Theorems · Theorem · group theory
AddSubgroup.add_mem_cancel_left
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G) {x y : G}, x ∈ H → (x + y ∈ H ↔ y ∈ H)- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- add_mem_cancel_leftproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.le_normalizerproof · cited by 6
- AddSubgroup.closure_add_image_eqproof · cited by 1
- leftAddCoset_eq_iffproof · cited by 0
- AddAction.stabilizer_addSubgroupproof · cited by 0