Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.ex
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α (n + 1) → L.BoundedFormula α nPuts an ∃ quantifier on a bounded formula.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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.notproof · cited by 27
Cited by25
Results whose statement or proof uses this declaration.
- FirstOrder.Language.noBotOrderSentenceproof · cited by 5
- FirstOrder.Language.noTopOrderSentenceproof · cited by 5
- FirstOrder.Language.denselyOrderedSentenceproof · cited by 5
- FirstOrder.Field.genericMonicPolyHasRootproof · cited by 4
- FirstOrder.Language.BoundedFormula.IsPrenex.recOnstatement and proof · cited by 4
- FirstOrder.Language.BoundedFormula.realize_exstatement · cited by 2
- FirstOrder.Field.FieldAxiom.toSentenceproof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_toPrenexImpRightproof · cited by 1
- FirstOrder.Language.BoundedFormula.relabel_exstatement · cited by 1
- FirstOrder.Language.BoundedFormula.all_iff_not_ex_notstatement · cited by 1
- FirstOrder.Language.BoundedFormula.induction_on_all_exstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.toPrenexImp.eq_defstatement and proof · cited by 1