Theorems · Theorem · commutative algebra
selfZPow_neg_natCast
∀ {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] (d : ℕ), selfZPow x B (-↑d) = IsLocalization.mk' B 1 (Submonoid.pow x d)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsLocalization.mk'statement and proof · cited by 218
- IsLocalization.Awaystatement and proof · cited by 218
- neg_nonposproof · cited by 31
- selfZPowstatement · cited by 14
- Submonoid.powstatement and proof · cited by 13
- IsLocalization.mk'.congr_simpproof · cited by 12
- selfZPow_of_nonposproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- selfZPow_sub_natCastproof · cited by 1