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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.Iff.realize_bd_iff

∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} {M : Type u_1} [Nonempty M] [inst : L.Structure M]
  [M ⊨ T] {φ ψ : L.BoundedFormula α n}, T.Iff φ ψ → ∀ {v : α → M} {xs : Fin n → M}, φ.Realize v xs ↔ ψ.Realize v xs
Defined in
Mathlib.ModelTheory.Equivalence
Cited by
5 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonemptyFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.Theory.Iff.realize_iff · cited by 1Iff.realize_iffFirstOrder.Language.Theory.Iff.ex · cited by 0Iff.exFirstOrder.Language.Theory.Iff.imp · cited by 0Iff.impFirstOrder.Language.Theory.Iff.not · cited by 0Iff.notFirstOrder.Language.Theory.Iff.all · cited by 0Iff.allFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.BoundedFormula.Realize · cited by 104BoundedFormula.RealizeFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.Iff · cited by 32Theory.IffFirstOrder.Language.BoundedFormula.realize_iff · cited by 7BoundedFormula.realize_iffFirstOrder.Language.Theory.ModelsBoundedFormula.realize_boundedFormula · cited by 1ModelsBoundedFormula.real…Iff.realize_bd_iffCITED BYCITES

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