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Theorems · Theorem · group theory

IsOfFinOrder.eq_one

∀ {G : Type u_1} [inst : Semiring G] [inst_1 : LinearOrder G] [IsStrictOrderedRing G] {a : G},
  0 ≤ a → IsOfFinOrder a → a = 1
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringLinearOrderIsStrictOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsOfFinOrder.norm_eq_one · cited by 2IsOfFinOrder.norm_eq_oneIsOfFinOrder.eq_neg_one · cited by 0IsOfFinOrder.eq_neg_oneSemiring · cited by 13802SemiringLinearOrder · cited by 8572LinearOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingLT.lt.ne' · cited by 1417lt.ne'IsOfFinOrder · cited by 113IsOfFinOrderIsOfFinOrder.exists_pow_eq_one · cited by 4IsOfFinOrder.exists_pow_e…pow_eq_one_iff_of_nonneg · cited by 4pow_eq_one_iff_of_nonnegIsOfFinOrder.eq_oneCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.