Theorems · Theorem · field theory

Polynomial.natDegree_cancelLeads_lt_of_natDegree_le_natDegree_of_comm

∀ {R : Type u_1} [inst : Ring R] {p q : Polynomial R},
  p.leadingCoeff * q.leadingCoeff = q.leadingCoeff * p.leadingCoeff →
    p.natDegree ≤ q.natDegree → 0 < q.natDegree → (p.cancelLeads q).natDegree < q.natDegree

Defined in: Mathlib.Algebra.Polynomial.CancelLeads
Cited by: 1 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring

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Cites42

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Ringstatement and proof · cited by 7,463
Polynomialstatement and proof · cited by 5,681
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zero_addproof · cited by 2,366
MulZeroClass.mul_zeroproof · cited by 2,091
le_reflproof · cited by 2,061
mul_assocproof · cited by 1,667
Polynomial.Xproof · cited by 1,639
MulZeroClass.zero_mulproof · cited by 1,625
map_zeroproof · cited by 1,614
Polynomial.Cproof · cited by 1,598

Cited by1

Results whose statement or proof uses this declaration.

Polynomial.natDegree_cancelLeads_lt_of_natDegree_le_natDegreeproof · cited by 1