Theorems · Theorem · group theory
AddGroup.rank_le_of_surjective
∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] [inst_2 : AddGroup.FG G]
[inst_3 : AddGroup.FG H] (f : G →+ H), Function.Surjective ⇑f → AddGroup.rank H ≤ AddGroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Finset.cardproof · cited by 2,327
- LE.le.trans_eqproof · cited by 328
- Finset.coe_imageproof · cited by 222
- AddSubgroup.mapproof · cited by 189
Cited by3
Results whose statement or proof uses this declaration.
- AddGroup.rank_congrproof · cited by 1
- AddCommGroup.freeRank_ge_of_surjectiveproof · cited by 0
- AddGroup.rank_range_leproof · cited by 0