Theorems · Theorem · order theory
IsCompl.sup_inf
∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : BoundedOrder α] {x y x' y' : α},
IsCompl x y → IsCompl x' y' → IsCompl (x ⊔ x') (y ⊓ y')- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- DistribLatticeBoundedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- sup_commproof · cited by 165
- DistribLatticestatement and proof · cited by 150
- inf_assocproof · cited by 53
- sup_assocproof · cited by 37
- bot_sup_eqproof · cited by 32
- top_inf_eqproof · cited by 30
- inf_sup_rightproof · cited by 26
- sup_inf_leftproof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- IsCompl.inf_supproof · cited by 1
- IsComplemented.supproof · cited by 1