Theorems · Theorem · order theory
IsCompl.inf_eq_bot
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : BoundedOrder α] {x y : α}, IsCompl x y → x ⊓ y = ⊥- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- LatticeBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Latticestatement and proof · cited by 916
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- Disjoint.eq_botproof · cited by 52
- IsCompl.disjointproof · cited by 42
Cited by11
Results whose statement or proof uses this declaration.
- IsCompl.sup_infproof · cited by 2
- ComplementedLattice.isStronglyAtomicproof · cited by 2
- LinearMap.finrank_maxGenEigenspace_zero_eqproof · cited by 2
- AffineSubspace.inter_eq_singleton_of_nonempty_of_isComplproof · cited by 1
- LinearMap.IsSymm.nondegenerate_restrict_of_isCompl_kerproof · cited by 1
- IsCompl.inf_left_le_of_le_sup_rightproof · cited by 1
- Set.range_inl_inter_range_inrproof · cited by 1
- Set.Iic.isCompl_inf_inf_of_isCompl_of_leproof · cited by 1
- Set.range_inr_inter_range_inlproof · cited by 0
- LinearMap.BilinForm.orthogonal_eq_top_iffproof · cited by 0
- Set.range_some_inter_noneproof · cited by 0