Theorems · Theorem · group theory
Submonoid.map_le_of_le_comap
∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] (S : Submonoid M) {F : Type u_4}
[inst_2 : FunLike F M N] [mc : MonoidHomClass F M N] {T : Submonoid N} {f : F},
S ≤ Submonoid.comap f T → Submonoid.map f S ≤ T- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 190
- Submonoid.comapstatement · cited by 179
- GaloisConnection.l_leproof · cited by 28
- Submonoid.gc_map_comapproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- Ideal.spanIntNorm_localizationproof · cited by 3
- Submonoid.closure_one_prodproof · cited by 1
- Submonoid.closure_prod_oneproof · cited by 1
- Submonoid.closure_piproof · cited by 0
- Submonoid.closure_prodproof · cited by 0
- Module.IsTorsionFree.of_isLocalizationproof · cited by 0