Theorems · Theorem · group theory
MonoidHom.domRestrict_apply
∀ {M : Type u_1} [inst : MulOneClass M] {N : Type u_5} {S : Type u_6} [inst_1 : MulOneClass N] [inst_2 : SetLike S M]
[inst_3 : SubmonoidClass S M] (f : M →* N) (s : S) (x : ↥s), (f.domRestrict s) x = f ↑x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MonoidHomstatement and proof · cited by 3,629
- SetLikestatement and proof · cited by 1,084
- MulOneClassstatement and proof · cited by 1,018
- SubmonoidClassstatement and proof · cited by 60
- MonoidHom.domRestrictstatement · cited by 59
Cited by4
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.lift_mul_rightproof · cited by 2
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfproof · cited by 1
- Submonoid.LocalizationMap.lift_surjective_iffproof · cited by 1
- MonoidHom.restrict_applyproof · cited by 0