Theorems · Theorem · logic and foundations
FirstOrder.Language.BoundedFormula.iff_toPrenex
∀ {L : FirstOrder.Language} {α : Type u'} {n : ℕ} (φ : L.BoundedFormula α n), ∅.Iff φ φ.toPrenex- Defined in
- Mathlib.ModelTheory.Complexity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Theorystatement · cited by 154
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Theory.ModelTypeproof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.Theory.Iffstatement · cited by 32
- FirstOrder.Language.BoundedFormula.realize_iffproof · cited by 7
- FirstOrder.Language.BoundedFormula.toPrenexstatement · cited by 5
- FirstOrder.Language.BoundedFormula.realize_toPrenexproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.induction_on_all_exproof · cited by 1