Theorems · Theorem · order theory
zsmul_left_inj
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a : α},
0 < a → ∀ {m n : ℤ}, m • a = n • a ↔ m = n- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- StrictMono.injectiveproof · cited by 94
- zsmul_left_strictMonoproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- AddCommGroup.not_modEq_iff_toIcoDiv_eq_toIocDivproof · cited by 3
- AddCommGroup.modEq_iff_toIcoDiv_eq_toIocDiv_add_oneproof · cited by 1
- AddSubgroup.isLeast_of_closure_iff_eq_absproof · cited by 0