Theorems · Theorem · ring theory
MonoidAlgebra.support_coeff_mul_subset
∀ {k : Type u₁} {G : Type u₂} [inst : Semiring k] [inst_1 : Mul G] [inst_2 : DecidableEq G] (x y : MonoidAlgebra k G),
(x * y).coeff.support ⊆ x.coeff.support * y.coeff.support- Defined in
- Mathlib.Algebra.MonoidAlgebra.Support
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulDecidableEq
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
- MonoidAlgebrastatement and proof · cited by 590
- le_imp_le_of_le_of_leproof · cited by 576
- Finsupp.sumproof · cited by 481
- MonoidAlgebra.singleproof · cited by 253
- MonoidAlgebra.coeffstatement and proof · cited by 224
- Finset.mulstatement · cited by 155
- Finset.singleton_subset_iffproof · cited by 38
Cited by3
Results whose statement or proof uses this declaration.
- MonoidAlgebra.support_coeff_single_mul_subsetproof · cited by 1
- MonoidAlgebra.support_coeff_mul_single_subsetproof · cited by 1
- MonoidAlgebra.support_single_mul_eq_imageproof · cited by 0