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Theorems · Theorem · logic and foundations

FirstOrder.Language.BoundedFormula.realize_toFormula

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {n : ℕ} (φ : L.BoundedFormula α n)
  (v : α ⊕ Fin n → M), φ.toFormula.Realize v ↔ φ.Realize (v ∘ Sum.inl) (v ∘ Sum.inr)
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language.MeetsDefinable.isElementary_closure · cited by 0MeetsDefinable.isElementa…DFunLike.coe · cited by 62936DFunLike.coeEquiv.symm · cited by 3681Equiv.symmFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Term · cited by 166Language.TermFirstOrder.Language.Relations · cited by 147Language.RelationsFin.snoc · cited by 113Fin.snocFirstOrder.Language.BoundedFormula.Realize · cited by 104BoundedFormula.RealizeFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Term.realize · cited by 81Term.realizeFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFirstOrder.Language.Structure.RelMap · cited by 68Structure.RelMapFin.snoc_castSucc · cited by 38Fin.snoc_castSuccfinSumFinEquiv · cited by 33finSumFinEquivBoundedFormula.realize_toForm…CITED BYCITES

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