Theorems · Theorem · logic and foundations
FirstOrder.Language.Hom.range_eq_top
∀ {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 = ⊤ ↔ Function.Surjective ⇑f- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- 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
- SetLike.ext'_iffproof · cited by 78
- Set.range_eq_univproof · cited by 50
- FirstOrder.Language.Hom.rangestatement · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Structure.FG.map_of_surjectiveproof · cited by 1
- FirstOrder.Language.Structure.CG.map_of_surjectiveproof · cited by 1