diracProba_comp_diracProbaEquiv_symm_eq_val

English

The composition of diracProba with the symmetric part of diracProbaEquiv equals the projection to the value component.

Русский

Компоновка diracProba с симметричной частью diracProbaEquiv равна проекции на значение узла.

LaTeX

$$$\\mathrm{diracProba} \\circ (\\mathrm{diracProbaEquiv})^{-1} = \\lambda \\mu. \\mu^{\\text{val}}$$$

Lean4

/-- The composition of `diracProbaEquiv.symm` and `diracProba` is the subtype inclusion. -/
theorem diracProba_comp_diracProbaEquiv_symm_eq_val [T0Space X] :
    diracProba ∘ (diracProbaEquiv (X := X)).symm = fun μ ↦ μ.val := by funext μ; simp [diracProbaEquiv]

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