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Theorems · Theorem · commutative algebra

IsRelPrime.pow_left_iff

∀ {α : Type u_1} [inst : CommMonoid α] [DecompositionMonoid α] {x y : α} {m : ℕ},
  0 < m → (IsRelPrime (x ^ m) y ↔ IsRelPrime x y)
Defined in
Mathlib.RingTheory.Coprime.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidDecompositionMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsRelPrime.pow_right_iff · cited by 1IsRelPrime.pow_right_iffIsRelPrime.pow_iff · cited by 0IsRelPrime.pow_iffCommMonoid · cited by 2264CommMonoidFinset.prod_const · cited by 154Finset.prod_constFinset.mem_range · cited by 140Finset.mem_rangeIsRelPrime · cited by 136IsRelPrimeFinset.card_range · cited by 108Finset.card_rangeDecompositionMonoid · cited by 39DecompositionMonoidIsRelPrime.pow_left · cited by 2IsRelPrime.pow_leftIsRelPrime.of_prod_left · cited by 1IsRelPrime.of_prod_leftIsRelPrime.pow_left_iffCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.