Theorems · Theorem · group theory
AddMonoidHom.mem_mrange
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_4}
[inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] {f : F} {y : N}, y ∈ AddMonoidHom.mrange f ↔ ∃ x, f x = y- Cited by
- 10 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
- AddMonoidHom.mrangestatement · cited by 61
Cited by10
Results whose statement or proof uses this declaration.
- AddSubmonoid.mem_supproof · cited by 8
- AddMonoidHom.exists_mrange_eq_mgraphproof · cited by 4
- AddSubmonoid.closure_induction_leftproof · cited by 3
- AddSubmonoid.mem_closure_singletonproof · cited by 2
- AddMonoidHom.exists_addEquiv_mrange_eq_mgraphproof · cited by 2
- AddMonoidHom.domRestrict_mrangeproof · cited by 1
- AddMonoidHom.exists_addEquiv_range_eq_graphproof · cited by 1
- AddMonoidHom.exists_range_eq_graphproof · cited by 0
- AddMonoidHom.noncommPiCoprod_mrangeproof · cited by 0
- AddMonoidHom.mgraph_eq_mrange_prodproof · cited by 0