reserve c,c1,c2,x,y,z,z1,z2 for set;
reserve C1,C2,C3 for non empty set;

theorem Th9:
  for f,g be RMembership_Func of C1,C2, x,y st x in C1 & y in C2
  holds f. [x,y] <= g. [x,y]
   implies (converse f). [y,x] <= (converse g). [y,x]
proof
  let f,g being RMembership_Func of C1,C2, x,y;
  assume that
A1: x in C1 and
A2: y in C2 and
A3: f. [x,y] <= g. [x,y];
A4: [y,x] in [:C2,C1:] by A1,A2,ZFMISC_1:87;
  then
A5: g.(x,y) = (converse g).(y,x) by Def1;
  f.(x,y) = (converse f).(y,x) by A4,Def1;
  hence thesis by A3,A5;
end;
