Theorems · Theorem · order theory
one_add_mul_sub_le_pow
∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R},
-1 ≤ a → ∀ (n : ℕ), 1 + ↑n * (a - 1) ≤ a ^ nBernoulli's inequality reformulated to estimate a^n.
- Defined in
- Mathlib.Algebra.Order.Ring.Pow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- sub_eq_add_negproof · cited by 1,023
- add_sub_cancelproof · cited by 195
- neg_addproof · cited by 69
- one_add_one_eq_twoproof · cited by 65
- sub_le_sub_iff_rightproof · cited by 15
- one_add_mul_le_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Nat.cast_le_pow_sub_div_subproof · cited by 1