Theorems · Theorem · order theory
IsCompl.inf_left_le_of_le_sup_right
∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : BoundedOrder α] {a b x y : α}, IsCompl x y → a ≤ b ⊔ y → a ⊓ x ≤ b- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 1 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_rflproof · cited by 1,558
- IsComplstatement and proof · cited by 351
- inf_le_leftproof · cited by 286
- BoundedOrderstatement and proof · cited by 270
- DistribLatticestatement and proof · cited by 150
- IsCompl.symmproof · cited by 80
- inf_le_infproof · cited by 54
- sup_bot_eqproof · cited by 31
- inf_sup_rightproof · cited by 26
- IsCompl.inf_eq_botproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsCompl.le_sup_right_iff_inf_left_leproof · cited by 2