Theorems · Theorem · ring theory
MonoidAlgebra.support_coeff_mul_single_subset
∀ {k : Type u₁} {G : Type u₂} [inst : Semiring k] [inst_1 : Mul G] [inst_2 : DecidableEq G] (x : MonoidAlgebra k G)
(r : k) (a : G), (x * MonoidAlgebra.single a r).coeff.support ⊆ Finset.image (fun x => x * a) x.coeff.support- Defined in
- Mathlib.Algebra.MonoidAlgebra.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 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.
Cites15
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 and proof · cited by 13,712
- Finsuppproof · cited by 5,255
- le_reflproof · cited by 2,061
- Finset.imagestatement and proof · cited by 910
- Finsupp.supportstatement and proof · cited by 828
- MonoidAlgebrastatement and proof · cited by 590
- le_imp_le_of_le_of_leproof · cited by 576
- mul_le_mul'proof · cited by 274
- MonoidAlgebra.singlestatement and proof · cited by 253
- MonoidAlgebra.coeffstatement and proof · cited by 224
- Finsupp.support_single_subsetproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- MonoidAlgebra.support_coeff_mul_single_eq_imageproof · cited by 2