Theorems · Theorem · order theory
Monotone.le_map_sup
∀ {α : Type u} {β : Type v} [inst : SemilatticeSup α] [inst_1 : SemilatticeSup β] {f : α → β},
Monotone f → ∀ (x y : α), f x ⊔ f y ≤ f (x ⊔ y)- Defined in
- Mathlib.Order.Lattice
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- SemilatticeSupSemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monotonestatement and proof · cited by 1,397
- SemilatticeSupstatement and proof · cited by 785
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
Cited by11
Results whose statement or proof uses this declaration.
- OrderEmbedding.le_map_supproof · cited by 1
- OrderHom.le_map_sup_fixedPointsproof · cited by 1
- ClosureOperator.closure_sup_closure_leproof · cited by 1
- Subgroup.comap_sup_comap_leproof · cited by 0
- AddSubgroup.comap_sup_comap_leproof · cited by 0
- Sublattice.le_comap_supproof · cited by 0
- SetRel.core_union_subsetproof · cited by 0
- BooleanSubalgebra.le_comap_supproof · cited by 0
- Ideal.le_comap_supproof · cited by 0
- MeasureTheory.SimpleFunc.le_sup_lintegralproof · cited by 0
- Antitone.map_sup_leproof · cited by 0