Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.IsMaximal.mem_of_models
∀ {L : FirstOrder.Language} {T : L.Theory}, T.IsMaximal → ∀ {φ : L.Sentence}, T ⊨ᵇ φ → φ ∈ T- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- Set.insert_eq_of_memproof · cited by 118
- Set.union_singletonproof · cited by 107
- FirstOrder.Language.Formulaproof · cited by 93
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.Formula.notproof · cited by 27
- FirstOrder.Language.Theory.IsSatisfiableproof · cited by 25
- FirstOrder.Language.Theory.IsMaximalstatement and proof · cited by 10
- FirstOrder.Language.Theory.models_iff_not_satisfiableproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsMaximal.mem_iff_modelsproof · cited by 3
- FirstOrder.Language.Theory.CompleteType.typesWith_topproof · cited by 1