Theorems · Inductive type · logic and foundations
FirstOrder.Language.LHom.Injective
{L : FirstOrder.Language} → {L' : FirstOrder.Language} → (L →ᴸ L') → PropA language homomorphism is injective when all the maps between symbol types are.
- Defined in
- Mathlib.ModelTheory.LanguageMap
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement · cited by 1,084
- FirstOrder.Language.LHomstatement · cited by 66
Cited by12
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.ModelType.defaultExpansionstatement and proof · cited by 3
- FirstOrder.Language.Theory.isSatisfiable_onTheory_iffstatement and proof · cited by 1
- FirstOrder.Language.LHom.sumInl_injectivestatement · cited by 1
- FirstOrder.Language.lhomWithConstants_injectivestatement · cited by 1
- FirstOrder.Language.LHom.Injective.onFunctionstatement and proof · cited by 1
- FirstOrder.Language.LHom.Injective.onRelationstatement and proof · cited by 1
- FirstOrder.Language.Theory.ModelType.defaultExpansion_Carrierstatement and proof · cited by 0
- FirstOrder.Language.Theory.ModelType.defaultExpansion_strucstatement and proof · cited by 0
- FirstOrder.Language.LHom.sumInr_injectivestatement · cited by 0
- FirstOrder.Language.LHom.Injective.casesOnstatement and proof · cited by 0
- FirstOrder.Language.LHom.Injective.isExpansionOn_defaultstatement and proof · cited by 0
- FirstOrder.Language.LHom.Injective.recOnstatement and proof · cited by 0