
theorem Th46:
  for a, b being Ordinal holds b -exponent <% a %> = <% b -exponent a %>
proof
  let a, b be Ordinal;
  A1: dom(b -exponent <% a %>) = dom <% a %> by Def1
    .= 1 by AFINSQ_1:def 4;
  0 in 1 by TARSKI:def 1, CARD_1:49;
  then 0 in dom <% a %> by AFINSQ_1:def 4;
  then (b -exponent <% a %>).0 = b -exponent(<% a %>.0) by Def1
    .= b -exponent a;
  hence thesis by A1, AFINSQ_1:def 4;
end;
