
theorem Th4:
  for f being Function, x being object st x in dom f
  holds (commute <*f*>).x = <*f.x*>
proof
  let f be Function, x be object;
  assume A1: x in dom f;
  thus (commute <*f*>).x = (commute{[1,f]}).x by FINSEQ_1:def 5
   .= (commute(1 .--> f)).x by FUNCT_4:82
   .= 1 .--> f.x by A1, TOPGEN_5:3
   .= {[1,f.x]} by FUNCT_4:82
   .= <*f.x*> by FINSEQ_1:def 5;
end;
