prod_def — Mathlib

English

The product of measures μ.prod ν equals μ.bind( x ↦ map(Prod.mk x) ν ).

Русский

Произведение мер μ.prod ν равно μ.bind( x ↦ map(Prod.mk x) ν ).

LaTeX

$$$\\mu.\\mathrm{prod}\\nu = \\mu \\mathrm{bind} (\\lambda x. \\mathrm{map}(\\mathrm{Prod.mk}\,x)\\nu)$$$

Lean4

theorem prod_def : eta_helper Eq✝ @prod.{} @(delta% @definition✝) :=
  by
  intros
  delta prod
  rw [show wrapped✝ = ⟨@definition✝.{}, rfl✝⟩ from Subtype.ext✝ wrapped✝.2.symm✝]
  rfl

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