Theorems · Theorem · group theory
Submonoid.map.congr_simp
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {F : Type u_4} [inst_2 : FunLike F M N]
[mc : MonoidHomClass F M N] (f f_1 : F),
f = f_1 → ∀ (S S_1 : Submonoid M), S = S_1 → Submonoid.map f S = Submonoid.map f_1 S_1- Cited by
- 9 results in Mathlib
- Foundations
- Depth 15 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.
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- MulOneClassstatement and proof · cited by 1,018
- MonoidHomClassstatement and proof · cited by 244
- Submonoid.mapstatement and proof · cited by 190
Cited by9
Results whose statement or proof uses this declaration.
- Submonoid.map_powersproof · cited by 10
- map_le_nonZeroDivisors_of_injectiveproof · cited by 5
- Ideal.disjoint_primeCompl_of_liesOverproof · cited by 3
- MonoidHom.map_mrangeproof · cited by 2
- RingHom.locally_localizationAwayPreservesproof · cited by 1
- Monoid.fg_iff_exists_freeMonoid_hom_surjectiveproof · cited by 1
- Submonoid.FG.piproof · cited by 1
- CategoryTheory.SubmonoidFunctor.image_comap_ιproof · cited by 0
- CategoryTheory.SubmonoidFunctor.image_compproof · cited by 0