Theorems · Theorem · order theory
inf_sup_assoc_of_le
∀ {α : Type u_1} [inst : Lattice α] [IsModularLattice α] {x : α} (y : α) {z : α}, z ≤ x → x ⊓ y ⊔ z = x ⊓ (y ⊔ z)- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- LatticeIsModularLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- le_infproof · cited by 107
- IsModularLatticestatement and proof · cited by 86
- ge_antisymmproof · cited by 51
- inf_le_inf_leftproof · cited by 25
- inf_sup_le_assoc_of_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsModularLattice.exists_inf_eq_and_sup_eqproof · cited by 2
- IsModularLattice.sup_inf_sup_assocproof · cited by 1
- eq_of_le_of_sup_le_of_le_infproof · cited by 1