Theorems · Theorem · group theory
Subgroup.mul_mem_cancel_right
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) {x y : G}, x ∈ H → (y * x ∈ H ↔ y ∈ H)- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- mul_mem_cancel_rightproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.le_normalizerproof · cited by 19
- Subgroup.isOpen_of_mem_nhdsproof · cited by 3
- rightCoset_eq_iffproof · cited by 3
- Subgroup.commutator_top_left_le_iffproof · cited by 2
- IsCusp.smul_of_memproof · cited by 0
- MulAction.stabilizer_subgroup_opproof · cited by 0
- MulAction.stabilizer_op_subgroupproof · cited by 0