Theorems · Theorem · order theory
zsmul_left_strictMono
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a : α},
0 < a → StrictMono fun n => n • a- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- StrictMonostatement · cited by 706
- lt_add_of_pos_rightproof · cited by 51
- add_one_zsmulproof · cited by 19
- strictMono_int_of_lt_succproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- zsmul_lt_zsmul_iff_leftproof · cited by 6
- zsmul_le_zsmul_iff_leftproof · cited by 3
- zsmul_left_injproof · cited by 3
- isAddFundamentalDomain_Ioc'proof · cited by 2
- isAddFundamentalDomain_Iocproof · cited by 1
- toIocMod_le_toIcoMod_addproof · cited by 0
- zsmul_lt_zsmul_leftproof · cited by 0
- AddSubgroup.mem_closure_singleton_iff_existsUnique_zsmulproof · cited by 0