Theorems · Theorem · commutative algebra
PowerSeries.map_constantCoeff_le_self_of_X_mem
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal (PowerSeries R)},
PowerSeries.X ∈ I → Ideal.map (PowerSeries.C.comp PowerSeries.constantCoeff) I ≤ I- Defined in
- Mathlib.RingTheory.PowerSeries.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- RingHom.compstatement · cited by 899
- PowerSeriesstatement and proof · cited by 797
- Ideal.mapstatement · cited by 692
- PowerSeries.coeffproof · cited by 324
- PowerSeries.Xstatement and proof · cited by 183
- PowerSeries.constantCoeffstatement and proof · cited by 126
- PowerSeries.Cstatement and proof · cited by 76
- Ideal.mul_mem_rightproof · cited by 71
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