Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.toFormula
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α n → L.Formula (α ⊕ Fin n)Turns all the in-scope bound variables into free variables.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Formulastatement · cited by 93
- FirstOrder.Language.BoundedFormula.brecOnproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementaryEmbedding.map_boundedFormulaproof · cited by 2
- FirstOrder.Language.Theory.models_toFormula_iffstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_toFormulastatement and proof · cited by 1
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_boundedFormulaproof · cited by 1
- FirstOrder.Language.MeetsDefinable.isElementary_closureproof · cited by 0
- FirstOrder.Language.BoundedFormula.toFormula.eq_defstatement and proof · cited by 0