expect_ne_zero_iff_eq_zero — Mathlib

English

The inner product wInner with cWeight yields 1 if ψ1 = ψ2 and 0 otherwise; i.e., a Boole-like property.

Русский

Внутреннее произведение wInner с cWeight равно 1, если ψ1 = ψ2, иначе 0.

LaTeX

$$$⟪\\psi_1, \\psi_2⟫_{R}^{\\text{cWeight}} = \\begin{cases} 1, & \\psi_1 = \\psi_2, \\\\ 0, & \\psi_1 \\neq \\psi_2. \\end{cases}$$$

Lean4

theorem expect_ne_zero_iff_eq_zero : 𝔼 x, ψ x ≠ 0 ↔ ψ = 0 :=
  expect_eq_zero_iff_ne_zero.not_left

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