Theorems · Theorem · commutative algebra
DividedPowers.OfInvertibleFactorial.dpow_one
∀ {A : Type u_1} [inst : CommSemiring A] {I : Ideal A} [inst_1 : DecidablePred fun x => x ∈ I] {x : A},
x ∈ I → DividedPowers.OfInvertibleFactorial.dpow I 1 x = x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- pow_oneproof · cited by 894
- Ring.inverseproof · cited by 160
- DividedPowers.OfInvertibleFactorial.dpowstatement · cited by 14
- DividedPowers.OfInvertibleFactorial.dpow_eq_of_memproof · cited by 10
- Ring.inverse_oneproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- DividedPowers.RatAlgebra.dividedPowersproof · cited by 2
- DividedPowers.OfInvertibleFactorial.dividedPowersproof · cited by 2