Theorems · Theorem · group theory
abs_mem_iff
∀ {S : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : LinearOrder G] {x : SetLike S G} [NegMemClass S G] {H : S}
{x_1 : G}, |x_1| ∈ H ↔ x_1 ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- absstatement and proof · cited by 1,814
- SetLikestatement and proof · cited by 1,084
- neg_mem_iffproof · cited by 42
- abs_choiceproof · cited by 16
- NegMemClassstatement and proof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.exists_isLeast_posproof · cited by 2