theorem
  c in dom f & f1 = f \/ g implies f1/.c = f/.c
proof
  assume that
A1: c in dom f and
A2: f1 = f \/ g;
  [c,(f qua Function).c] in f by A1,FUNCT_1:1;
  then [c,(f qua Function).c] in f1 by A2,XBOOLE_0:def 3;
  then
A3: c in dom f1 by FUNCT_1:1;
  (f1 qua Function).c = (f qua Function).c by A1,A2,GRFUNC_1:15;
  then f1/.c = (f qua Function).c by A3,PARTFUN1:def 6;
  hence thesis by A1,PARTFUN1:def 6;
end;
