theorem
  (SC --> d)|SC is constant
proof
  take d;
  let c;
  assume
A1: c in dom((SC --> d)|SC);
  then
A2: c in SC /\ dom (SC --> d) by RELAT_1:61;
  then c in SC by XBOOLE_0:def 4;
  then (SC --> d)/.c = d by Th29;
  then ((SC --> d)|SC)/.c = d by A2,Th16;
  hence thesis by A1,PARTFUN1:def 6;
end;
