reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A,B,C,D,E,F for a_partition of Y;
reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A, B, C, D, E, F, J, M for a_partition of Y,
  x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set;

theorem Th54:
  G={A,B,C,D,E,F,J,M} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J &
A<>M & B<>C & B<>D & B<>E & B<>F & B<>J & B<>M & C<>D & C<>E & C<>F & C<>J & C
  <>M & D<>E & D<>F & D<>J & D<>M & E<>F & E<>J & E<>M & F<>J & F<>M & J<>M
  implies CompF(A,G) = B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M
proof
  assume that
A1: G={A,B,C,D,E,F,J,M} and
A2: A<>B and
A3: A<>C and
A4: A<>D & A<>E and
A5: A<>F & A<>J and
A6: A<>M and
A7: B<>C & B<>D & B<>E & B<>F & B<>J & B<>M & C<>D & C<>E & C<>F & C<>J
& C<> M & D<>E & D<>F & D<>J & D<>M & E<>F & E<>J & E<>M & F<>J & F<>M & J<>M;
A8: not B in {A} by A2,TARSKI:def 1;
  G \ {A}={A} \/ {B,C,D,E,F,J,M} \ {A} by A1,ENUMSET1:22;
  then
A9: G \ {A} = ({A} \ {A}) \/ ({B,C,D,E,F,J,M} \ {A}) by XBOOLE_1:42;
A10: ( not D in {A})& not E in {A} by A4,TARSKI:def 1;
A11: not C in {A} by A3,TARSKI:def 1;
A12: not M in {A} by A6,TARSKI:def 1;
A13: ( not F in {A})& not J in {A} by A5,TARSKI:def 1;
  {B,C,D,E,F,J,M} \ {A} =({B} \/ {C,D,E,F,J,M}) \ {A} by ENUMSET1:16
    .=({B} \ {A}) \/ ({C,D,E,F,J,M} \ {A}) by XBOOLE_1:42
    .={B} \/ ({C,D,E,F,J,M} \ {A}) by A8,ZFMISC_1:59
    .={B} \/ (({C} \/ {D,E,F,J,M}) \ {A}) by ENUMSET1:11
    .={B} \/ (({C} \ {A}) \/ ({D,E,F,J,M} \ {A})) by XBOOLE_1:42
    .={B} \/ (({C} \ {A}) \/ (({D,E} \/ {F,J,M}) \ {A})) by ENUMSET1:8
    .={B} \/ (({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J,M} \ {A}))) by XBOOLE_1:42
    .={B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J,M} \ {A}))) by A10,ZFMISC_1:63
    .={B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ {M} \ {A}))) by ENUMSET1:3
    .={B} \/ (({C} \ {A}) \/ ({D,E} \/ (({F,J} \ {A}) \/ ({M} \ {A})))) by
XBOOLE_1:42
    .={B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ ({M} \ {A})))) by A13,
ZFMISC_1:63
    .={B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ ({M} \ {A})))) by A11,ZFMISC_1:59
    .={B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ {M}))) by A12,ZFMISC_1:59
    .={B} \/ ({C} \/ ({D,E} \/ {F,J,M})) by ENUMSET1:3
    .={B} \/ ({C} \/ {D,E,F,J,M}) by ENUMSET1:8
    .={B} \/ {C,D,E,F,J,M} by ENUMSET1:11
    .={B,C,D,E,F,J,M} by ENUMSET1:16;
  then
A14: G \ {A} = {} \/ {B,C,D,E,F,J,M} by A9,XBOOLE_1:37;
A15: '/\' (G \ {A}) c= B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M
  proof
    let x be object;
     reconsider xx=x as set by TARSKI:1;
    assume x in '/\' (G \ {A});
    then consider h being Function, FF being Subset-Family of Y such that
A16: dom h=(G \ {A}) and
A17: rng h = FF and
A18: for d being set st d in (G \ {A}) holds h.d in d and
A19: x=Intersect FF and
A20: x<>{} by BVFUNC_2:def 1;
A21: C in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A22: h.C in C by A18;
    set mbcdef=((h.B /\ h.C) /\ h.D) /\ h.E /\ h.F;
    set mbcde=(h.B /\ h.C) /\ h.D /\ h.E;
    set mbcdefj=((h.B /\ h.C) /\ h.D) /\ h.E /\ h.F /\ h.J;
A23: not x in {{}} by A20,TARSKI:def 1;
A24: J in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A25: h.J in rng h by A16,FUNCT_1:def 3;
    set mbc=h.B /\ h.C;
A26: B in (G \ {A}) by A14,ENUMSET1:def 5;
    then h.B in B by A18;
