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;
reserve f for Function of A,B;

theorem
  for E being non empty set, p,q being FinSequence of E st k in dom p
  holds (p ^ q)/.k = p/.k
proof
  let E be non empty set, p,q be FinSequence of E;
  assume
A1: k in dom p;
  then k in dom(p ^ q) by FINSEQ_3:22;
  hence (p ^ q)/.k = (p ^ q).k by PARTFUN1:def 6
    .= p.k by A1,FINSEQ_1:def 7
    .= p/.k by A1,PARTFUN1:def 6;
end;
