Theorems · Theorem · order theory
Left.neg_le_self
∀ {α : Type u} [inst : AddGroup α] [inst_1 : Preorder α] [AddLeftMono α] {a : α}, 0 ≤ a → -a ≤ a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddGroupPreorderAddLeftMono
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
- AddGroupstatement and proof · cited by 4,410
- le_transproof · cited by 985
- AddLeftMonostatement and proof · cited by 687
- Left.neg_nonpos_iffproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- neg_le_selfproof · cited by 8