Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.subset
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} (p : T.CompleteType α), (L.lhomWithConstants α).onTheory T ⊆ ↑p- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.withConstantsstatement · cited by 108
- FirstOrder.Language.lhomWithConstantsstatement · cited by 39
- FirstOrder.Language.Theory.CompleteTypestatement and proof · cited by 35
- FirstOrder.Language.LHom.onTheorystatement · cited by 27
- FirstOrder.Language.Theory.CompleteType.subset'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.setOfPred_subset_eq_empty_iffproof · cited by 3
- FirstOrder.Language.Theory.CompleteType.mem_of_modelsproof · cited by 0
- FirstOrder.Language.Theory.exists_modelType_is_realized_inproof · cited by 0