Theorems · Theorem · order theory
pow_le_pow_of_le_one
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a : M₀} [PosMulMono M₀],
0 ≤ a → a ≤ 1 → ∀ {m n : ℕ}, m ≤ n → a ^ n ≤ a ^ m- Cited by
- 12 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MonoidWithZerostatement and proof · cited by 456
- PosMulMonostatement and proof · cited by 165
- pow_right_anti₀proof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Real.sin_ltproof · cited by 4
- integral_sin_pow_succ_leproof · cited by 3
- FormalMultilinearSeries.comp_summable_nnrealproof · cited by 2
- RightDerivMeasurableAux.D_subset_differentiable_setproof · cited by 1
- RightDerivMeasurableAux.differentiable_set_subset_Dproof · cited by 1
- norm_exp_mul_sq_leproof · cited by 1
- pow_le_of_le_oneproof · cited by 1
- CStarAlgebra.pow_antitoneproof · cited by 1
- FDerivMeasurableAux.differentiable_set_subset_Dproof · cited by 1
- FDerivMeasurableAux.D_subset_differentiable_setproof · cited by 1
- NNReal.pow_antitone_expproof · cited by 0
- Bound.pow_le_pow_right_of_le_one_or_one_leproof · cited by 0