Theorems · Theorem · group theory
IsOfFinOrder.eq_neg_one
∀ {G : Type u_1} [inst : Ring G] [inst_1 : LinearOrder G] [IsStrictOrderedRing G] {a : G},
a ≤ 0 → IsOfFinOrder a → a = -1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
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
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.not_geproof · cited by 305
- IsOfFinOrderstatement and proof · cited by 113
- sq_nonnegproof · cited by 106
- one_posproof · cited by 102
- sq_eq_one_iffproof · cited by 14
- IsOfFinOrder.eq_oneproof · cited by 2
- IsOfFinOrder.powproof · cited by 2
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