Theorems · Theorem · group theory
Submonoid.le_comap_of_map_le
∀ {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},
Submonoid.map f S ≤ T → S ≤ Submonoid.comap f T- Cited by
- 3 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
- Submonoid.gc_map_comapproof · cited by 16
- GaloisConnection.le_uproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- nonZeroDivisors_le_comap_nonZeroDivisors_of_injectiveproof · cited by 7
- IsLocalization.algEquivOfAlgEquiv_eq_mapstatement · cited by 0
- IsLocalization.ringEquivOfRingEquiv_eq_mapstatement · cited by 0