at any rate = at any case

[vil]

Dear teachers,

Would you be kind enough to tell me whether I am right with my interpretation of the expression in bold in the following sentences?

"At any rate I do wash my face," said Polly,

It isn't much of a car, but at any rate it was not expensive.

at any rate = in any event, whatever the case may be; also, at least = at any case

Thank you for your efforts.

Regards,

V.

[Tdol]

In those two, the meaning is at least IMO.