Theorems · Theorem · order theory
strictMono_inf_prod_sup
∀ {α : Type u_1} [inst : Lattice α] [IsModularLattice α] {z : α}, StrictMono fun x => (x ⊓ z, x ⊔ z)- Defined in
- Mathlib.Order.ModularLattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- LatticeIsModularLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- Latticestatement and proof · cited by 916
- StrictMonostatement · cited by 706
- LT.lt.not_geproof · cited by 305
- IsModularLatticestatement and proof · cited by 86
- inf_le_inf_rightproof · cited by 23
- sup_le_sup_rightproof · cited by 14
- sup_lt_sup_of_lt_of_inf_le_infproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- wellFounded_lt_exact_sequenceproof · cited by 2
- Submodule.map_strict_mono_or_ker_sup_lt_ker_supproof · cited by 2