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Theorems · Theorem · order theory

pow_le_of_le_one

∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [inst_1 : Preorder M₀] {a : M₀} {n : ℕ} [PosMulMono M₀],
  0 ≤ a → a ≤ 1 → n ≠ 0 → a ^ n ≤ a
Defined in
Mathlib.Algebra.Order.GroupWithZero.Basic
Cited by
1 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidWithZeroPreorderPosMulMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sq_le · cited by 0sq_lePreorder · cited by 7952Preorderpow_one · cited by 894pow_oneMonoidWithZero · cited by 456MonoidWithZeroPosMulMono · cited by 165PosMulMonopow_le_pow_of_le_one · cited by 12pow_le_pow_of_le_onepow_le_of_le_oneCITED BYCITES

Cites5

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Cited by1

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