    then
A27: mbc in INTERSECTION(B,C) by A22,SETFAM_1:def 5;
A28: h.B in rng h by A16,A26,FUNCT_1:def 3;
    then
A29: Intersect FF = meet (rng h) by A17,SETFAM_1:def 9;
A30: h.C in rng h by A16,A21,FUNCT_1:def 3;
A31: F in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A32: h.F in rng h by A16,FUNCT_1:def 3;
    set mbcd=(h.B /\ h.C) /\ h.D;
A33: E in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A34: h.E in rng h by A16,FUNCT_1:def 3;
A35: M in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A36: h.M in rng h by A16,FUNCT_1:def 3;
A37: D in (G \ {A}) by A14,ENUMSET1:def 5;
    then
A38: h.D in rng h by A16,FUNCT_1:def 3;
A39: xx c= ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J /\ h.M
    proof
      let p be object;
      assume
A40:  p in xx;
      then p in h.B & p in h.C by A19,A28,A30,A29,SETFAM_1:def 1;
      then
A41:  p in h.B /\ h.C by XBOOLE_0:def 4;
      p in h.D by A19,A38,A29,A40,SETFAM_1:def 1;
      then
A42:  p in h.B /\ h.C /\ h.D by A41,XBOOLE_0:def 4;
      p in h.E by A19,A34,A29,A40,SETFAM_1:def 1;
      then
A43:  p in h.B /\ h.C /\ h.D /\ h.E by A42,XBOOLE_0:def 4;
      p in h.F by A19,A32,A29,A40,SETFAM_1:def 1;
      then
A44:  p in h.B /\ h.C /\ h.D /\ h.E /\ h.F by A43,XBOOLE_0:def 4;
      p in h.J by A19,A25,A29,A40,SETFAM_1:def 1;
      then
A45:  p in ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J by A44,XBOOLE_0:def 4
;
      p in h.M by A19,A36,A29,A40,SETFAM_1:def 1;
      hence thesis by A45,XBOOLE_0:def 4;
    end;
    then mbcd<>{} by A20;
    then
A46: not mbcd in {{}} by TARSKI:def 1;
    ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J /\ h.M c= xx
    proof
A47:  rng h c= {h.B,h.C,h.D,h.E,h.F,h.J,h.M}
      proof
        let u be object;
        assume u in rng h;
        then consider x1 being object such that
A48:    x1 in dom h and
A49:    u = h.x1 by FUNCT_1:def 3;
        x1=B or x1=C or x1=D or x1=E or x1=F or x1=J or x1=M by A14,A16,A48,
ENUMSET1:def 5;
        hence thesis by A49,ENUMSET1:def 5;
      end;
      let p be object;
      assume
A50:  p in ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J /\ h.M;
      then
A51:  p in h.M by XBOOLE_0:def 4;
A52:  p in ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J by A50,XBOOLE_0:def 4
;
      then
A53:  p in h.J by XBOOLE_0:def 4;
A54:  p in h.B /\ h.C /\ h.D /\ h.E /\ h.F by A52,XBOOLE_0:def 4;
      then
A55:  p in h.B /\ h.C /\ h.D /\ h.E by XBOOLE_0:def 4;
      then
A56:  p in h.E by XBOOLE_0:def 4;
A57:  p in h.B /\ h.C /\ h.D by A55,XBOOLE_0:def 4;
      then
A58:  p in h.D by XBOOLE_0:def 4;
      p in h.B /\ h.C by A57,XBOOLE_0:def 4;
      then
A59:  p in h.B & p in h.C by XBOOLE_0:def 4;
      p in h.F by A54,XBOOLE_0:def 4;
      then for y being set holds y in rng h implies p in y by A59,A58,A56,A53
,A51,A47,ENUMSET1:def 5;
      hence thesis by A19,A28,A29,SETFAM_1:def 1;
    end;
    then
A60: ((((h.B /\ h.C) /\ h.D) /\ h.E) /\ h.F) /\ h.J /\ h.M = x by A39,
XBOOLE_0:def 10;
    mbc<>{} by A20,A39;
    then not mbc in {{}} by TARSKI:def 1;
    then mbc in INTERSECTION(B,C) \ {{}} by A27,XBOOLE_0:def 5;
    then
A61: mbc in B '/\' C by PARTIT1:def 4;
    h.D in D by A18,A37;
    then mbcd in INTERSECTION(B '/\' C,D) by A61,SETFAM_1:def 5;
    then mbcd in INTERSECTION(B '/\' C,D) \ {{}} by A46,XBOOLE_0:def 5;
    then
A62: mbcd in B '/\' C '/\' D by PARTIT1:def 4;
