Theorems · Theorem · field theory
RatFunc.intDegree_div
∀ {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
- 1 results in Mathlib
- Foundations
- Depth 136 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.
Cites7
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
- sub_eq_add_negproof · cited by 1,023
- div_eq_mul_invproof · cited by 715
- RatFuncstatement and proof · cited by 301
- RatFunc.intDegreestatement and proof · cited by 18
- RatFunc.intDegree_mulproof · cited by 3
- RatFunc.intDegree_invproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_Xproof · cited by 1