Theorems · Theorem · commutative algebra
LaurentSeries.valuation_X_pow
∀ (K : Type u_2) [inst : Field K] (s : ℕ), Valued.v ((HahnSeries.ofPowerSeries ℤ K) PowerSeries.X ^ s) = WithZero.exp (-↑s)
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Multiplicativestatement and proof · cited by 875
- Valuationstatement and proof · cited by 823
- PowerSeriesstatement and proof · cited by 797
- WithZerostatement and proof · cited by 586
- HahnSeriesstatement · cited by 528
- map_powproof · cited by 503
- PowerSeries.Xstatement and proof · cited by 183
- smul_negproof · cited by 181
- Valued.vstatement and proof · cited by 163
Cited by3
Results whose statement or proof uses this declaration.
- LaurentSeries.valuation_single_zpowproof · cited by 3
- LaurentSeries.coeff_zero_of_lt_valuationproof · cited by 2
- LaurentSeries.exists_ratFunc_val_ltproof · cited by 1