I need to run a sub panel box right next to the main panel box to add am40 amp double pole breaker for a range.

I have seen where u can use say a 60 amp breaker and have the wiring coming from the breaker into the subpanel.

Here’s my main question. The main panel has 2’large lugs
To receive the main feeds. However the feed or line wires are not attached to them but rather a large double pole breaker that covers
Both buses. When I turn the breaker off the lugs
Also lose power since the power is coming into box thru the breaker.
So could I just tap into the lugs and go into my sub panel that way since it is protected by the main breaker.