Theorems · Theorem · order theory
add_nonpos
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b : α}, a ≤ 0 → b ≤ 0 → a + b ≤ 0Alias of Left.add_nonpos.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- AddZeroClassstatement · cited by 1,237
- AddLeftMonostatement · cited by 687
- Left.add_nonposproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- pos_add_self_iffproof · cited by 2
- tsum_nonposproof · cited by 1
- exists_forall_closed_ball_dist_add_le_two_mul_subproof · cited by 0
- Real.qaryEntropy_nonpos_of_nonposproof · cited by 0