Theorems · Theorem · order theory
zsmul_nonneg
∀ {G : Type u_2} [inst : SubNegMonoid G] [inst_1 : Preorder G] [AddLeftMono G] {x : G},
0 ≤ x → ∀ {n : ℤ}, 0 ≤ n → 0 ≤ n • x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 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.
- Preorderstatement and proof · cited by 7,952
- AddLeftMonostatement and proof · cited by 687
- natCast_zsmulproof · cited by 118
- SubNegMonoidstatement and proof · cited by 79
- nsmul_nonnegproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- AddCircle.coe_eq_zero_of_pos_iffproof · cited by 1
- zsmul_mono_rightproof · cited by 1
- AddSubgroup.isLeast_of_closure_iff_eq_absproof · cited by 0