Theorems · Theorem · order theory
le_iff_oneLePart_leOnePart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : CommGroup α] [MulLeftMono α] (a b : α), a ≤ b ↔ a⁺ᵐ ≤ b⁺ᵐ ∧ b⁻ᵐ ≤ a⁻ᵐ- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeCommGroupMulLeftMono
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommGroupstatement and proof · cited by 990
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- LeOnePart.leOnePartstatement and proof · cited by 41
- OneLePart.oneLePartstatement and proof · cited by 40
- div_le_div''proof · cited by 8
- oneLePart_div_leOnePartproof · cited by 6
- oneLePart_monoproof · cited by 1
- leOnePart_antiproof · cited by 1
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