Theorems · Theorem · field theory
RatFunc.num_inv_dvd
∀ {K : Type u} [inst : Field K] {x : RatFunc K}, x ≠ 0 → x⁻¹.num ∣ x.denom- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- RatFuncstatement and proof · cited by 301
- inv_divproof · cited by 92
- RatFunc.denomstatement and proof · cited by 59
- RatFunc.numstatement and proof · cited by 49
- RatFunc.denom_ne_zeroproof · cited by 20
- RatFunc.num_div_denomproof · cited by 18
- RatFunc.num_ne_zeroproof · cited by 9
- RatFunc.num_dvdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.associated_num_invproof · cited by 1