Theorems · Inductive type · logic and foundations
FirstOrder.Language.BoundedFormula.IsUniversal
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α n → PropA universal formula is a formula defined by applying only universal quantifiers to a quantifier-free formula.
- Defined in
- Mathlib.ModelTheory.Complexity
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement · cited by 207
Cited by18
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.IsQF.isUniversalstatement · cited by 7
- FirstOrder.Language.Theory.IsUniversal.isUniversal_of_memstatement · cited by 2
- FirstOrder.Language.BoundedFormula.IsUniversal.belowstatement · cited by 1
- FirstOrder.Language.BoundedFormula.IsUniversal.realize_embeddingstatement and proof · cited by 1
- FirstOrder.Language.Theory.IsUniversal.casesOnstatement and proof · cited by 0
- FirstOrder.Language.Theory.IsUniversal.insertstatement and proof · cited by 0
- FirstOrder.Language.Theory.IsUniversal.recOnstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.IsUniversal.brecOnstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.IsUniversal.casesOnstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.IsUniversal.recOnstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.IsUniversal.below.casesOnstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.IsAtomic.isUniversalstatement · cited by 0