Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.IsSatisfiable.mono
∀ {L : FirstOrder.Language} {T T' : L.Theory}, T'.IsSatisfiable → T ⊆ T' → T.IsSatisfiable- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nonempty.someproof · cited by 340
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentencestatement · cited by 127
- FirstOrder.Language.Theory.IsSatisfiablestatement and proof · cited by 25
- FirstOrder.Language.Theory.Model.bundledproof · cited by 5
- FirstOrder.Language.Theory.Model.monoproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.setOfPred_subset_eq_empty_iffproof · cited by 3
- FirstOrder.Language.Theory.models_iff_finset_modelsproof · cited by 1
- FirstOrder.Language.Theory.isSatisfiable_directed_union_iffproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.not_mem_iffproof · cited by 1
- FirstOrder.Language.Theory.IsSatisfiable.isFinitelySatisfiableproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.mem_of_modelsproof · cited by 0