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Theorems · Theorem · logic and foundations

FirstOrder.Language.Formula.realize_exClosure

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} [inst_1 : DecidableEq α]
  (φ : L.Formula α),
  M ⊨ φ.exClosure ↔ ∃ v, FirstOrder.Language.Formula.Realize (FirstOrder.Language.BoundedFormula.restrictFreeVar φ id) v
Defined in
Mathlib.ModelTheory.Semantics
Cited by
2 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureDecidableEq
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FirstOrder.Language.Formula.realize_exClosure_of_realize_equivSentence · cited by 0Formula.realize_exClosure…FirstOrder.Language.Formula.exists_realize_equivSentence_iff_realize_exClosure · cited by 0Formula.exists_realize_eq…Finset · cited by 13712FinsetFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.BoundedFormula.freeVarFinset · cited by 9BoundedFormula.freeVarFin…FirstOrder.Language.BoundedFormula.restrictFreeVar · cited by 7BoundedFormula.restrictFr…FirstOrder.Language.Formula.exClosure · cited by 4Formula.exClosureFormula.realize_exClosureCITED BYCITES

Cites9

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Cited by2

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