Theorems · Theorem · order theory
IsCompl.inf_left_eq_bot_iff
∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : BoundedOrder α] {x y z : α}, IsCompl y z → (x ⊓ y = ⊥ ↔ x ≤ z)- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- DistribLatticeBoundedOrder
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.
- Bot.botstatement · cited by 4,720
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- DistribLatticestatement and proof · cited by 150
- le_bot_iffproof · cited by 116
- bot_sup_eqproof · cited by 32
- IsCompl.le_sup_right_iff_inf_left_leproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCompl.inf_right_eq_bot_iffproof · cited by 1
- IsCompl.disjoint_left_iffproof · cited by 1