Lattice α] {a b : α}, a ⊔ b = a ⊓ b ↔ a = b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- Lattice
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.
- Latticestatement and proof · cited by 916
- LE.le.ge_iff_eq'proof · cited by 50
- inf_le_supproof · cited by 14
- sup_le_infproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- inf_eq_and_sup_eq_iffproof · cited by 0