let T be non empty TopSpace; for A being Subset of T holds Kurat14Set A = ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
let A be Subset of T; Kurat14Set A = ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
set Y1 = {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))};
set Y2 = {A,(A `)};
set Y3 = {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)};
set Y = ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)};
A1:
{((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} c= ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by XBOOLE_1:7;
A2:
({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} c= Kurat14Set A
proof
let x be
object ;
TARSKI:def 3 ( not x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} or x in Kurat14Set A )
assume
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
;
x in Kurat14Set A
then A3:
(
x in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)} or
x in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} )
by XBOOLE_0:def 3;
per cases
( x in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} or x in {A,(A `)} or x in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} )
by A3, XBOOLE_0:def 3;
end;
end;
A4:
{(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)} c= ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by XBOOLE_1:7;
(Cl ((Cl A) `)) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A5:
(Cl ((Cl A) `)) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
(Cl A) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A6:
(Cl A) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
{A,(A `)} c= {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}
by XBOOLE_1:7;
then A7:
{A,(A `)} c= ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A4;
(Cl ((Cl ((Cl (A `)) `)) `)) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A8:
(Cl ((Cl ((Cl (A `)) `)) `)) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
(Cl ((Cl (A `)) `)) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A9:
(Cl ((Cl (A `)) `)) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
(Cl (A `)) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A10:
(Cl (A `)) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
(Cl ((Cl ((Cl A) `)) `)) ` in {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by ENUMSET1:def 4;
then A11:
(Cl ((Cl ((Cl A) `)) `)) ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A1;
A in {A,(A `)}
by TARSKI:def 2;
then A12:
A in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A7;
{(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} c= {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}
by XBOOLE_1:7;
then A13:
{(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} c= ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A4;
A ` in {A,(A `)}
by TARSKI:def 2;
then A14:
A ` in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A7;
Cl ((Cl ((Cl (A `)) `)) `) in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A15:
Cl ((Cl ((Cl (A `)) `)) `) in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Cl ((Cl (A `)) `) in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A16:
Cl ((Cl (A `)) `) in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Cl (A `) in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A17:
Cl (A `) in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Cl ((Cl ((Cl A) `)) `) in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A18:
Cl ((Cl ((Cl A) `)) `) in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Cl ((Cl A) `) in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A19:
Cl ((Cl A) `) in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Cl A in {(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))}
by ENUMSET1:def 4;
then A20:
Cl A in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A13;
Kurat14Set A c= ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
proof
let x be
object ;
TARSKI:def 3 ( not x in Kurat14Set A or x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)} )
assume A21:
x in Kurat14Set A
;
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
per cases
( x in {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)} or x in {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)} )
by A21, XBOOLE_0:def 3;
suppose
x in {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)}
;
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}hence
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A20, A19, A18, A12, A6, A5, A11, ENUMSET1:def 5;
verum end; suppose
x in {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
;
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}hence
x in ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A17, A16, A15, A14, A10, A9, A8, ENUMSET1:def 5;
verum end;
end;
hence
Kurat14Set A = ({(Cl A),(Cl ((Cl A) `)),(Cl ((Cl ((Cl A) `)) `)),(Cl (A `)),(Cl ((Cl (A `)) `)),(Cl ((Cl ((Cl (A `)) `)) `))} \/ {A,(A `)}) \/ {((Cl A) `),((Cl ((Cl A) `)) `),((Cl ((Cl ((Cl A) `)) `)) `),((Cl (A `)) `),((Cl ((Cl (A `)) `)) `),((Cl ((Cl ((Cl (A `)) `)) `)) `)}
by A2, XBOOLE_0:def 10; verum