theorem Th63:
  for X being set st X c= bound_QC-variables(Al) holds dom (v|X) = dom
  (v.(x|a)|X) & dom (v|X) = X
proof
  let X be set;
A1: dom (v.(x|a)|X) = dom (v.(x|a)) /\ X by RELAT_1:61;
  dom (v|X) = dom v /\ X by RELAT_1:61;
  then
A2: dom (v|X) = bound_QC-variables(Al) /\ X by Th58;
  assume X c= bound_QC-variables(Al);
  hence thesis by A2,A1,Th58,XBOOLE_1:28;
end;
