Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.Model.mono
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {T T' : L.Theory}, M ⊨ T' → T ⊆ T' → M ⊨ T- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 25 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 and proof · cited by 154
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Theory.realize_sentence_of_memproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.IsSatisfiable.monoproof · cited by 7
- FirstOrder.Field.modelField_of_modelACFproof · cited by 3
- FirstOrder.Field.isAlgClosed_of_model_ACFproof · cited by 2
- FirstOrder.Language.Theory.model_union_iffproof · cited by 1
- FirstOrder.Language.Theory.exists_large_model_of_infinite_modelproof · cited by 1