Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.isSatisfiable_onTheory_iff
∀ {L : FirstOrder.Language} {T : L.Theory} {L' : FirstOrder.Language} {φ : L →ᴸ L'},
φ.Injective → ((φ.onTheory T).IsSatisfiable ↔ T.IsSatisfiable)- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 27
- FirstOrder.Language.Theory.IsSatisfiablestatement and proof · cited by 25
- FirstOrder.Language.LHom.Injectivestatement and proof · cited by 9
- FirstOrder.Language.Theory.Model.isSatisfiableproof · cited by 5
- Classical.inhabited_of_nonempty'proof · cited by 4
- FirstOrder.Language.Theory.ModelType.defaultExpansionproof · cited by 3
- FirstOrder.Language.Theory.isSatisfiable_of_isSatisfiable_onTheoryproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.CompleteType.nonempty_iffproof · cited by 0