Theorems · Theorem · order theory
negPart_pos_iff
∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : AddGroup α] {a : α} [AddLeftMono α], 0 < a⁻ ↔ a < 0- 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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Cites8
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
- NegPart.negPartstatement · cited by 107
- lt_iff_lt_of_le_iff_leproof · cited by 54
- LE.le.ge_iff_eq'proof · cited by 50
- negPart_nonnegproof · cited by 7
- negPart_eq_zeroproof · cited by 4
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