Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.isSatisfiable_iUnion_iff_isSatisfiable_iUnion_finset

∀ {L : FirstOrder.Language} {ι : Type u_1} (T : ι → L.Theory),
  FirstOrder.Language.Theory.IsSatisfiable (⋃ i, T i) ↔
    ∀ (s : Finset ι), FirstOrder.Language.Theory.IsSatisfiable (⋃ i ∈ s, T i)

Defined in: Mathlib.ModelTheory.Satisfiability
Cited by: 0 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

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Setproof · cited by 53,352
Finsetstatement and proof · cited by 13,712
SetLike.coeproof · cited by 8,199
Set.iUnionstatement and proof · cited by 2,483
FirstOrder.Languagestatement and proof · cited by 1,084
FirstOrder.Language.Theorystatement and proof · cited by 154
FirstOrder.Language.Sentencestatement and proof · cited by 127
reflproof · cited by 80
Monotone.directed_leproof · cited by 25
FirstOrder.Language.Theory.IsSatisfiablestatement and proof · cited by 25
Set.iUnion_monoproof · cited by 21
Set.iUnion_subset_iffproof · cited by 15

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