Theorems · Theorem · group theory
Subsemigroup.mem_map_of_mem
∀ {M : Type u_1} {N : Type u_2} [inst : Mul M] [inst_1 : Mul N] (f : M →ₙ* N) {S : Subsemigroup M} {x : M},
x ∈ S → f x ∈ Subsemigroup.map f S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.mem_image_of_memproof · cited by 371
- Subsemigroupstatement and proof · cited by 323
- MulHomstatement and proof · cited by 299
- Subsemigroup.mapstatement · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- Subsemigroup.apply_coe_mem_mapproof · cited by 0