deffunc H₁( Ordinal, set ) -> Cardinal = nextcard (union {$2});
deffunc H₂( Ordinal, T-Sequence) -> Cardinal = card (sup $2);
set B = card omega ;
thus ( ex x being set ex S being T-Sequence st
( x = last S & dom S = succ A & S . {} = card omega & ( for C being Ordinal st succ C in succ A holds
S . (succ C) = H₁(C,S . C) ) & ( for C being Ordinal st C in succ A & C <> {} & C is limit_ordinal holds
S . C = H₂(C,S | C) ) ) & ( for x1, x2 being set st ex S being T-Sequence st
( x1 = last S & dom S = succ A & S . {} = card omega & ( for C being Ordinal st succ C in succ A holds
S . (succ C) = H₁(C,S . C) ) & ( for C being Ordinal st C in succ A & C <> {} & C is limit_ordinal holds
S . C = H₂(C,S | C) ) ) & ex S being T-Sequence st
( x2 = last S & dom S = succ A & S . {} = card omega & ( for C being Ordinal st succ C in succ A holds
S . (succ C) = H₁(C,S . C) ) & ( for C being Ordinal st C in succ A & C <> {} & C is limit_ordinal holds
S . C = H₂(C,S | C) ) ) holds
x1 = x2 ) ) from ORDINAL2:sch 7(); :: thesis: verum