Theorems · Theorem · field theory
RatFunc.natDegree_num_mul_right_sub_natDegree_denom_mul_left_eq_intDegree
∀ {K : Type u} [inst : Field K] {x : RatFunc K},
x ≠ 0 → ∀ {s : Polynomial K}, s ≠ 0 → ↑(x.num * s).natDegree - ↑(s * x.denom).natDegree = x.intDegree- Defined in
- Mathlib.FieldTheory.RatFunc.Degree
- 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.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- mul_assocproof · cited by 1,667
- Polynomial.natDegreestatement · cited by 1,105
- RatFuncstatement and proof · cited by 301
- mul_ne_zeroproof · cited by 178
- RatFunc.denomstatement and proof · cited by 59
- RatFunc.numstatement and proof · cited by 49
- RatFunc.denom_ne_zeroproof · cited by 20
- RatFunc.intDegreestatement · cited by 18
- RatFunc.num_ne_zeroproof · cited by 9
- Polynomial.natDegree_sub_eq_of_prod_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.intDegree_add_leproof · cited by 1