
theorem Th74:
  for X being non empty set for R being Relation of X for x be
  Element of X, y being set st R reduces x,y holds y in X
proof
  let X be non empty set;
  let R be Relation of X;
  let x be Element of X, y be set;
  given p being RedSequence of R such that
A1: p.1 = x and
A2: p.len p = y;
  len p >= 0+1 by NAT_1:13;
  then len p in dom p by FINSEQ_3:25;
  then
A3: y in rng p by A2,FUNCT_1:3;
  p is FinSequence of X by A1,Th73;
  then rng p c= X by FINSEQ_1:def 4;
  hence thesis by A3;
end;
