Theorems · Theorem · order theory
le_iff_posPart_negPart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddCommGroup α] [AddLeftMono α] (a b : α), a ≤ b ↔ a⁺ ≤ b⁺ ∧ b⁻ ≤ a⁻- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- PosPart.posPartstatement and proof · cited by 113
- NegPart.negPartstatement and proof · cited by 107
- sub_le_subproof · cited by 24
- posPart_sub_negPartproof · cited by 9
- negPart_antiproof · cited by 1
- posPart_monoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicOn.negPart_divisor_add_le_maxproof · cited by 1