theorem
  f1 is total & f2 is total implies (f1+f2)/.c = (f1/.c) + (f2/.c) &
  (f1-f2)/.c = (f1/.c) - (f2/.c)
proof
  assume
A1: f1 is total & f2 is total;
  then dom (f1+f2) = C by PARTFUN1:def 2;
  hence (f1+f2)/.c = (f1/.c) + (f2/.c) by Def1;
  dom (f1-f2) = C by A1,PARTFUN1:def 2;
  hence thesis by Def2;
end;
