Theorems · Theorem · ring theory

MonoidAlgebra.mem_smulAntidiagonal_of_group

∀ {G : Type u_1} {P : Type u_2} {R : Type u_3} {V : Type u_4} [inst : Group G] [inst_1 : MulAction G P]
  [inst_2 : Semiring R] [inst_3 : Zero V] (f : MonoidAlgebra R G) (x : P → V) (p : P) (gh : G × P),
  gh ∈ Finset.SMulAntidiagonal p ⋯ ↔ f.coeff gh.1 ≠ 0 ∧ x gh.2 ≠ 0 ∧ gh.2 = gh.1⁻¹ • p

Defined in

Mathlib.Algebra.MonoidAlgebra.PointwiseSMul

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionSemiringZero