Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.FG.map
∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {N : Type u_2} [inst_1 : L.Structure N]
(f : L.Hom M N) {s : L.Substructure M}, s.FG → (FirstOrder.Language.Substructure.map f s).FG- Defined in
- Mathlib.ModelTheory.FinitelyGenerated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.imageproof · cited by 5,609
- Set.Finiteproof · cited by 1,814
- 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.Homstatement and proof · cited by 107
- LowerAdjoint.toFunproof · cited by 105
- Set.Finite.imageproof · cited by 96
- FirstOrder.Language.Substructure.closureproof · cited by 70
- FirstOrder.Language.Substructure.mapstatement and proof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.fg_iff_structure_fgproof · cited by 12
- FirstOrder.Language.Structure.FG.rangeproof · cited by 7