Theorems · Theorem · commutative algebra
selfZPow_of_neg
∀ {R : Type u_1} [inst : CommSemiring R] (x : R) (B : Type u_2) [inst_1 : CommSemiring B] [inst_2 : Algebra R B]
[inst_3 : IsLocalization.Away x B] {n : ℤ}, n < 0 → selfZPow x B n = IsLocalization.mk' B 1 (Submonoid.pow x n.natAbs)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submonoid.powersstatement · cited by 408
- LT.lt.not_geproof · cited by 305
- IsLocalization.mk'statement · cited by 218
- IsLocalization.Awaystatement and proof · cited by 218
- selfZPowstatement · cited by 14
- Submonoid.powstatement · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- selfZPow_of_nonposproof · cited by 2
- selfZPow_addproof · cited by 1