Theorems · Theorem · group theory
AddSubgroup.exists_left_transversal_of_le
∀ {G : Type u_1} [inst : AddGroup G] {H' H : AddSubgroup G},
H' ≤ H → ∃ S, S + ↑H' = ↑H ∧ Nat.card ↑S * Nat.card ↥H' = Nat.card ↥HGiven two subgroups H' ⊆ H, there exists a transversal to H' inside H
- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- Equiv.symmproof · cited by 3,681
- AddSubgroupstatement and proof · cited by 3,232
- Nat.cardstatement and proof · cited by 844
- Set.addstatement · cited by 338
- Set.image_univproof · cited by 322
- AddSubgroup.mapproof · cited by 189
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.