Theorems · Theorem · logic and foundations
FirstOrder.Language.mem_completeTheory
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {φ : L.Sentence}, φ ∈ L.completeTheory M ↔ M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 3 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.
Cites6
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 · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
- FirstOrder.Language.completeTheorystatement · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsComplete.eq_complete_theoryproof · cited by 2
- FirstOrder.Language.realize_iff_of_model_completeTheoryproof · cited by 0
- FirstOrder.Language.Theory.CompleteType.mem_typeOfproof · cited by 0