Theorems · Theorem · group theory
self_ne_neg
∀ {G : Type u_2} [inst : AddGroup G] [IsAddTorsionFree G] {a : G}, a ≠ -a ↔ a ≠ 0- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddTorsionFree
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- IsAddTorsionFreestatement and proof · cited by 155
- Iff.neproof · cited by 52
- self_eq_negproof · cited by 5
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