Theorems · Definition · logic and foundations
FirstOrder.Language.LHom.comp
{L : FirstOrder.Language} →
{L' : FirstOrder.Language} → {L'' : FirstOrder.Language} → (L' →ᴸ L'') → (L →ᴸ L') → (L →ᴸ L'')The composition of two language homomorphisms.
- Defined in
- Mathlib.ModelTheory.LanguageMap
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
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.Functionsproof · cited by 153
- FirstOrder.Language.Relationsproof · cited by 147
- FirstOrder.Language.LHomstatement and proof · cited by 66
- FirstOrder.Language.LHom.onFunctionproof · cited by 27
- FirstOrder.Language.LHom.onRelationproof · cited by 27
Cited by26
Results whose statement or proof uses this declaration.
- FirstOrder.Language.LEquiv.transproof · cited by 2
- FirstOrder.Language.LHom.comp_onRelationstatement and proof · cited by 1
- FirstOrder.Language.LHom.comp_onTermstatement and proof · cited by 1
- FirstOrder.Language.LEquiv.mk.injstatement and proof · cited by 1
- FirstOrder.Language.LEquiv.mk.noConfusionstatement and proof · cited by 1
- FirstOrder.Language.LEquiv.recOnstatement and proof · cited by 0
- FirstOrder.Language.LEquiv.right_invstatement · cited by 0
- FirstOrder.Language.LEquiv.trans_invLHomstatement · cited by 0
- FirstOrder.Language.LEquiv.trans_toLHomstatement · cited by 0
- FirstOrder.Language.LHom.comp_assocstatement · cited by 0
- FirstOrder.Language.LHom.comp_idstatement and proof · cited by 0
- FirstOrder.Language.LHom.comp_onBoundedFormulastatement and proof · cited by 0