Theorems · Theorem · order theory
lt_neg_self_iff
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {a : α}, a < -a ↔ a < 0- Defined in
- Mathlib.Algebra.Order.Group.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
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
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- not_ltproof · cited by 306
- neg_le_self_iffproof · cited by 4
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