let T be non empty TopSpace; :: thesis: for A being Subset of T holds card (Kurat14Set A) <= 14
let A be Subset of T; :: thesis: card (Kurat14Set A) <= 14
set X = {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)};
set Y = {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)};
( card {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)} <= 7 & card {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)} <= 7 ) by CARD_2:55;
then ( card ({A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)} \/ {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)}) <= (card {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)}) + (card {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)}) & (card {A,(Cl A),((Cl A) `),(Cl ((Cl A) `)),((Cl ((Cl A) `)) `),(Cl ((Cl ((Cl A) `)) `)),((Cl ((Cl ((Cl A) `)) `)) `)}) + (card {(A `),(Cl (A `)),((Cl (A `)) `),(Cl ((Cl (A `)) `)),((Cl ((Cl (A `)) `)) `),(Cl ((Cl ((Cl (A `)) `)) `)),((Cl ((Cl ((Cl (A `)) `)) `)) `)}) <= 7 + 7 ) by CARD_2:43, XREAL_1:7;
hence card (Kurat14Set A) <= 14 by XXREAL_0:2; :: thesis: verum