let T be non empty RelStr ; :: thesis: for A being Subset of T st T is filled holds
for n being Nat holds Fint (A,(n + 1)) c= Fint (A,n)
let A be Subset of T; :: thesis: ( T is filled implies for n being Nat holds Fint (A,(n + 1)) c= Fint (A,n) )
assume A1: T is filled ; :: thesis: for n being Nat holds Fint (A,(n + 1)) c= Fint (A,n)
let n be Nat; :: thesis: Fint (A,(n + 1)) c= Fint (A,n)
reconsider n = n as Element of NAT by ORDINAL1:def 12;
((Fint A) . n) ^i = Fint (A,(n + 1)) by Def4;
hence Fint (A,(n + 1)) c= Fint (A,n) by A1, FIN_TOPO:22; :: thesis: verum