Theorems · Theorem · field theory
Polynomial.mod_eq_self_iff
∀ {R : Type u} [inst : Field R] {p q : Polynomial R}, q ≠ 0 → (p % q = p ↔ p.degree < q.degree)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 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.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.leadingCoeffproof · cited by 498
- not_le_of_gtproof · cited by 97
- Polynomial.monic_mul_leadingCoeff_invproof · cited by 19
- Polynomial.divModByMonicAuxproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.div_eq_zero_iffproof · cited by 1