Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.toPrenex
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α n → L.BoundedFormula α nFor any bounded formula φ, φ.toPrenex is a semantically-equivalent formula in prenex normal
form.
- Defined in
- Mathlib.ModelTheory.Complexity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.BoundedFormula.brecOnproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.toPrenex_isPrenexstatement and proof · cited by 2
- FirstOrder.Language.BoundedFormula.iff_toPrenexstatement · cited by 1
- FirstOrder.Language.BoundedFormula.induction_on_all_exproof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_toPrenexstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.toPrenex.eq_defstatement and proof · cited by 0