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 Fcl A,n c= Fcl A,(n + 1)
let A be Subset of T; :: thesis: ( T is filled implies for n being Element of NAT holds Fcl A,n c= Fcl A,(n + 1) )
assume A1: T is filled ; :: thesis: for n being Element of NAT holds Fcl A,n c= Fcl A,(n + 1)
let n be Element of NAT ; :: thesis: Fcl A,n c= Fcl A,(n + 1)
((Fcl A) . n) ^b = Fcl A,(n + 1) by Def2;
hence Fcl A,n c= Fcl A,(n + 1) by A1, FIN_TOPO:18; :: thesis: verum