Theorems · Theorem · logic and foundations
FirstOrder.Language.Hom.range_eq_map
∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] (f : L.Hom M N),
f.range = FirstOrder.Language.Substructure.map f ⊤- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topstatement · cited by 9,680
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- FirstOrder.Language.Homstatement and proof · cited by 107
- FirstOrder.Language.Substructure.mapstatement · cited by 49
- FirstOrder.Language.Hom.rangestatement · cited by 30
- FirstOrder.Language.Substructure.extproof · cited by 6
Cited by7
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
- FirstOrder.Language.age.countable_quotientproof · cited by 2
- FirstOrder.Language.DirectLimit.range_liftproof · cited by 1
- FirstOrder.Language.Structure.CG.rangeproof · cited by 1
- FirstOrder.Language.Substructure.cg_iff_structure_cgproof · cited by 0
- FirstOrder.Language.Hom.range_le_iff_comapproof · cited by 0