ofBoolAlg_sdiff — Mathlib

English

The image under ofBoolAlg of the symmetric difference a ∆ b equals the sum of images: ofBoolAlg(a ∆ b) = ofBoolAlg(a) + ofBoolAlg(b).

Русский

Образ симметрической разности через ofBoolAlg равен сумме образов: ofBoolAlg(a ∆ b) = ofBoolAlg(a) + ofBoolAlg(b).

LaTeX

$$$\mathrm{ofBoolAlg}(a \Delta b) = \mathrm{ofBoolAlg}(a) + \mathrm{ofBoolAlg}(b)$$$

Lean4

@[simp]
theorem ofBoolAlg_sdiff (a b : AsBoolAlg α) : ofBoolAlg (a \ b) = ofBoolAlg a * (1 + ofBoolAlg b) :=
  rfl

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