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Theorems · Definition · logic and foundations

FirstOrder.Language.Theory.ModelType.subtheoryModel

{L : FirstOrder.Language} → {T : L.Theory} → T.ModelType → {T' : L.Theory} → T' ⊆ T → T'.ModelType

A model of a theory is also a model of any subtheory.

Defined in
Mathlib.ModelTheory.Bundled
Cited by
4 results in Mathlib
Foundations
Depth 26 from the axioms · uses Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.Theory.models_iff_not_satisfiable · cited by 4Theory.models_iff_not_sat…FirstOrder.Language.Theory.ModelType.subtheoryModel_struc · cited by 0ModelType.subtheoryModel_…FirstOrder.Language.Theory.exists_modelType_is_realized_in · cited by 0Theory.exists_modelType_i…FirstOrder.Language.Theory.ModelType.subtheoryModel_Carrier · cited by 0ModelType.subtheoryModel_…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelType.Carrier · cited by 59ModelType.CarrierModelType.subtheoryModelCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.