let V be set ; :: thesis: for C being finite set
for u being Element of (SubstLatt (V,C))
for X being set st X c= u holds
X is Element of (SubstLatt (V,C))
let C be finite set ; :: thesis: for u being Element of (SubstLatt (V,C))
for X being set st X c= u holds
X is Element of (SubstLatt (V,C))
let u be Element of (SubstLatt (V,C)); :: thesis: for X being set st X c= u holds
X is Element of (SubstLatt (V,C))
let X be set ; :: thesis: ( X c= u implies X is Element of (SubstLatt (V,C)) )
reconsider u9 = u as Element of SubstitutionSet (V,C) by SUBSTLAT:def 4;
assume X c= u ; :: thesis: X is Element of (SubstLatt (V,C))
then X c= u9 ;
then X in SubstitutionSet (V,C) by Lm4;
hence X is Element of (SubstLatt (V,C)) by SUBSTLAT:def 4; :: thesis: verum