
theorem Th15:
  for D being non empty set,f,g being FinSequence of D
  holds len ovlcon(f,g)=len f+len g -len ovlpart(f,g) &
  len ovlcon(f,g)=len f+len g -'len ovlpart(f,g) &
  len ovlcon(f,g)=len f+(len g -'len ovlpart(f,g))
proof
  let D be non empty set,f,g be FinSequence of D;
A1: len ovlpart(f,g) <= len g by Def2;
A2: len ovlcon(f,g)=len f +len (g/^(len ovlpart(f,g))) by FINSEQ_1:22
    .=len f+(len g-'len ovlpart(f,g)) by RFINSEQ:29
    .=len f+(len g -len ovlpart(f,g)) by A1,XREAL_1:233;
  hence
A3: len ovlcon(f,g)=len f+len g -len ovlpart(f,g);
A4: len ovlpart(f,g)<=len g by Def2;
  hence len ovlcon(f,g)
  =len f+len g -'len ovlpart(f,g) by A3,NAT_1:12,XREAL_1:233;
  thus thesis by A2,A4,XREAL_1:233;
end;
