reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;

theorem Th42:
  x in rng p & n = len p - x..p implies dom(p |-- x) = Seg n
proof
  assume x in rng p;
  then len(p |-- x) = len p - x..p by Def6;
  hence thesis by FINSEQ_1:def 3;
end;
