This follows from the invariance theorem applied to a machine that copies the input (which is delimited with a blank) to the worktape and halts.
This follows from a machine that works like but which starts out by erasing the given string from its worktape.
This follows from a machine that expects an input of the form , where is a selfdelimiting program for and a selfdelimiting program to compute given . After simulating to obtain on its worktype, it continues to simulate again, thus obtaining .
This follows from a machine which uses a given number to copy bits from input to its worktape.
