Theorems · Theorem · ring theory
AddMonoidAlgebra.support_coeff_mul_subset
∀ {k : Type u₁} {G : Type u₂} [inst : Semiring k] [inst_1 : Add G] [inst_2 : DecidableEq G]
(x y : AddMonoidAlgebra k G), (x * y).coeff.support ⊆ x.coeff.support + y.coeff.support- Defined in
- Mathlib.Algebra.MonoidAlgebra.Support
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- LE.le.transproof · cited by 3,151
- le_reflproof · cited by 2,061
- Finsupp.supportstatement and proof · cited by 828
- AddMonoidAlgebrastatement and proof · cited by 649
- le_imp_le_of_le_of_leproof · cited by 576
- Finsupp.sumproof · cited by 481
- AddMonoidAlgebra.coeffstatement and proof · cited by 365
- AddMonoidAlgebra.singleproof · cited by 250
- Finset.addstatement · cited by 133
- Finset.singleton_subset_iffproof · cited by 38
Cited by5
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.sup_support_coeff_mul_leproof · cited by 5
- MvPolynomial.support_mulproof · cited by 1
- AddMonoidAlgebra.support_coeff_mul_single_subsetproof · cited by 1
- AddMonoidAlgebra.support_coeff_single_mul_subsetproof · cited by 1
- Polynomial.card_support_mul_leproof · cited by 1