OK, let me point out something else. This friend of mine just checked up what you did and said something like "oh yes, I had already thought THAT, but I have a feeling that there is something wrong lurking in there." Since he's not comfortable with all this at 100% (and I'm getting tired of writing on his behalf!) Do you have any references where he can strive to get confident about what you just did? Yours and yours alone are this well earned 15 points! Cheers.

Sure, an inflator in a frame $F$ is a function $d:F\rightarrow F$ such that $d$ is order preserving and inflatory, this meaning that $a\leq d(a)$ holds for all $a\in F$.