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Theorems · Theorem · commutative algebra

IsRelPrime.pow_left

∀ {α : Type u_1} [inst : CommMonoid α] [DecompositionMonoid α] {x y : α} {m : ℕ}, IsRelPrime x y → IsRelPrime (x ^ m) y
Defined in
Mathlib.RingTheory.Coprime.Lemmas
Cited by
2 results in Mathlib
Foundations
Depth 62 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_left_iff · cited by 2IsRelPrime.pow_left_iffIsRelPrime.pow · cited by 0IsRelPrime.powCommMonoid · cited by 2264CommMonoidFinset.range · cited by 1341Finset.rangeFinset.prod_const · cited by 154Finset.prod_constIsRelPrime · cited by 136IsRelPrimeFinset.card_range · cited by 108Finset.card_rangeDecompositionMonoid · cited by 39DecompositionMonoidIsRelPrime.prod_left · cited by 2IsRelPrime.prod_leftIsRelPrime.pow_leftCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.