theorem
  x in dom h implies <*f,g,h*>..(3,x) = h.x
proof
A1: dom <*f,g,h*> = Seg 3 by FINSEQ_1:89;
  <*f,g,h*>.3 = h & 3 in Seg 3 by Th1,ENUMSET1:def 1;
  hence thesis by A1,FUNCT_5:38;
end;
