Theorems · Theorem · commutative algebra
PowerSeries.monomial_eq_C_mul_X_pow
∀ {R : Type u_1} [inst : Semiring R] (r : R) (n : ℕ), (PowerSeries.monomial n) r = PowerSeries.C r * PowerSeries.X ^ n- Defined in
- Mathlib.RingTheory.PowerSeries.Trunc
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- PowerSeriesstatement · cited by 797
- PowerSeries.Xstatement and proof · cited by 183
- mul_iteproof · cited by 159
- PowerSeries.Cstatement · cited by 76
- PowerSeries.extproof · cited by 69
Cited by4
Results whose statement or proof uses this declaration.
- PowerSeries.WithPiTopology.hasSum_pentagonalSeriesproof · cited by 2
- PowerSeries.eq_of_le_of_X_notMem_of_fg_of_isPrimeproof · cited by 1
- MvPowerSeries.optionEquivLeft_X_noneproof · cited by 0
- MvPowerSeries.optionEquivLeft_X_someproof · cited by 0