Theorems · Theorem · group theory
Group.rank_le_of_surjective
∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] [inst_2 : Group.FG G] [inst_3 : Group.FG H]
(f : G →* H), Function.Surjective ⇑f → Group.rank H ≤ Group.rank G- Defined in
- Mathlib.GroupTheory.Rank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupproof · cited by 3,593
- Finset.cardproof · cited by 2,327
- LE.le.trans_eqproof · cited by 328
- Subgroup.mapproof · cited by 301
- Finset.coe_imageproof · cited by 222
Cited by3
Results whose statement or proof uses this declaration.
- Group.rank_congrproof · cited by 1
- Group.rank_range_leproof · cited by 0
- CommGroup.freeRank_ge_of_surjectiveproof · cited by 0