fact: Fixpoint seq_cut_up (s : seq (R*R)) (x : R) : seq (R*R) := match s with | [::] => [:: (x,x)] | h :: t => match Rle_dec (fst h) x with | right _ => (x,x)::(fst h,Rmax (snd h) x)::t | left _ => seq_cut_up t x end end.
imports: Coq(Reals Psatz ssreflect ssrbool) mathcomp(seq) Rcomplements Rbar Lub Hierarchy