    mbcde<>{} by A20,A39;
    then
A63: not mbcde in {{}} by TARSKI:def 1;
    h.E in E by A18,A33;
    then mbcde in INTERSECTION(B '/\' C '/\' D,E) by A62,SETFAM_1:def 5;
    then mbcde in INTERSECTION(B '/\' C '/\' D,E) \ {{}} by A63,XBOOLE_0:def 5;
    then
A64: mbcde in (B '/\' C '/\' D '/\' E) by PARTIT1:def 4;
    mbcdef<>{} by A20,A39;
    then
A65: not mbcdef in {{}} by TARSKI:def 1;
    h.F in F by A18,A31;
    then mbcdef in INTERSECTION(B '/\' C '/\' D '/\' E,F) by A64,SETFAM_1:def 5
;
    then mbcdef in INTERSECTION(B '/\' C '/\' D '/\' E,F) \ {{}} by A65,
XBOOLE_0:def 5;
    then
A66: mbcdef in (B '/\' C '/\' D '/\' E '/\' F) by PARTIT1:def 4;
    mbcdefj<>{} by A20,A39;
    then
A67: not mbcdefj in {{}} by TARSKI:def 1;
    h.J in J by A18,A24;
    then mbcdefj in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F,J) by A66,
SETFAM_1:def 5;
    then mbcdefj in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F,J) \ {{}} by A67
,XBOOLE_0:def 5;
    then
A68: mbcdefj in (B '/\' C '/\' D '/\' E '/\' F '/\' J) by PARTIT1:def 4;
    h.M in M by A18,A35;
    then x in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F '/\' J,M) by A60,A68,
SETFAM_1:def 5;
    then x in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F '/\' J,M) \ {{}} by
A23,XBOOLE_0:def 5;
    hence thesis by PARTIT1:def 4;
  end;
A69: B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M c= '/\' (G \ {A})
  proof
    let x be object;
     reconsider xx=x as set by TARSKI:1;
    assume
A70: x in B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M;
    then
A71: x<>{} by EQREL_1:def 4;
    x in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F '/\' J,M) \ {{}} by A70,
PARTIT1:def 4;
    then consider bcdefj,m being set such that
A72: bcdefj in B '/\' C '/\' D '/\' E '/\' F '/\' J and
A73: m in M and
A74: x = bcdefj /\ m by SETFAM_1:def 5;
    bcdefj in INTERSECTION(B '/\' C '/\' D '/\' E '/\' F,J) \ {{}} by A72,
PARTIT1:def 4;
    then consider bcdef,j being set such that
A75: bcdef in B '/\' C '/\' D '/\' E '/\' F and
A76: j in J and
A77: bcdefj = bcdef /\ j by SETFAM_1:def 5;
    bcdef in INTERSECTION(B '/\' C '/\' D '/\' E,F) \ {{}} by A75,PARTIT1:def 4
;
    then consider bcde,f being set such that
A78: bcde in B '/\' C '/\' D '/\' E and
A79: f in F and
A80: bcdef = bcde /\ f by SETFAM_1:def 5;
    bcde in INTERSECTION(B '/\' C '/\' D,E) \ {{}} by A78,PARTIT1:def 4;
    then consider bcd,e being set such that
A81: bcd in B '/\' C '/\' D and
A82: e in E and
A83: bcde = bcd /\ e by SETFAM_1:def 5;
    bcd in INTERSECTION(B '/\' C,D) \ {{}} by A81,PARTIT1:def 4;
    then consider bc,d being set such that
A84: bc in B '/\' C and
A85: d in D and
A86: bcd = bc /\ d by SETFAM_1:def 5;
    bc in INTERSECTION(B,C) \ {{}} by A84,PARTIT1:def 4;
    then consider b,c being set such that
A87: b in B & c in C and
A88: bc = b /\ c by SETFAM_1:def 5;
    set h = (B .--> b) +* (C .--> c) +* (D .--> d) +* (E .--> e) +* (F .--> f)
    +* (J .--> j) +* (M .--> m);
A89: h.B = b by A7,Th49;
A90: dom ((B .--> b) +* (C .--> c) +* (D .--> d) +* (E .--> e) +* (F .-->
    f) +* (J .--> j) +* (M .--> m)) = {M,B,C,D,E,F,J} by Th50
      .= {M} \/ {B,C,D,E,F,J} by ENUMSET1:16
      .= {B,C,D,E,F,J,M} by ENUMSET1:21;
    then
A91: E in dom h & F in dom h by ENUMSET1:def 5;
A92: D in dom h by A90,ENUMSET1:def 5;
    then
