Theorems · Theorem · order theory
IsCompl.of_eq
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : BoundedOrder α] {x y : α}, x ⊓ y = ⊥ → x ⊔ y = ⊤ → IsCompl x y- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- LatticeBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- Latticestatement and proof · cited by 916
- IsComplstatement · cited by 351
- BoundedOrderstatement and proof · cited by 270
- disjoint_iffproof · cited by 76
- codisjoint_iffproof · cited by 53
Cited by7
Results whose statement or proof uses this declaration.
- isCompl_complproof · cited by 21
- isCompl_top_botproof · cited by 5
- LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerateproof · cited by 3
- isCompl_bot_topproof · cited by 2
- IsCompl.sup_infproof · cited by 2
- compl_uniqueproof · cited by 1
- Filter.isCompl_principalproof · cited by 1