Theorems · Theorem · commutative algebra
PowerSeries.exp_pow_eq_rescale_exp
∀ {A : Type u_4} [inst : CommRing A] [inst_1 : Algebra ℚ A] (k : ℕ),
PowerSeries.exp A ^ k = (PowerSeries.rescale ↑k) (PowerSeries.exp A)Shows that $(e^{X})^k = e^{kX}$.
- Defined in
- Mathlib.RingTheory.PowerSeries.Exp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- pow_zeroproof · cited by 1,094
- map_oneproof · cited by 861
- PowerSeriesstatement · cited by 797
- Nat.cast_addproof · cited by 586
- pow_succproof · cited by 374
- PowerSeries.Cproof · cited by 76
Cited by2
Results whose statement or proof uses this declaration.
- sum_range_powproof · cited by 2
- PowerSeries.exp_pow_sumproof · cited by 1