Theorems · Theorem · group theory
zero_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (a : G), 0 • a = 0- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- SubNegMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SubNegMonoidstatement and proof · cited by 79
- SubNegMonoid.zsmul_zero'proof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_closure_singletonproof · cited by 6
- Finsupp.sum_zsmulproof · cited by 4
- norm_le_norm_add_norm_neg_addproof · cited by 3
- AddSubgroup.exists_isLeast_posproof · cited by 2
- controlled_sum_of_mem_closureproof · cited by 2
- IsSMulRegular.natAbs_iffproof · cited by 1
- zsmul_induction_rightproof · cited by 1
- AddSubgroup.closure_add_image_add_eq_topproof · cited by 1
- SubAddAction.fixingAddSubgroup_map_addConj_eqproof · cited by 1
- mpullback_addInvariantVectorFieldproof · cited by 1
- FreeAddGroup.reduceCyclically.reduce_flatten_replicate_succproof · cited by 1