theorem Th84:
  for f being Function, a,b,c,d being object st a <> b holds
  (f +* ((a,b)-->(c,d))) .a = c & (f +* ((a,b)-->(c,d))) .b = d
proof
  let f be Function, a,b,c,d be object such that
A1: a <> b;
  set g = (a,b)-->(c,d);
A2: dom g = {a,b} by Th62;
  then a in dom g by TARSKI:def 2;
  hence (f +* g).a = g.a by Th13
    .= c by A1,Th63;
  b in dom g by A2,TARSKI:def 2;
  hence (f +* g).b = g.b by Th13
    .= d by Th63;
end;