A93: h.D in rng h by FUNCT_1:def 3;
A94: J in dom h & M in dom h by A90,ENUMSET1:def 5;
A95: B in dom h & C in dom h by A90,ENUMSET1:def 5;
A96: {h.B,h.C,h.D,h.E,h.F,h.J,h.M} c= rng h
    proof
      let t be object;
      assume t in {h.B,h.C,h.D,h.E,h.F,h.J,h.M};
      then t=h.D or t=h.B or t=h.C or t=h.E or t=h.F or t=h.J or t=h.M by
ENUMSET1:def 5;
      hence thesis by A92,A95,A91,A94,FUNCT_1:def 3;
    end;
A97: for p being set st p in (G \ {A}) holds h.p in p
    proof
      let p be set;
      assume p in (G \ {A});
      then p=D or p=B or p=C or p=E or p=F or p=J or p=M by A14,ENUMSET1:def 5;
      hence thesis by A7,A73,A76,A79,A82,A85,A87,Th49;
    end;
A98: h.C = c by A7,Th49;
A99: h.M = m by A7,Th49;
A100: h.J = j by A7,Th49;
A101: h.F = f by A7,Th49;
A102: rng h c= {h.B,h.C,h.D,h.E,h.F,h.J,h.M}
    proof
      let t be object;
      assume t in rng h;
      then consider x1 being object such that
A103: x1 in dom h and
A104: t = h.x1 by FUNCT_1:def 3;
      x1=D or x1=B or x1=C or x1=E or x1=F or x1=J or x1=M by A90,A103,
ENUMSET1:def 5;
      hence thesis by A104,ENUMSET1:def 5;
    end;
    then
A105: rng h = {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by A96,XBOOLE_0:def 10;
A106: h.E = e by A7,Th49;
A107: h.D = d by A7,Th49;
    rng h c= bool Y
    proof
      let t be object;
      assume t in rng h;
      then
      t=h.D or t=h.B or t=h.C or t=h.E or t=h.F or t=h.J or t=h.M by A102,
ENUMSET1:def 5;
      hence thesis by A73,A76,A79,A82,A85,A87,A107,A89,A98,A106,A101,A100,A99;
    end;
    then reconsider FF=rng h as Subset-Family of Y;
    reconsider h as Function;
A108: xx c= Intersect FF
    proof
      let u be object;
      assume
A109: u in xx;
      for y be set holds y in FF implies u in y
      proof
        let y be set;
        assume
A110:   y in FF;
        now
          per cases by A102,A110,ENUMSET1:def 5;
          case
A111:       y=h.D;
            u in (d /\ ((b /\ c) /\ e)) /\ f /\ j /\ m by A74,A77,A80,A83,A86
,A88,A109,XBOOLE_1:16;
            then u in (d /\ ((b /\ c) /\ e /\ f)) /\ j /\ m by XBOOLE_1:16;
            then u in d /\ (((b /\ c) /\ e /\ f) /\ j) /\ m by XBOOLE_1:16;
            then u in d /\ ((((b /\ c) /\ e /\ f) /\ j) /\ m) by XBOOLE_1:16;
            hence thesis by A107,A111,XBOOLE_0:def 4;
          end;
          case
A112:       y=h.B;
            u in (c /\ (d /\ b)) /\ e /\ f /\ j /\ m by A74,A77,A80,A83,A86,A88
,A109,XBOOLE_1:16;
            then u in c /\ ((d /\ b) /\ e) /\ f /\ j /\ m by XBOOLE_1:16;
            then u in c /\ ((d /\ e) /\ b) /\ f /\ j /\ m by XBOOLE_1:16;
            then u in c /\ (((d /\ e) /\ b) /\ f) /\ j /\ m by XBOOLE_1:16;
            then u in c /\ ((((d /\ e) /\ b) /\ f) /\ j) /\ m by XBOOLE_1:16;
            then u in c /\ (((d /\ e) /\ (f /\ b)) /\ j) /\ m by XBOOLE_1:16;
            then u in c /\ ((d /\ e) /\ ((f /\ b) /\ j)) /\ m by XBOOLE_1:16;
            then u in c /\ ((d /\ e) /\ (f /\ (j /\ b))) /\ m by XBOOLE_1:16;
            then u in (c /\ (d /\ e)) /\ (f /\ (j /\ b)) /\ m by XBOOLE_1:16;
            then u in ((c /\ (d /\ e)) /\ f) /\ (j /\ b) /\ m by XBOOLE_1:16;
            then u in (((c /\ (d /\ e)) /\ f) /\ j) /\ b /\ m by XBOOLE_1:16;
            then u in (((c /\ (d /\ e)) /\ f) /\ j) /\ m /\ b by XBOOLE_1:16;
            hence thesis by A89,A112,XBOOLE_0:def 4;
          end;
