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

theorem
  for f be RMembership_Func of C1,C2 holds converse converse f = f
proof
  let f being RMembership_Func of C1,C2;
A1: dom f = [:C1,C2:] by FUNCT_2:def 1;
A2: for c being Element of [:C1,C2:] st c in [:C1,C2:] holds (converse
  converse f).c = f.c
  proof
    let c being Element of [:C1,C2:];
    assume c in [:C1,C2:];
    consider x,y being object such that
A3: x in C1 and
A4: y in C2 and
A5: c = [x,y] by ZFMISC_1:def 2;
A6: [y,x] in [:C2,C1:] by A3,A4,ZFMISC_1:87;
    (converse converse f).(x,y) = (converse f).(y,x) by A5,Def1
      .= f.(x,y) by A6,Def1;
    hence thesis by A5;
  end;
  dom(converse converse f) = [:C1,C2:] by FUNCT_2:def 1;
  hence thesis by A2,A1,PARTFUN1:5;
end;
