let T be non empty RelStr ; :: thesis: for A being Subset of T st T is filled holds
for n being Nat holds Finf (A,n) c= Finf (A,(n + 1))
let A be Subset of T; :: thesis: ( T is filled implies for n being Nat holds Finf (A,n) c= Finf (A,(n + 1)) )
assume A1: T is filled ; :: thesis: for n being Nat holds Finf (A,n) c= Finf (A,(n + 1))
let n be Nat; :: thesis: Finf (A,n) c= Finf (A,(n + 1))
reconsider n = n as Element of NAT by ORDINAL1:def 12;
((Finf A) . n) ^f = Finf (A,(n + 1)) by Def6;
hence Finf (A,n) c= Finf (A,(n + 1)) by A1, Th1; :: thesis: verum