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Theorems · Theorem · logic and foundations

FirstOrder.Language.Formula.realize_exClosure_of_realize_equivSentence

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} [inst_1 : DecidableEq α]
  [inst_2 : (L.withConstants α).Structure M] [(L.lhomWithConstants α).IsExpansionOn M] {φ : L.Formula α},
  M ⊨ FirstOrder.Language.Formula.equivSentence φ → M ⊨ φ.exClosure
Defined in
Mathlib.ModelTheory.Semantics
Cited by
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Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureDecidableEqFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOn
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DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.lhomWithConstants · cited by 39Language.lhomWithConstantsFirstOrder.Language.LHom.IsExpansionOn · cited by 31LHom.IsExpansionOnFirstOrder.Language.constantMap · cited by 28Language.constantMapFirstOrder.Language.con · cited by 21Language.conFirstOrder.Language.Formula.equivSentence · cited by 11Formula.equivSentenceFirstOrder.Language.BoundedFormula.freeVarFinset · cited by 9BoundedFormula.freeVarFin…FirstOrder.Language.Formula.exClosure · cited by 4Formula.exClosureFormula.realize_exClosure_of_…CITED BYCITES

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