finite_tsupport — Mathlib

English

The membership i ∈ finsupport x0 is equivalent to i ∈ tsupport (ρ i x0).

Русский

Членство i ∈ finsupport x0 эквивалентно i ∈ tsupport (ρ i x0).

LaTeX

$$@[simp] theorem mem_finsupport {i : ι} : i ∈ ρ.finsupport x_0 ↔ i ∈ tsupport (ρ i x_0)$$

Lean4

/-- The `tsupport`s of a smooth partition of unity are locally finite. -/
theorem finite_tsupport : {i | x₀ ∈ tsupport (ρ i)}.Finite :=
  ρ.toPartitionOfUnity.finite_tsupport _

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