reserve U1,U2,U3 for Universal_Algebra,
  m,n for Nat,
  a for set,
  A for non empty set,
  h for Function of U1,U2;

theorem
  for g be Function, a be Element of A for k be Nat st 1 <= k & k <= n
  holds (a .--> g).((n |-> a)/.k) = g
proof
  let g be Function;
  let a be Element of A;
  let k be Nat;
  assume 1 <= k & k <= n;
  then
A1: k in Seg n by FINSEQ_1:1;
  then k in dom (n |-> a);
  then (n |-> a)/.k = (n |-> a).k by PARTFUN1:def 6
    .= a by A1,FUNCOP_1:7;
  hence thesis by FUNCOP_1:72;
end;
