Theorems · Theorem · order theory
neg_le_self
∀ {α : Type u} [inst : AddGroup α] [inst_1 : Preorder α] [AddLeftMono α] {a : α}, 0 ≤ a → -a ≤ aAlias of Left.neg_le_self.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- AddGroupPreorderAddLeftMono
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
- AddGroupstatement · cited by 4,410
- AddLeftMonostatement · cited by 687
- Left.neg_le_selfproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- Real.arcsin_of_le_neg_oneproof · cited by 7
- Real.arcsin_of_one_leproof · cited by 7
- Real.arcsin_oneproof · cited by 6
- Real.surjOn_sinproof · cited by 2
- Real.arcsin_projIccstatement and proof · cited by 2
- Nat.cast_le_pow_sub_div_subproof · cited by 1
- Real.arcsin_neg_oneproof · cited by 1
- integral_sqrt_one_sub_sqproof · cited by 0