Theorems · Theorem · order theory
Monotone.map_inf
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : SemilatticeInf β] {f : α → β},
Monotone f → ∀ (x y : α), f (min x y) = f x ⊓ f y- Defined in
- Mathlib.Order.Lattice
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrderSemilatticeInf
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.
- LinearOrderstatement and proof · cited by 8,572
- Monotonestatement and proof · cited by 1,397
- SemilatticeInfstatement and proof · cited by 634
- inf_of_le_leftproof · cited by 186
- inf_of_le_rightproof · cited by 128
Cited by8
Results whose statement or proof uses this declaration.
- Valuation.subgroups_basisproof · cited by 5
- Finset.apply_inf_eq_inf_comp_of_linearOrderproof · cited by 1
- Set.image_subtype_val_uIccproof · cited by 1
- Set.image_subtype_val_uIocproof · cited by 1
- Set.image_subtype_val_uIooproof · cited by 1
- RelHomClass.map_infproof · cited by 1
- Finset.apply_inf_eq_inf_comp_of_nonemptyproof · cited by 0
- Antitone.map_infproof · cited by 0