Theorems · Theorem · commutative algebra
right_div_gcd_ne_zero
∀ {R : Type u_1} [inst : EuclideanDomain R] [inst_1 : GCDMonoid R] {p q : R}, q ≠ 0 → q / gcd p q ≠ 0- Defined in
- Mathlib.RingTheory.EuclideanDomain
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomainGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- GCDMonoid.gcdstatement and proof · cited by 143
- EuclideanDomainstatement and proof · cited by 124
- GCDMonoidstatement and proof · cited by 96
- mul_div_cancel_right₀proof · cited by 70
- mul_ne_zero_iffproof · cited by 39
- GCDMonoid.gcd_dvd_rightproof · cited by 34
Cited by5
Results whose statement or proof uses this declaration.
- RatFunc.num_div_denomproof · cited by 18
- RatFunc.num_div_dvdproof · cited by 2
- RatFunc.denom_div_dvdproof · cited by 1
- RatFunc.isCoprime_num_denomproof · cited by 1
- RatFunc.monic_denomproof · cited by 1