To make your proof easier to comprehend I recommend you insert a few more steps.
If you insert an object into something, you put the object inside it. He took a small key from his pocket and slowly inserted it into the lock Wait for a couple of minutes with your mouth closed before inserting the thermometer. + insertion insertions in·ser·tion the first experiment involving the insertion of a new gene into a human being
(1) In stripping, a section of film carrying printing detail that is spliced into a larger piece of film; also called Strip-in or Set-in (2) In printing, a page, etc , that is printed separately and then placed into or bound with the main publication (3) In typesetting, copy to be added to top
Key on a keyboard or function of word processing software that is used to insert text without deleting previously keyed text (Kybdy, Gr 1)
an artifact that is inserted or is to be inserted a folded section placed between the leaves of another publication introduce; "Insert your ticket here"
A piece of material, usually metal, which is placed in a die before each shot When molten metal is cast around it, it becomes an integral part of the die casting
If you insert a comment into a piece of writing or a speech, you include it. They joined with the monarchists to insert a clause calling for a popular vote on the issue. + insertion in·ser·tion He recorded an item for insertion in the programme
(film) a still picture that is inserted and that interrupts the action of a film
A port or connection on an audio mixer that gives the ability to take an audio signal from one channel of the mixer, process it in some way, and feed the signal back into the same channel of the mixer This new signal may then be mixed in with other signals in the mixer
1) A punch in of the all of the tracks being recorded in a recording session 2) On Solid State Logic consoles, placing an outboard piece of gear in the channel by patching and activating a switch