Theorems · Theorem · commutative algebra
EuclideanDomain.div_self
∀ {R : Type u} [inst : EuclideanDomain R] {a : R}, a ≠ 0 → a / a = 1- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_right₀proof · cited by 70
Cited by10
Results whose statement or proof uses this declaration.
- RatFunc.num_zeroproof · cited by 5
- RatFunc.num_algebraMapproof · cited by 4
- RatFunc.denom_algebraMapproof · cited by 4
- RatFunc.denom_zeroproof · cited by 3
- Polynomial.isIntegral_of_mahlerMeasure_eq_oneproof · cited by 2
- RatFunc.num_oneproof · cited by 2
- RatFunc.denom_oneproof · cited by 2
- RatFunc.numDenom_divproof · cited by 1
- EuclideanDomain.div_powproof · cited by 0
- jacobiSym.at_fourproof · cited by 0