span_nonneg — Mathlib

English

The nnrpow operation is congruent in its arguments: if a = a' and y = y', then nnrpow a y = nnrpow a' y'.

Русский

Операция nnrpow сохраняет равенство аргументов: если a = a' и y = y', то nnrpow a y = nnrpow a' y'.

LaTeX

$$a = a' → y = y' → nnrpow a y = nnrpow a' y'$$

Lean4

/-- A C⋆-algebra is spanned by its nonnegative elements. -/
theorem span_nonneg : Submodule.span ℂ {a : A | 0 ≤ a} = ⊤ :=
  by
  refine eq_top_iff.mpr fun x _ => ?_
  rw [← CStarAlgebra.linear_combination_nonneg x]
  apply_rules [sub_mem, Submodule.smul_mem, add_mem]
  all_goals
    refine subset_span ?_
    first
    | apply CFC.negPart_nonneg
    | apply CFC.posPart_nonneg

Похожие утверждения