Theorems · Theorem · order theory
le_of_inf_le_sup_le
∀ {α : Type u} [inst : DistribLattice α] {x y z : α}, x ⊓ z ≤ y ⊓ z → x ⊔ z ≤ y ⊔ z → x ≤ y- Defined in
- Mathlib.Order.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- DistribLattice
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_reflproof · cited by 2,061
- inf_le_leftproof · cited by 286
- le_sup_rightproof · cited by 242
- sup_commproof · cited by 165
- sup_leproof · cited by 159
- DistribLatticestatement and proof · cited by 150
- inf_le_inf_leftproof · cited by 25
- sup_inf_leftproof · cited by 22
- sup_inf_rightproof · cited by 22
- sup_le_sup_leftproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- Disjoint.left_le_of_le_sup_rightproof · cited by 4
- eq_of_inf_eq_sup_eqproof · cited by 3
- disjoint_sdiff_iff_leproof · cited by 2
- le_iff_eq_sup_sdiffproof · cited by 0