Theorems · Theorem · commutative algebra
PowerSeries.rescale_map
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] (φ : R →+* S) (r : R)
(f : PowerSeries R),
(PowerSeries.rescale (φ r)) ((PowerSeries.map φ) f) = (PowerSeries.map φ) ((PowerSeries.rescale r) f)- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- map_mulproof · cited by 1,137
- PowerSeriesstatement and proof · cited by 797
- map_powproof · cited by 503
- PowerSeries.coeffproof · cited by 324
- PowerSeries.mapstatement and proof · cited by 82
- PowerSeries.extproof · cited by 69
- PowerSeries.rescalestatement · cited by 23
- PowerSeries.coeff_rescaleproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.rescale_algebraMap_mapproof · cited by 0