theorem
  [c,e] in (s*f) implies [c,f/.c] in f & [f/.c,e] in s
proof
  assume
A1: [c,e] in (s*f);
  then
A2: [(f qua Function).c,e] in s by GRFUNC_1:4;
A3: [c,(f qua Function).c] in f by A1,GRFUNC_1:4;
  then c in dom f by FUNCT_1:1;
  hence thesis by A3,A2,PARTFUN1:def 6;
end;
