theorem Th49:
  x = y implies v.(x|a).y = a
proof
  assume
A1: x = y;
  then y in {x} by TARSKI:def 1;
  then
A2: y in dom (x .--> a);
  (x .--> a).y = a by A1,FUNCOP_1:72;
  hence thesis by A2,FUNCT_4:13;
end;
