Theorems · Theorem · group theory
vadd_coe_set
∀ {G : Type u_2} {S : Type u_4} [inst : AddGroup G] [inst_1 : SetLike S G] [AddSubgroupClass S G] {s : S} {a : G},
a ∈ s → a +ᵥ ↑s = ↑s- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- Set.extproof · cited by 2,266
- HVAdd.hVAddstatement · cited by 1,820
- SetLikestatement and proof · cited by 1,084
- Set.vaddSetstatement · cited by 403
- SetLike.mem_coeproof · cited by 302
- AddSubgroupClassstatement and proof · cited by 240
- neg_mem_iffproof · cited by 42
- Set.mem_vadd_set_iff_neg_vadd_memproof · cited by 24
- add_mem_cancel_leftproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- AddAction.isBlock_addSubgroupproof · cited by 0
- Set.add_addSubgroupClosureproof · cited by 0