Theorems · Theorem · group theory
AddSubgroup.zmultiples_neg
∀ {G : Type u_1} [inst : AddGroup G] {g : G}, AddSubgroup.zmultiples (-g) = AddSubgroup.zmultiples g- Cited by
- 6 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddSubgroup.zmultiplesstatement · cited by 493
- eq_of_forall_ge_iffproof · cited by 96
- neg_mem_iffproof · cited by 42
- AddSubgroup.zmultiples_leproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.zmultiples_eq_zmultiples_iffproof · cited by 3
- LinearOrderedAddCommGroup.Subgroup.exists_neg_generatorproof · cited by 2
- zmultiples_absproof · cited by 1
- AddSubgroup.closure_toAddSubmonoid_of_isOfFinAddOrderproof · cited by 1
- ergodic_vadd_of_denseRange_zsmulproof · cited by 1
- AddSubgroup.le_zmultiples_iffproof · cited by 0