Theorems · Definition · logic and foundations
FirstOrder.Language.LHom.sumMap
{L : FirstOrder.Language} →
{L' : FirstOrder.Language} →
(L →ᴸ L') → {L₁ : FirstOrder.Language} → {L₂ : FirstOrder.Language} → (L₁ →ᴸ L₂) → (L.sum L₁ →ᴸ L'.sum L₂)The map between two sum-languages induced by maps on the two factors.
- Defined in
- Mathlib.ModelTheory.LanguageMap
- Cited by
- 4 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.
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
- FirstOrder.Language.Functionsproof · cited by 153
- FirstOrder.Language.Relationsproof · cited by 147
- FirstOrder.Language.LHomstatement and proof · cited by 66
- FirstOrder.Language.sumstatement · cited by 31
- FirstOrder.Language.LHom.onFunctionproof · cited by 27
- FirstOrder.Language.LHom.onRelationproof · cited by 27
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.lhomWithConstantsMapproof · cited by 3
- FirstOrder.Language.LHom.addConstantsproof · cited by 2
- FirstOrder.Language.LHom.sumMap_comp_inlstatement · cited by 0
- FirstOrder.Language.LHom.sumMap_comp_inrstatement · cited by 0
- FirstOrder.Language.LHom.sumMap_onFunctionstatement and proof · cited by 0
- FirstOrder.Language.LHom.sumMap_onRelationstatement and proof · cited by 0