let T be non empty RelStr ; :: thesis: for A being Subset of T st T is filled holds
for n being Element of NAT holds Fint A,(n + 1) c= Fint A,n
let A be Subset of T; :: thesis: ( T is filled implies for n being Element of NAT holds Fint A,(n + 1) c= Fint A,n )
assume A1: T is filled ; :: thesis: for n being Element of NAT holds Fint A,(n + 1) c= Fint A,n
let n be Element of NAT ; :: thesis: Fint A,(n + 1) c= Fint A,n
((Fint A) . n) ^i = Fint A,(n + 1) by Def4;
hence Fint A,(n + 1) c= Fint A,n by A1, FIN_TOPO:28; :: thesis: verum