Theorems · Theorem · ring theory
AddMonoidAlgebra.leadingCoeff_add_eq_left
∀ {R : Type u_1} {A : Type u_3} {B : Type u_5} [inst : Semiring R] [inst_1 : LinearOrder B] [inst_2 : OrderBot B]
{p q : AddMonoidAlgebra R A} {D : A → B} [inst_3 : AddZeroClass A],
AddMonoidAlgebra.supDegree D q < AddMonoidAlgebra.supDegree D p →
AddMonoidAlgebra.leadingCoeff D (p + q) = AddMonoidAlgebra.leadingCoeff D p- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 2 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.
Cites20
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
- Finsuppproof · cited by 5,255
- add_zeroproof · cited by 2,707
- 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
- LT.lt.not_geproof · cited by 305
- Function.invFunproof · cited by 60
- AddMonoidAlgebra.supDegreestatement and proof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.supDegree_leadingCoeff_sum_eqproof · cited by 1
- AddMonoidAlgebra.leadingCoeff_add_eq_rightproof · cited by 0