Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.subst
{L : FirstOrder.Language} →
{α : Type u'} → {β : Type v'} → {n : ℕ} → L.BoundedFormula α n → (α → L.Term β) → L.BoundedFormula β nSubstitutes the free variables in a bounded formula with terms, leaving bound variables unchanged.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Termstatement and proof · cited by 166
- FirstOrder.Language.Term.relabelproof · cited by 27
- FirstOrder.Language.BoundedFormula.mapTermRelproof · cited by 10
- FirstOrder.Language.Term.substproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.genericPolyMapSurjOnOfInjOnproof · cited by 4
- FirstOrder.realize_genericPolyMapSurjOnOfInjOnproof · cited by 2
- FirstOrder.Language.MeetsDefinable.isElementary_closureproof · cited by 0
- FirstOrder.Language.BoundedFormula.realize_subststatement · cited by 0