Theorems · Theorem · order theory
zsmul_left_strictAnti
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a : α},
a < 0 → StrictAnti fun n => n • a- Defined in
- Mathlib.Algebra.Order.Group.Basic
- Cited by
- 1 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
- StrictAntistatement · cited by 204
- add_one_zsmulproof · cited by 19
- strictAnti_int_of_succ_ltproof · cited by 3
- add_lt_of_neg_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_closure_singleton_iff_existsUnique_zsmulproof · cited by 0