theorem
  f/.1 = N-max L~f & N-max L~f <> E-max L~f implies (N-max L~f)..f < (
  E-max L~f)..f
proof
  assume that
A1: f/.1 = N-max L~f and
A2: N-max L~f <> E-max L~f;
A3: E-max L~f in rng f by SPRECT_2:46;
  then (E-max L~f)..f in dom f by FINSEQ_4:20;
  then
A4: (E-max L~f)..f >= 1 by FINSEQ_3:25;
  N-max L~f in rng f & (N-max L~f)..f = 1 by A1,FINSEQ_6:43,SPRECT_2:40;
  hence thesis by A3,A2,A4,FINSEQ_5:9,XXREAL_0:1;
end;
