Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.CG.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).CG → s.CG- 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.
Cites24
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
- 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
- Set.Countableproof · cited by 545
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.Embeddingstatement and proof · cited by 128
- LowerAdjoint.toFunproof · cited by 105
- FirstOrder.Language.Substructure.closureproof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.cg_iff_structure_cgproof · cited by 0