Theorems · Theorem · order theory
pow_right_monotone
∀ {M : Type u_3} [inst : Monoid M] [inst_1 : Preorder M] [MulLeftMono M] {a : M}, 1 ≤ a → Monotone fun n => a ^ n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidPreorderMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Monoidstatement and proof · cited by 3,887
- Monotonestatement · cited by 1,397
- MulLeftMonostatement and proof · cited by 410
- pow_succproof · cited by 374
- monotone_nat_of_le_succproof · cited by 45
- le_mul_of_one_le_right'proof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- pow_le_pow_right'proof · cited by 6
- Set.pow_right_monotoneproof · cited by 3
- Finset.pow_right_monotoneproof · cited by 1