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Theorems · Definition · logic and foundations

FirstOrder.Language.BoundedFormula.relabel

{L : FirstOrder.Language} →
  {α : Type u'} →
    {β : Type v'} → {n : ℕ} → (α → β ⊕ Fin n) → {k : ℕ} → L.BoundedFormula α k → L.BoundedFormula β (n + k)

Relabels a bounded formula's variables along a particular function.

Defined in
Mathlib.ModelTheory.Syntax
Cited by
17 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
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FirstOrder.Language.Formula.iExs · cited by 8Formula.iExsFirstOrder.Language.Formula.relabel · cited by 7Formula.relabelFirstOrder.Language.Formula.iAlls · cited by 6Formula.iAllsFirstOrder.Language.BoundedFormula.realize_relabel · cited by 3BoundedFormula.realize_re…FirstOrder.Language.BoundedFormula.relabel_all · cited by 2BoundedFormula.relabel_allSet.Definable.image_comp_sumInl_fin · cited by 2Definable.image_comp_sumI…FirstOrder.realize_genericPolyMapSurjOnOfInjOn · cited by 2FirstOrder.realize_generi…FirstOrder.Language.Formula.realize_relabel_sumInr · cited by 1Formula.realize_relabel_s…FirstOrder.Language.BoundedFormula.IsQF.relabel · cited by 1IsQF.relabelFirstOrder.Language.BoundedFormula.realize_toFormula · cited by 1BoundedFormula.realize_to…FirstOrder.Language.BoundedFormula.relabel_ex · cited by 1BoundedFormula.relabel_exFirstOrder.Language.BoundedFormula.relabel_not · cited by 1BoundedFormula.relabel_notFirstOrder.Language.BoundedFormula.IsAtomic.relabel · cited by 1IsAtomic.relabelFirstOrder.Language.Embedding.isElementary_of_exists · cited by 1Embedding.isElementary_of…FirstOrder.Language.BoundedFormula.toFormula.eq_def · cited by 0toFormula.eq_defFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.Term.relabel · cited by 27Term.relabelFirstOrder.Language.BoundedFormula.castLE · cited by 13BoundedFormula.castLEFirstOrder.Language.BoundedFormula.mapTermRel · cited by 10BoundedFormula.mapTermRelFirstOrder.Language.BoundedFormula.relabelAux · cited by 4BoundedFormula.relabelAuxBoundedFormula.relabelCITED BYCITES

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