The shortest path distance from v to t in Rf is non-decreasing.
Consider first time SP (in residual graph) to t decreases from some node v. Let v be the closest such node to t. SP in f’ from v to t begins with edge (v,w)
Claim: f(v,w)=c(v,w). If not (v,w) in Rf
d(v) <= d(w)+1 <= d’(w)+1 = d’(v). Contradiction.