isNonneg_iff — Mathlib

English

The sum of two nonnegative bilinear forms is nonnegative (alternate formulation).

Русский

Сумма двух неотрицательных билинейных форм неотрицательна (вариант формулировки).

LaTeX

$$B.IsNonneg → C.IsNonneg → (B + C).IsNonneg$$

Lean4

/-- A bilinear form is nonnegative if and only if it is nonnegative as a sesquilinear form. -/
theorem isNonneg_iff [LE R] {B : BilinForm R M} : B.IsNonneg ↔ LinearMap.IsNonneg B :=
  isNonneg_def.trans LinearMap.isNonneg_def.symm

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