Theorems · Theorem · logic and foundations
Set.Definable.union
∀ {M : Type w} {A : Set M} {L : FirstOrder.Language} [inst : L.Structure M] {α : Type u₁} {f g : Set (α → M)},
A.Definable L f → A.Definable L g → A.Definable L (f ∪ g)- Defined in
- Mathlib.ModelTheory.Definability
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.extproof · cited by 2,266
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Set.mem_ofPred_eqproof · cited by 122
- FirstOrder.Language.withConstantsproof · cited by 108
- FirstOrder.Language.Formulaproof · cited by 93
- FirstOrder.Language.Formula.Realizeproof · cited by 81
- Set.mem_unionproof · cited by 47
- Set.Definablestatement and proof · cited by 39
Cited by3
Results whose statement or proof uses this declaration.
- Set.definable_finset_supproof · cited by 2
- Set.DefinableFun.iteproof · cited by 0
- Set.Definable.himpproof · cited by 0