Theorems · Theorem · order theory
nsmul_two_semiclosed
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] [AddRightMono α] {a : α}, 0 ≤ 2 • a → 0 ≤ a- Defined in
- Mathlib.Algebra.Order.Group.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- inf_of_le_leftproof · cited by 186
- inf_commproof · cited by 139
- two_nsmulproof · cited by 67
- inf_eq_rightproof · cited by 64
- inf_assocproof · cited by 53
- add_eq_leftproof · cited by 37
Cited by1
Results whose statement or proof uses this declaration.
- abs_nonnegproof · cited by 168