Theorems · Theorem · logic and foundations
Set.Definable.mono
∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {B : Set M} {s : Set (α → M)},
A.Definable L s → A ⊆ B → B.Definable L s- Defined in
- Mathlib.ModelTheory.Definability
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.inclusionproof · cited by 145
- Set.Definablestatement and proof · cited by 39
- FirstOrder.Language.lhomWithConstantsMapproof · cited by 3
- Set.Definable.map_expansionproof · cited by 1
- Set.definable_iff_empty_definable_with_paramsproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Set.DefinableFun.of_emptyproof · cited by 1
- Set.definable_iff_finitely_definableproof · cited by 1
- Set.DefinableFun.monoproof · cited by 0
- Set.Definable.singleton_of_memproof · cited by 0