What is the name of the rule which states:
Let be a function which such that for some . Given an equation:
by repeatedly apply to we get a series of equation:
I'm not aware of the rule you are referring to.
The rule of substitution?
For a general equality with free variable ,
means it is true for all values .
For convenience, since is a free variable, we can rename it to .
, now substitute for .
You can repeat this to show: