theorem Th24:
  i in dom F & v = F.i implies (f (#) F).i = f.v * v
proof
  assume that
A1: i in dom F and
A2: v = F.i;
A3: F/.i = F.i by A1,PARTFUN1:def 6;
  len(f (#) F) = len F by Def7;
  then i in dom(f (#) F) by A1,FINSEQ_3:29;
  hence thesis by A2,A3,Def7;
end;
