Theorems · Theorem · group theory
op_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 → AddOpposite.op a +ᵥ ↑s = ↑s- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddOppositestatement · cited by 452
- Set.vaddSetstatement · cited by 403
- SetLike.mem_coeproof · cited by 302
- AddSubgroupClassstatement and proof · cited by 240
- AddOpposite.opstatement · cited by 192
- neg_mem_iffproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- Set.addSubgroupClosure_addproof · cited by 0
- AddAction.isBlock_addSubgroup'proof · cited by 0