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Theorems · Theorem · logic and foundations

FirstOrder.Language.Formula.realize_iExs

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {γ : Type u_3} [inst_1 : Finite γ]
  {φ : L.Formula (α ⊕ γ)} {v : α → M}, (FirstOrder.Language.Formula.iExs γ φ).Realize v ↔ ∃ i, φ.Realize (Sum.elim v i)
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFinite
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Around this declaration

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FirstOrder.Language.BoundedFormula.realize_iExs · cited by 0BoundedFormula.realize_iE…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmFinite · cited by 3029FiniteFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureEquiv.apply_symm_apply · cited by 346Equiv.apply_symm_applyEquiv.symm_apply_apply · cited by 320Equiv.symm_apply_applyFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.BoundedFormula.Realize · cited by 104BoundedFormula.RealizeFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFinite.exists_equiv_fin · cited by 23Finite.exists_equiv_finEquiv.exists_congr · cited by 13Equiv.exists_congrFirstOrder.Language.Formula.iExs · cited by 8Formula.iExsFormula.realize_iExsCITED BYCITES

Cites15

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Cited by1

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