Theorems · Theorem · group theory
Ring.inverse_pow_mul_eq_iff_eq_mul
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {a : M₀} (b c : M₀),
IsUnit a → ∀ {k : ℕ}, Ring.inverse a ^ k * b = c ↔ b = a ^ k * c- Defined in
- Mathlib.Algebra.GroupWithZero.Commute
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- MonoidWithZerostatement and proof · cited by 456
- Ring.inversestatement · cited by 160
- IsUnit.powproof · cited by 48
- Ring.inverse_mul_eq_iff_eq_mulproof · cited by 6
- Ring.inverse_powproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- DividedPowers.OfInvertibleFactorial.dpow_comp_of_mul_ltproof · cited by 1