Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.constantsVarsEquiv
{L : FirstOrder.Language} →
{α : Type u'} → {γ : Type u_1} → {n : ℕ} → (L.withConstants γ).BoundedFormula α n ≃ L.BoundedFormula (γ ⊕ α) nA bijection sending formulas with constants to formulas with extra free variables.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement · cited by 207
- FirstOrder.Language.Relationsproof · cited by 147
- FirstOrder.Language.withConstantsstatement · cited by 108
- FirstOrder.Language.constantsOnproof · cited by 22
- Equiv.sumEmptyproof · cited by 8
- FirstOrder.Language.Term.constantsVarsEquivLeftproof · cited by 3
- FirstOrder.Language.BoundedFormula.mapTermRelEquivproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Formula.equivSentenceproof · cited by 11
- FirstOrder.Language.Formula.realize_equivSentence_symm_conproof · cited by 4
- Set.definable_iff_exists_formula_sumproof · cited by 2
- FirstOrder.Language.BoundedFormula.realize_constantsVarsEquivstatement · cited by 1
- FirstOrder.Language.ElementarySubstructure.meetsDefinableproof · cited by 0