Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.constants_mem
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {S : L.Substructure M} (c : L.Constants), ↑c ∈ S- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- finZeroElimproof · cited by 29
- FirstOrder.Language.constantMapstatement · cited by 28
- FirstOrder.Language.Constantsstatement and proof · cited by 14
- FirstOrder.Language.Substructure.fun_memproof · cited by 5
- FirstOrder.Language.Substructure.mem_carrierproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.subset_closure_withConstantsproof · cited by 1