Theorems · Theorem · group theory
AddSubmonoid.apply_coe_mem_map
∀ {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) (S : AddSubmonoid M) (x : ↥S),
f ↑x ∈ AddSubmonoid.map f S- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
- AddSubmonoid.mapstatement · cited by 99
- AddSubmonoid.mem_map_of_memproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.map_injective_of_injectivestatement and proof · cited by 0
- AddSubmonoid.LocalizationMap.map_surjective_of_surjectivestatement and proof · cited by 0