Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheory
∀ {L : FirstOrder.Language} {T : L.Theory} {L' : FirstOrder.Language} (φ : L →ᴸ L'),
(φ.onTheory T).IsSatisfiable → T.IsSatisfiable- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- FirstOrder.Languagestatement and proof · cited by 1,084
- Nonempty.someproof · cited by 340
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.LHomstatement and proof · cited by 66
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.LHom.onTheorystatement and proof · cited by 27
- FirstOrder.Language.Theory.IsSatisfiablestatement and proof · cited by 25
- FirstOrder.Language.Theory.ModelType.reductproof · cited by 5
- FirstOrder.Language.Theory.Model.isSatisfiableproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.isSatisfiable_onTheory_iffproof · cited by 1