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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence

∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {φ : L.Formula α},
  T ⊨ᵇ φ ↔ (L.lhomWithConstants α).onTheory T ⊨ᵇ FirstOrder.Language.Formula.equivSentence φ
Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
1 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formula · cited by 2ModelsBoundedFormula.real…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelType.Carrier · cited by 59ModelType.CarrierFirstOrder.Language.lhomWithConstants · cited by 39Language.lhomWithConstantsFirstOrder.Language.Theory.ModelsBoundedFormula · cited by 30Theory.ModelsBoundedFormu…FirstOrder.Language.constantMap · cited by 28Language.constantMapFirstOrder.Language.LHom.onTheory · cited by 27LHom.onTheoryTheory.models_formula_iff_onT…CITED BYCITES

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