Theorems · Theorem · group theory
sub_mem_comm_iff
∀ {G : Type u_1} [inst : AddGroup G] {S : Type u_6} {H : S} [inst_1 : SetLike S G] [AddSubgroupClass S G] {a b : G},
a - b ∈ H ↔ b - a ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- SetLikestatement and proof · cited by 1,084
- neg_subproof · cited by 272
- AddSubgroupClassstatement and proof · cited by 240
- neg_mem_iffproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.sub_mem_comm_iffproof · cited by 0