Theorems · Theorem · commutative algebra
factorPowSucc.isUnit_of_isUnit_image
∀ {R : Type u_3} [inst : CommRing R] {I : Ideal R} {n : ℕ},
n > 0 → ∀ {a : R ⧸ I ^ (n + 1)}, IsUnit ((Ideal.Quotient.factorPow I ⋯) a) → IsUnit a- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites29
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
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- HasQuotient.Quotientstatement and proof · cited by 2,301
- IsUnitstatement and proof · cited by 1,602
- map_mulproof · cited by 1,137
- map_oneproof · cited by 861
- Ideal.Quotient.mkproof · cited by 610
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