Theorems · Theorem · group theory
AddSubgroup.closure_add_image_add_eq_top
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {R S : Set G} (hR : AddSubgroup.IsComplement (↑H) R),
0 ∈ R → AddSubgroup.closure S = ⊤ → ↑(AddSubgroup.closure ((fun g => g + -↑(hR.toRightFun g)) '' (R + S))) + R = ⊤- Defined in
- Mathlib.GroupTheory.Schreier
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- mul_oneproof · cited by 3,885
- AddSubgroupstatement and proof · cited by 3,232
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- neg_negproof · cited by 960
- add_assocproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_add_image_eqproof · cited by 1