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Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.IsAtomic.relabel

∀ {L : FirstOrder.Language} {α : Type u'} {β : Type v'} {n m : ℕ} {φ : L.BoundedFormula α m},
  φ.IsAtomic → ∀ (f : α → β ⊕ Fin n), (FirstOrder.Language.BoundedFormula.relabel f φ).IsAtomic
Defined in
Mathlib.ModelTheory.Complexity
Cited by
1 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
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FirstOrder.Language.BoundedFormula.IsQF.relabel · cited by 1IsQF.relabelFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.Relations · cited by 147Language.RelationsFirstOrder.Language.Term.relabel · cited by 27Term.relabelFirstOrder.Language.BoundedFormula.IsAtomic · cited by 22BoundedFormula.IsAtomicFirstOrder.Language.BoundedFormula.relabel · cited by 17BoundedFormula.relabelFirstOrder.Language.BoundedFormula.relabelAux · cited by 4BoundedFormula.relabelAuxFirstOrder.Language.BoundedFormula.IsAtomic.recOn · cited by 3IsAtomic.recOnIsAtomic.relabelCITED BYCITES

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