let T be non empty RelStr ; :: thesis: for A being Subset of T st T is filled holds
for n being Nat holds Fdfl (A,(n + 1)) c= Fdfl (A,n)
let A be Subset of T; :: thesis: ( T is filled implies for n being Nat holds Fdfl (A,(n + 1)) c= Fdfl (A,n) )
assume A1: T is filled ; :: thesis: for n being Nat holds Fdfl (A,(n + 1)) c= Fdfl (A,n)
let n be Nat; :: thesis: Fdfl (A,(n + 1)) c= Fdfl (A,n)
reconsider n = n as Element of NAT by ORDINAL1:def 12;
((Fdfl A) . n) ^d = Fdfl (A,(n + 1)) by Def8;
hence Fdfl (A,(n + 1)) c= Fdfl (A,n) by A1, Th3; :: thesis: verum