Theorems · Definition · logic and foundations
FirstOrder.Language.LEquiv.addEmptyConstants
(L : FirstOrder.Language) → (α : Type w') → [ie : IsEmpty α] → L ≃ᴸ L.withConstants α
The language map removing an empty constant set.
- Defined in
- Mathlib.ModelTheory.LanguageMap
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- IsEmpty
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
- IsEmptystatement and proof · cited by 759
- FirstOrder.Language.withConstantsstatement · cited by 108
- FirstOrder.Language.lhomWithConstantsproof · cited by 39
- FirstOrder.Language.constantsOnproof · cited by 22
- FirstOrder.Language.LEquivstatement · cited by 19
- FirstOrder.Language.LHom.idproof · cited by 18
- FirstOrder.Language.LHom.sumElimproof · cited by 9
- FirstOrder.Language.LHom.ofIsEmptyproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Set.empty_definable_iffproof · cited by 2
- FirstOrder.Language.LEquiv.addEmptyConstants_invLHomstatement and proof · cited by 2
- Set.termDefinable_empty_iffproof · cited by 1
- FirstOrder.Language.LEquiv.addEmptyConstants.congr_simpstatement and proof · cited by 0
- FirstOrder.Language.LEquiv.addEmptyConstants_toLHomstatement and proof · cited by 0