Theorems · Theorem · order theory
pow_lt_one_iff_of_nonneg
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : LinearOrder M₀] [PosMulStrictMono M₀] {a : M₀} {n : ℕ}
[ZeroLEOneClass M₀], 0 ≤ a → n ≠ 0 → (a ^ n < 1 ↔ a < 1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MonoidWithZerostatement and proof · cited by 456
- ZeroLEOneClassstatement and proof · cited by 304
- PosMulStrictMonostatement and proof · cited by 151
- lt_iff_lt_of_le_iff_leproof · cited by 54
- one_le_pow_iff_of_nonnegproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- sq_lt_one_iff₀proof · cited by 3
- Complex.UnitDisc.exists_continuousOn_pow_eqproof · cited by 0
- tendsto_zero_geometric_tsum_pnatproof · cited by 0