toList_cons — Mathlib

English

The toList' of cons equals the think of the map of toList by List.cons.

Русский

toList' для cons равен think от отображения List.cons к toList.

LaTeX

$$$$toList(\mathrm{cons}\ a\ s) = \mathrm{think}\left( \mathrm{map}(\mathrm{List}.cons\ a) (toList\, s) \right).$$$$

Lean4

@[simp]
theorem toList_cons (a : α) (s) : toList (cons a s) = (List.cons a <$> toList s).think :=
  destruct_eq_think <| by
    unfold toList
    simp only [toList'_cons, Computation.destruct_think, Sum.inr.injEq]
    rw [toList'_map]
    simp only [List.reverse_cons, List.reverse_nil, List.nil_append, List.singleton_append]
    rfl

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