Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.realize_sentence_of_mem
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] (T : L.Theory) [M ⊨ T] {φ : L.Sentence}, φ ∈ T → M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
- FirstOrder.Language.Theory.Model.realize_of_memproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.Model.monoproof · cited by 5
- FirstOrder.Language.Theory.models_iff_not_satisfiableproof · cited by 4
- FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiableproof · cited by 3
- FirstOrder.Language.Theory.models_sentence_of_memproof · cited by 3
- FirstOrder.Language.Theory.IsUniversal.models_of_embeddingproof · cited by 1
- FirstOrder.Language.denselyOrdered_of_dloproof · cited by 1
- FirstOrder.Language.noBotOrder_of_dloproof · cited by 1
- FirstOrder.Language.noTopOrder_of_dloproof · cited by 1
- FirstOrder.Language.realize_iff_of_model_completeTheoryproof · cited by 0
- FirstOrder.Field.FieldAxiom.toProp_of_modelproof · cited by 0
- FirstOrder.Language.StrongHomClass.theory_modelproof · cited by 0