scheme :: ORDINAL6:sch 1
CriticalNumber2{ F1() -> Universe, F2() -> Ordinal of F1(), F3() -> Ordinal-Sequence of omega,F1(), F4( Ordinal) -> Ordinal } :
( F2() c= Union F3() & F4((Union F3())) = Union F3() & ( for b being Ordinal st F2() c= b & b in F1() & F4(b) = b holds
Union F3() c= b ) )
provided
A1: omega in F1() and
A2: for a being Ordinal st a in F1() holds
F4(a) in F1() and
A3: for a, b being Ordinal st a in b & b in F1() holds
F4(a) in F4(b) and
A4: for a being Ordinal of F1() st not a is empty & a is limit_ordinal holds
for phi being Ordinal-Sequence st dom phi = a & ( for b being Ordinal st b in a holds
phi . b = F4(b) ) holds
F4(a) is_limes_of phi and
A5: F3() . 0 = F2() and
A6: for a being Ordinal st a in omega holds
F3() . (succ a) = F4((F3() . a))