Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.FG.of_map_embedding
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : Type u_2} [inst_1 : L.Structure N]
(f : L.Embedding M N) {s : L.Substructure M}, (FirstOrder.Language.Substructure.map f.toHom s).FG → s.FG- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Function.Injective.injOnproof · cited by 280
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- Finset.finite_toSetproof · cited by 210
- FirstOrder.Language.Embeddingstatement and proof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.fg_iff_structure_fgproof · cited by 12