Theorems · Theorem · order theory
negPart_lt
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : AddGroup α] {a b : α} [AddLeftMono α] [AddRightMono α],
a⁻ < b ↔ -b < a ∧ 0 < b- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- NegPart.negPartstatement · cited by 107
- neg_ltproof · cited by 21
- sup_lt_iffproof · cited by 9
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