Theorems · Theorem · field theory
Nat.cast_le_pow_sub_div_sub
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α},
1 < a → ∀ (n : ℕ), ↑n ≤ (a ^ n - 1) / (a - 1)Bernoulli's inequality reformulated to estimate (n : α).
- Defined in
- Mathlib.Algebra.Order.Field.Power
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Fieldstatement and proof · cited by 7,404
- LE.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- zero_le_oneproof · cited by 316
- sub_posproof · cited by 147
- le_div_iff₀proof · cited by 75
- neg_le_selfproof · cited by 8
- one_add_mul_sub_le_powproof · cited by 1
- le_sub_left_of_add_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_le_pow_div_subproof · cited by 1