prove_abs_fn_one_one : thm -> thm
|- (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r))then prove_abs_fn_one_one th proves from this theorem that the function abs is one-to-one for values that satisfy P, returning the theorem:
|- !r r'. P r ==> P r' ==> ((abs r = abs r') = (r = r'))