Order of command substitution and arithmetic expansion

[Dongbo Hu]

The Bash reference manual claims that of the seven kinds of shell
expansions, "arithmetic expansion" is done before "command substitution":
https://www.gnu.org/software/bash/manual/bash.html#Shell-Expansions
Quote: "The order of expansions is: brace expansion; tilde expansion,
parameter and variable expansion, arithmetic expansion, and command
substitution (done in a left-to-right fashion) ..."

But I feel that "arithmetic expansion" is done AFTER "command substitution".

If the manual is correct, it would make more sense to cover "arithmetic
expansion" before "command substitution" in the manual.