Theorems · Theorem · field theory
RatFunc.intDegree_mul
∀ {K : Type u} [inst : Field K] {x y : RatFunc K}, x ≠ 0 → y ≠ 0 → (x * y).intDegree = x.intDegree + y.intDegree- Defined in
- Mathlib.FieldTheory.RatFunc.Degree
- Cited by
- 3 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- RatFuncstatement and proof · cited by 301
- mul_ne_zeroproof · cited by 178
- RatFunc.denomproof · cited by 59
- sub_subproof · cited by 54
- sub_addproof · cited by 51
- RatFunc.numproof · cited by 49
- Polynomial.natDegree_mulproof · cited by 23
- add_subproof · cited by 21
- RatFunc.denom_ne_zeroproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.InftyValuation.map_mul'proof · cited by 1
- RatFunc.intDegree_divproof · cited by 1
- RatFunc.intDegree_invproof · cited by 1