reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;

theorem
  z in p implies ex k st k in dom p & z=[k,p.k]
proof
  assume
A1: z in p;
  then consider x,y being object such that
A2: z=[x,y] by RELAT_1:def 1;
  x in dom p by A1,A2,FUNCT_1:1;
  then reconsider k = x as Element of NAT;
  take k;
  thus thesis by A1,A2,FUNCT_1:1;
end;
