Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.ModelsBoundedFormula.realize_sentence
∀ {L : FirstOrder.Language} {T : L.Theory} {φ : L.Sentence},
T ⊨ᵇ φ → ∀ (M : Type u_1) [inst : L.Structure M] [M ⊨ T] [Nonempty M], M ⊨ φ- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- Set.union_singletonproof · cited by 107
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Sentence.Realizestatement and proof · cited by 62
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.Formula.notproof · cited by 27
- FirstOrder.Language.Theory.Model.isSatisfiableproof · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiableproof · cited by 4
- FirstOrder.Language.Theory.model_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsComplete.realize_sentence_iffproof · cited by 3
- FirstOrder.Language.Theory.IsComplete.eq_complete_theoryproof · cited by 2
- FirstOrder.Language.Theory.ModelsBoundedFormula.realize_formulaproof · cited by 2
- FirstOrder.Language.Theory.models_of_models_theoryproof · cited by 1