Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.mem_of_models
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} (p : T.CompleteType α) {φ : (L.withConstants α).Sentence},
(L.lhomWithConstants α).onTheory T ⊨ᵇ φ → φ ∈ p- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 0 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.
Cites16
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
- Set.singleton_subset_iffproof · cited by 206
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.withConstantsstatement and proof · cited by 108
- Set.union_subsetproof · cited by 71
- FirstOrder.Language.lhomWithConstantsstatement and proof · cited by 39
- FirstOrder.Language.Theory.CompleteTypestatement and proof · cited by 35
- FirstOrder.Language.Theory.ModelsBoundedFormulastatement and proof · cited by 30
- FirstOrder.Language.LHom.onTheorystatement and proof · cited by 27
- FirstOrder.Language.Formula.notproof · cited by 27
- FirstOrder.Language.Theory.CompleteType.isMaximalproof · cited by 8
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.