Theorems · Theorem · ring theory
AddMonoidAlgebra.leadingCoeff_eq_zero
∀ {R : Type u_1} {A : Type u_3} {B : Type u_5} [inst : Semiring R] [inst_1 : LinearOrder B] [inst_2 : OrderBot B]
{p : AddMonoidAlgebra R A} {D : A → B} [inst_3 : AddZeroClass A],
Function.Injective D → (AddMonoidAlgebra.leadingCoeff D p = 0 ↔ p = 0)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- AddZeroClassstatement and proof · cited by 1,237
- OrderBotstatement and proof · cited by 1,055
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
- Finsupp.mem_support_iffproof · cited by 89
- Function.invFunproof · cited by 60
- AddMonoidAlgebra.supDegreeproof · cited by 49
- AddMonoidAlgebra.leadingCoeffstatement · cited by 23
- Function.mtrproof · cited by 12
Cited by9
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_leftproof · cited by 4
- MvPolynomial.esymmAlgHom_fin_injectiveproof · cited by 2
- MvPolynomial.supDegree_esymmAlgHomMonomialproof · cited by 2
- AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_rightproof · cited by 1
- MvPolynomial.esymmAlgHom_fin_bijectiveproof · cited by 1
- MvPolynomial.IsSymmetric.antitone_supDegreeproof · cited by 1
- AddMonoidAlgebra.supDegree_sub_lt_of_leadingCoeff_eqproof · cited by 1
- AddMonoidAlgebra.leadingCoeff_mulproof · cited by 0
- AddMonoidAlgebra.leadingCoeff_ne_zeroproof · cited by 0