Theorems · Theorem · field theory
Nat.cast_le_pow_div_sub
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a : α},
1 < a → ∀ (n : ℕ), ↑n ≤ a ^ n / (a - 1)For any a > 1 and a natural n we have n ≤ a ^ n / (a - 1). See also
Nat.cast_le_pow_sub_div_sub for a stronger inequality with a ^ n - 1 in the numerator.
- Defined in
- Mathlib.Algebra.Order.Field.Power
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- 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_nonnegproof · cited by 167
- div_le_div_of_nonneg_rightproof · cited by 77
- sub_le_selfproof · cited by 14
- Nat.cast_le_pow_sub_div_subproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isLittleO_pow_const_const_pow_of_one_ltproof · cited by 3