          case
A113:       y=h.C;
            u in (c /\ (d /\ b)) /\ e /\ f /\ j /\ m by A74,A77,A80,A83,A86,A88
,A109,XBOOLE_1:16;
            then u in c /\ ((d /\ b) /\ e) /\ f /\ j /\ m by XBOOLE_1:16;
            then u in c /\ ((d /\ e) /\ b) /\ f /\ j /\ m by XBOOLE_1:16;
            then u in c /\ (((d /\ e) /\ b) /\ f) /\ j /\ m by XBOOLE_1:16;
            then u in c /\ ((((d /\ e) /\ b) /\ f) /\ j) /\ m by XBOOLE_1:16;
            then u in c /\ (((((d /\ e) /\ b) /\ f) /\ j) /\ m) by XBOOLE_1:16;
            hence thesis by A98,A113,XBOOLE_0:def 4;
          end;
          case
A114:       y=h.E;
            u in ((b /\ c) /\ d) /\ (f /\ e) /\ j /\ m by A74,A77,A80,A83,A86
,A88,A109,XBOOLE_1:16;
            then u in ((b /\ c) /\ d) /\ ((f /\ e) /\ j) /\ m by XBOOLE_1:16;
            then u in ((b /\ c) /\ d) /\ ((f /\ j) /\ e) /\ m by XBOOLE_1:16;
            then u in (((b /\ c) /\ d) /\ (f /\ j)) /\ e /\ m by XBOOLE_1:16;
            then u in (((b /\ c) /\ d) /\ (f /\ j)) /\ m /\ e by XBOOLE_1:16;
            hence thesis by A106,A114,XBOOLE_0:def 4;
          end;
          case
A115:       y=h.F;
            u in (((b /\ c) /\ d) /\ e) /\ j /\ f /\ m by A74,A77,A80,A83,A86
,A88,A109,XBOOLE_1:16;
            then u in (((b /\ c) /\ d) /\ e) /\ j /\ m /\ f by XBOOLE_1:16;
            hence thesis by A101,A115,XBOOLE_0:def 4;
          end;
          case
A116:       y=h.J;
            u in (((b /\ c) /\ d) /\ e) /\ f /\ m /\ j by A74,A77,A80,A83,A86
,A88,A109,XBOOLE_1:16;
            hence thesis by A100,A116,XBOOLE_0:def 4;
          end;
          case
            y=h.M;
            hence thesis by A74,A99,A109,XBOOLE_0:def 4;
          end;
        end;
        hence thesis;
      end;
      then u in meet FF by A105,SETFAM_1:def 1;
      hence thesis by A105,SETFAM_1:def 9;
    end;
A117: Intersect FF = meet (rng h) by A93,SETFAM_1:def 9;
    Intersect FF c= xx
    proof
      let t be object;
      assume
A118: t in Intersect FF;
      h.C in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then
A119: t in c by A98,A96,A117,A118,SETFAM_1:def 1;
      h.B in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in b by A89,A96,A117,A118,SETFAM_1:def 1;
      then
A120: t in b /\ c by A119,XBOOLE_0:def 4;
      h.D in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in d by A107,A96,A117,A118,SETFAM_1:def 1;
      then
A121: t in (b /\ c) /\ d by A120,XBOOLE_0:def 4;
      h.E in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in e by A106,A96,A117,A118,SETFAM_1:def 1;
      then
A122: t in (b /\ c) /\ d /\ e by A121,XBOOLE_0:def 4;
      h.F in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in f by A101,A96,A117,A118,SETFAM_1:def 1;
      then
A123: t in (b /\ c) /\ d /\ e /\ f by A122,XBOOLE_0:def 4;
      h.J in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in j by A100,A96,A117,A118,SETFAM_1:def 1;
      then
A124: t in (b /\ c) /\ d /\ e /\ f /\ j by A123,XBOOLE_0:def 4;
      h.M in {h.B,h.C,h.D,h.E,h.F,h.J,h.M} by ENUMSET1:def 5;
      then t in m by A99,A96,A117,A118,SETFAM_1:def 1;
      hence thesis by A74,A77,A80,A83,A86,A88,A124,XBOOLE_0:def 4;
    end;
    then x = Intersect FF by A108,XBOOLE_0:def 10;
    hence thesis by A14,A90,A97,A71,BVFUNC_2:def 1;
  end;
  CompF(A,G)='/\' (G \ {A}) by BVFUNC_2:def 7;
  hence thesis by A69,A15,XBOOLE_0:def 10;
end;
