hello codeforces, I have been trying to learn about splay trees from this.In the analysis of alternate implementations insertion and deletion it has been mentioned that this follows from a modification of the proof of lemma 1(Access lemma).

I could find proofs for this when all weights are taken as 1 for example here

but i could'nt find one for the general weighted case nor can prove it myself. so can anyone please help ? thanks!