Theorems · Theorem · order theory
eq_top_of_isCompl_bot
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : BoundedOrder α] {x : α}, IsCompl x ⊥ → x = ⊤- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- 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 and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- sup_bot_eqproof · cited by 31
- IsCompl.sup_eq_topproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- isCoatomic_of_isAtomic_of_complementedLattice_of_isModularproof · cited by 2
- LinearMap.IsPerfectCompl.left_top_iffproof · cited by 1
- eq_top_of_bot_isComplproof · cited by 1
- eq_bot_of_isCompl_topproof · cited by 0