support_eq_empty — Mathlib

English

For any p, p.support = ∅ iff p = 0; equivalently, p.support = ∅ ⇔ p = 0.

Русский

Для любого p: p.support = ∅ тогда и только тогда, когда p = 0; эквивалентно p.support = ∅ ⇔ p = 0.

LaTeX

$$$ p.\mathrm{support} = \emptyset \iff p = 0 $$$

Lean4

@[simp]
theorem support_eq_empty {p} : p.support = ∅ ↔ (p : SkewMonoidAlgebra k G) = 0 :=
  by
  rcases p
  simp only [support, Finsupp.support_eq_empty, ofFinsupp_eq_zero]

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