let T be non empty RelStr ; 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; ( T is filled implies for n being Nat holds Fdfl (A,(n + 1)) c= Fdfl (A,n) )
assume A1:
T is filled
; for n being Nat holds Fdfl (A,(n + 1)) c= Fdfl (A,n)
let n be Nat; 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; verum