Theorems · Theorem · order theory
IsModularLattice.inf_sup_inf_assoc
∀ {α : Type u_1} [inst : Lattice α] [IsModularLattice α] {x y z : α}, x ⊓ z ⊔ y ⊓ z = (x ⊓ z ⊔ y) ⊓ z- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- LatticeIsModularLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- inf_le_rightproof · cited by 238
- IsModularLatticestatement and proof · cited by 86
- sup_inf_assoc_of_leproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Codisjoint.codisjoint_inf_right_of_codisjoint_inf_leftproof · cited by 2
- Set.Iic.isCompl_inf_inf_of_isCompl_of_leproof · cited by 1
- isModularLattice_iff_inf_sup_inf_assocproof · cited by 0