
theorem
  for f being Function, x being object st x in dom f
  holds (uncurry <*f*>).(1,x) = f.x
proof
  let f be Function, x be object;
  assume A1: x in dom f;
  len <*f*> = 1 by FINSEQ_1:40;
  then A2: 1 in dom <*f*> by FINSEQ_3:25;
  <*f*>.1 = f;
  hence thesis by A1, A2, FUNCT_5:38;
end;
