reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem Th72:
  i in dom(f|n) implies (Ins(f,n,p)).i = f.i
proof
  assume
A1: i in dom(f|n);
  thus (Ins(f,n,p)).i = ((f|n)^(<*p*>^(f/^n))).i by FINSEQ_1:32
    .= (f|n).i by A1,Lm1
    .= f.i by A1,FUNCT_1:47;
end;
