Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.fun_mem
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] (self : L.Substructure M) {n : ℕ} (f : L.Functions n),
FirstOrder.Language.ClosedUnder f ↑self- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 5 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.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.Functionsstatement · cited by 153
- FirstOrder.Language.ClosedUnderstatement · cited by 13
- FirstOrder.Language.Substructure.carrierstatement · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.mem_closed_iffproof · cited by 1
- FirstOrder.Language.Substructure.constants_memproof · cited by 1
- FirstOrder.Language.Substructure.mem_iSup_of_directedproof · cited by 1
- FirstOrder.Language.Term.realize_memproof · cited by 1
- FirstOrder.Language.Substructure.skolem₁_reduct_isElementaryproof · cited by 0