reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;

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 Nat;
  take k;
  thus thesis by A1,A2,FUNCT_1:1;
end;
