theorem
  (f +* (x .-->y)).x = y
proof
A1: x in {x} by TARSKI:def 1;
  then dom(x .--> y) = {x} & x in dom f \/ {x} by XBOOLE_0:def 3;
 hence (f +* (x .-->y) ).x = (x .-->y).x by A1,Def1
    .= y by FUNCOP_1:72;
end;
